DWise1: Kent Hovind's Solar Mass Loss Claim


"There are three kinds of lies: lies, damned lies, and statistics" - Benjamin Disraeli (quoted by Mark Twain)

"Do the math!" - Sega 16-bit video game-set commercial, c. mid-1980's


Table of Contents


Abstract

Kent Hovind made the claim that, given the rate at which the sun is losing mass by "burning its fuel", then if we extrapolate back by the accepted age of the solar system then the sun's mass and gravity would have been so immensely great that it would have "suck[ed] the earth in and destroy[ed] everything". Therefore the sun and the solar system and the earth must be much younger, like about 10,000 years old.

The rate of mass loss that Hovind provided, 5 million tons per second, is very close to correct, as is the accepted age of the solar system that he provided, 5 billion years (5×109). However, he never applies that rate to that time to obtain the total amount of mass lost over that time. Instead, he just leaves that up to his audience's imagination and thus misleads and deceives them.

When we do what Hovind would not do -- i.e, actually do the math -- , we find that the total mass loss is insignificant compared to the sun's total mass, a few hundredths of one percent. When we add that total mass loss back to the sun to obtain its original mass, the change is almost imperceptible, as is the resultant greater gravity. And the earth would have been "sucked in" by far less than 100,000 miles. In short, none of the dire consequences Hovind cited are even remotely true.

Discussion of this subject can raise many questions which I have tried to anticipate and respond to in the section, More Details. Basically, the short answers are:

Follow those links for a more complete presentation and discussion.


A Note about Units and an Errata Notification

Yes, I am sure that you will find this to be a boring digression. However, it is important that we know what we are talking about.

For example, Hovind uses the term "tons" without every specifying which of the three types of weight/mass measurement unit he was talking about (it is also used to measure volume in shipping, but we ignore that here). Therefore, we need to establish which "ton" we're using on this page.

Similarly, most Americans are unaware that there are two different systems of large-number names which use the same names for different values. Therefore we need to establish just exactly how big a billion is.

Please bear with me or else skip ahead. And please don't let my footnote digression put you off, kind of a little diatribe about how much I like metric and cannot understand many Americans' negative attitudes about it.

Number Names:

Basically, there are two different systems for naming large numbers, so my use of "billion" on this page could be confusing, since it has two different values depending on which system you use. Those two systems are often referred to as the "U.S. System" and the "British System" (or also "European System"), though Wikipedia calls them the long ("European") and short ("U.S.") scales. Still referring to the long scale as "British" is now problematic, since the UK switched from the long scale to the short in 1974, which is apparently what prompted the French to come up with the terms "long scale" and "short scale" in 1975 (read the Wikipedia article linked to above).

Basically, past one million (106) the short scale (US) increments number names by multiplying successively by a factor of one thousand (103). On the other hand, past one million (106) the long scale (European) increments number names by multiplying successively by a factor of one million (106).

The values of some large numbers in both scales would be:

Number Name Short Scale Value
(US)
Long Scale Value
(European)
one billion 109 1012
one trillion 1012 1018
one quadrillion 1015 1024
one quintillion 1018 1030

I use the US System (short scale). Hence, on all my pages, including this one, "billion" means 109, a thousand millions. In the long scale, 109 would be a "milliard" while a billion would be 1012, a million millions.

If you are interested in Names of large numbers, then follow that link to the Wikipedia article of the same name. Share and enjoy!

Tons:

There was a point of confusion for me from the start of researching this claim. All the sources I found, including the astronomical ones, gave the Sun's mass in "tons", but without ever specifying which tons. There are several definitions for "ton" which measure different things, including three definitions for measuring mass/weight ... well, two for weight, which is a force, and one for mass even though that is often confused as measuring weight. See what I mean? It gets confusing. But the main confusion was in figuring out which ton a source was referring to.

Here's part of a table I borrowed from Wikipedia's Ton article:

Full name(s) Common name Quantity
long ton, weight ton, gross ton "ton" (UK) 2,240 lb (1,016.047 kg)
short ton, net ton "ton" (US) 2,000 lb (907.1847 kg)
tonne "tonne"; "metric ton"
(mainly UK)
1,000 kg (2,204.623 lb)

Despite my confusion, I noticed that all three tons are fairly close to being the same amount -- note that the long ton is only 16 kg greater than the metric ton while the short ton is about 93 kg less. So I took the lazy route and decided that for our purposes they were "close enough" to being the same so we would almost consider them to be interchangeable, especially at the scales that we are working with. I originally ended up settling on the short ton, since it was Kent Hovind's claim I was examining and I just assumed that he would be using the US measurement, the short ton, and may even believe that metric measurements are the work of the Devil or at least "un-American" (I have no direct evidence of that, but I suspect it's very likely [1]).

But then when I went back over my notes, I decided that I had chosen unwisely. I now feel that I should use the metric ton, also called a "tonne". For one thing, it measures mass, not weight, which is what we are talking about. Another reason is that by keeping everything in metric, I can be exactly sure of all of my units and of my unit conversions. For that matter, I suspect that within the context of astronomy, "tons" is supposed to mean "tonnes".

Errata:

In light of my decision about which tons to use, I have gone through this page and redone all measurements of mass and calculations involving mass to be in metric tons. Therefore, I plan to use the term, "tonne", in order to keep that clear for you. When I do write "tons", that will normally be meant to mean "metric tons", unless the context indicates otherwise. Such context would include any text that I quote and references to that quote. But when I present a meaningful number, it will be in tonnes and I will endeavor to keep my terminology straight.

Thank you for your understanding and for your patience.


Footnote [1]:

Kent Hovind has written very little, but rather almost all of his material is verbal, some of which is preserved in the videos of his seminars (which had the perennial nasty habit of disappearing and getting replaced by newer versions, not to mention that there would be no indication of when or where they had been recorded). Even his claims that I examine on this page only exist verbally outside of my having transcribed it. Of course, that makes it extremely tedious (and nauseating, kind of like watching the 2016 Republican National Convention) to search through his claims. Fortunately, some of those seminars have been transcribed and can be found on-line, such as this pertinent transcript, Seminar 4a: Lies in the Textbooks:
They even had the kids do activities on this one. “Boys and girls get a large piece of black paper one meter square.” (By the way, I like to kick this dog every time I walk by. Did you know all of the new textbooks that I'm aware of are metric? Now, I understand the metric system very thoroughly. I taught physics. I'll take a metric quiz against anyone you know. But I'm not sure I want a kid coming to help build my house that doesn't know what a two by four is. So if you are a patriot, make your paper a 39.37 inches square instead.)

"So if you are a patriot, ... ." Yeah, I think it's safe to assume that he is against the metric system and would have chosen to use the short ton instead of the metric tonne, assuming that that would have even occurred to him.

And FWIW, two-by-fours no longer measure two inches by four inches. Haven't for well over half a century. I know that because I have encountered some of the old two-by-fours when we remodeled some older houses; when closing off a doorway in an old house we used new two-by-fours (only about 3.5 inches across) and had to fir them out (add a strip of wood the desired thickness) to make that new part of the wall as thick as the rest of the wall.


Sorry, couldn't resist sharing a joke. There was an American-Swedish sit-com, Welcome to Sweden, about an American trying to adjust to living in Sweden with his Swedish fiancée. In one scene she's giving him directions over the phone:
Her: Then go 200 meters and turn right.
Him: What's a meter?
Her: It's like a yard only much more logical.
Very much more logical. And I'm speaking as one who was raised entirely on the American system, but the moment I started learning metric it just made so much more sense and was so much easier to use and especially to work with.

In elementary school, I could never remember the American system's multitude of odd conversion factors so I always had to look them up in the conversion tables in the back of the math textbook. But then one year (¿5th grade?) the math book didn't list the conversion factors and I was really lost. But the moment I learned the prefixes in metric, converting from one measurement to another in metric was trivially simple.

For another example, after working construction for 5 years in the USA (weekends and summer) and having to always struggle to figure out how many 32-nds or 64-ths of an inch each mark on the tape was, the very first time in Germany that I was handed a Meterstock and told to take a measurement I could do it immediately and with absolutely no difficulty whatsoever. Immediately upon my return to the USA, I bought myself a dual-scale steel tape with a metric scale for my own use and a US scale for working with another carpenter.

The main problem (and the only one for most people) in switching to metric lies in learning to visualize what a given measurement would be (eg, estimating someone's height, realizing how heavy something would feel), but that comes with experience. A secondary problem would be for some professions which have standard sizes and measurements (eg, a 2×4, door sizes, 8½×11-inch paper), in which case they would either have to convert them all to metric or else retain those specialized measurements as a secondary measuring system. The latter is something already done by the US system with separate weight and volume systems for medications (apothocary) and for precious metals (troy).

Of course, there can be a danger when mixing the two systems, such as could happen when transitioning to metric. Such was the case of the Gimli Glider, an Air Canada airliner that on 1983 July 23, because the ground crew miscalculated the amount of fuel to load, ran out of fuel in mid-flight and had to glide to an emergency landing in an abandoned military airfield. Successfully.


Introduction

It has long been my practice to approach a new creationist claim by taking it seriously and at face value,and evaluating it on its own merits. This has proven to be an effective approach to debunking many claims. I want to see how they had arrived at their conclusion and I especially want to see their figures and calculations when the claim is about rates and how by extrapolating back 4.5 billion years it would yield an impossibly large size/mass/intensity/whatever. Almost every time, they have nothing to offer except for a lot of hand-waving and desperate attempts to change the subject. Furthermore, just by doing the math that they describe or allude to, their claim evaporates, hence my quote above, "Do the math!"

As for the Disraeli quote, in my statistical analysis class we learned that a statistic is a single data point, a raw value apart from other data points, devoid of any intrinsic meaning outside of the context of that of which it is a measurement and its relationship to the other measurements. Statistical analysis then works with a collection of statistics to determine the actual context and significance of the data. Lying with statistics is often practiced by presenting single data points out of their context in order to mislead the audience with an impressive-sounding number or percentage while keeping them ignorant of its true significance or lack thereof.

The claim in question here alludes to incredibly large numbers which are truly astronomical but removes them from their context in order to mislead its audience to false conclusions. The moment we place those numbers in their proper context, the claim falls apart completely as I will demonstrate.


The Claim

The claim in question is one made repeatedly by Kent Hovind that the Sun is losing its mass at such a high rate that 4.5 billion years ago it would have been so large and massive that it would have sucked the earth in and/or burned it up.

This version from his seminar videos is representative of the claim and provides important specifics, including the rate of mass loss:

All you got to do is step outside and look up. Obviously the Sun is burning. It's losing 5 million tons every second. You can't just keep losing 5 million tons a second, pretty soon you start to lose weight. And so the Sun is losing this mass -- 5 million tons every second -- which means it used to be larger. And it used to be more massive. If you increase the mass of the Sun, going backwards in time for several billion years, you start to create a problem with the gravitational balance between the earth and the Sun. It's going to suck the earth in and destroy everything.

(Hovind in his seminar tape video downloaded from his site circa 2003. From my transcription taken from the audio of video #7, "Questions and Answers", from 37 minutes 40 seconds to 39 minutes 54 seconds)

Big numbers. Impressive sounding numbers. Astronomical numbers, quite literally. Numbers that the human mind finds difficult to comprehend (eg, I was taught that the ancient Greek definition for infinity was any number greater than 10,000).

5 million tons lost every second is a big number, an impressive sounding figure that Hovind's audience finds nearly incomprehensible. 5 billion years is another big, impressive sounding number nearly as incomprehensible to Hovind's audience as the first. Multiply them together and you get incredibly bigger and far more impressive sounding numbers. Even though Hovind leaves those other numbers entirely up to the fevered imagination of his audience, thus magnifying them even more, they are no less large or impressive sounding when we actually figure them out (because we can and because we must):

OK, those are the figures we get from Hovind's claim. Impressed? Well, don't be. What happens when we do the math, which includes examining the context?


Footnote [2]:

Please note that if Hovind was using short tons, then his "5 million tons" figure would actually be 4.536 million tonnes, which is actually closer to the actual mass lost through hydrogen fusion. However, Hovind indicated in correspondence (which had otherwise proven to be useless) that he gotten his value from a book which doubtless was as ambiguous about the kind of tons it was using as astronomy sites have proven to be. Therefore, given my assumption that astronomy's "tons" are actual metric tonnes, I will treat that "5 million tons each second" rate and the resultant total mass lost as being in tonnes. And since his rate isn't accurate anyway, it will still be close enough to be acceptable.


Let's Do the Math!

That astronomical (literally!) number, 7.88923×1023 tonnes of solar mass lost in 5 billion years, only appears huge in isolation, out of context. Or when compared to the wrong things, like the earth's mass, 5.97237×1021 tonnes -- the total solar mass lost is 132 times the mass of the earth, which still sounds impressive. But once we return it to its proper context, the total mass of the Sun, we find it to be very insignificant:

Adding that lost mass back in we get 1.98933892×1027 as the mass of the Sun 5 billion years ago, just 1.00039673 times the Sun's current mass -- a factor of 1.0 would mean no change. Since gravity is directly proportional to mass, the Sun's gravity 5 billion years ago would have been only 1.00039673 times what it is now. And since the size of the earth's orbit is inversely proportional to gravity, 5 billion years ago the earth's orbit would have been 0.9996 what it is now, or 92,919,038 miles. So the more massive ancient Sun would have "sucked the earth in" by about 36,864 miles, about twice the earth's diameter, far too little to have had the dire consequences Hovind claims it would have.

Yes, I hear you start to raise your hand. "But creationists keep pointing out how earth is at just the right distance from the sun and how finely balanced earth's orbit is, so that any closer we'd burn up and any farther away and we'd freeze." If it were true that our distance from the sun were so tightly constrained that we couldn't change our distance from the sun by even the slightest amount, then we'd be in a lot of trouble because of what I will tell you in the next paragraph. But how much is "too much"? There's a little something called the circumstellar habitable zone (CHZ), more popularly "the Goldylocks Zone" within life could exist because it's not too close and it's not too far away, but rather it's "just right". So what are the inner and outer limits of the earth's CHZ? Well, there are different estimates based on different factors. One that I heard several years ago ranged from almost to the orbit of Venus out to just beyond the orbit of Mars. A fairly tight estimate from 1979 places it as ranging from 0.95 AU out to 1.01 AU (1 AU = the earth's distance from the sun = 92.956 million miles). A more recent estimate from 2013 tightens up the inner edge at 0.99 AU and loosens the outer to 1.68 AU. The tightest inner and outer edges in those estimates is about 1% or ±929,560 miles. That's more than 25 times greater than how much the earth would have been "sucked in" as per Hovind, so the earth wouldn't have been too hot. However, what we experience very single year shows that those estimates are too restrictive.

As you should already know, the earth's orbit around the sun is elliptical, which causes the earth's distance from the Sun to vary by 3 million miles, bringing it 1.5 million miles closer in towards the Sun at the same time each year and 1.5 million miles farther out from the Sun six months later. And BTW, the earth is at perihelion, its closest to the Sun, every year around 03 January, the dead of winter in the Northern Hemisphere, so variations in the distance from the Sun has far less effect than the seasonal changes due to the tilt of the earth's axis. And so that 36,864 mile change ends up being very insignificant compared to the changes that happens to the earth's distance from the sun every single year.

This is what happens to creationist claims when we do the math. In his seminar videos, Hovind keeps bragging about being an expert in math and science because he taught it in high school for 15 years (actually, for 13 years in nonaccredited private Christian schools, one school which he owned), yet he never did the math. Nor did any of his followers who bought into this claim. All he did was wave his hands and they believed every lie he fed them.


BTW, Hovind seems to always tie this claim in with another claim, that of the "shrinking sun" which claims that the sun's diameter is shrinking a such a high rate that mere millions of years ago it would have been so large as to have engulfed and burned the earth. Of course that claim is utterly false, being an unjustified extrapolation based on a single unpublished report of flawed observations, but since when has the truth ever meant anything to creationists?

While creationists use gravitational contraction (see below in How does the Sun shine?) to explain that "shrinkage", Hovind tries to add in massive levels of mass loss to bolster that claim. He fails for three reasons:

  1. The sun is in fact not shrinking (follow this link to a classic rebuttal by a scientist who was a Calvinist at the time, and this other link to a recent article on the Answers in Genesis, a leading creationist organization and web site, in which a creationist astronomer disowns the "shrinking sun" claim).
  2. The actual amount of mass loss as calculated from Hovind's own figures, a few hundredths of one percent of the sun's total mass, would result in a miniscule change in the sun's size if at all. See below for further discussion.
  3. Hovind is proposing that the sun is powered both by gravitational contraction and by "burning its fuel". The former results in no mass loss while the latter results in insignificant mass loss (unless Hovind is thinking of a campfire instead of a fusion reaction, in which case it wouldn't result in any mass loss either; there is reason to suspect that Hovind may believe that).

    But Hovind's rate of mass loss is based on the sun being powered exclusively by fusion and not in the least bit by gravitational contraction. If he wants part of the sun's energy to come from gravitational contraction, then that requires that less of its mass loss is from fusion, which would mean that even less mass is lost which would mean that mass loss would contribute even less to the sun's supposed shrinkage. Hovind is trying to have it both ways, but he simply cannot.

Yet again, it is painfully obvious that Hovind not only did not do the math, but he also did not think this claim through. As today's young'uns might say, "Epic fail!"


QED

That refutes Kent Hovind's solar-mass-loss claim. The amount of mass lost is so minute and insignificant that it could not have possibly caused the effects that Hovind claims. And Hovind would have known that if he had bothered to do the math.

If all you wanted was the refutation, then you need not read any further.

If you are curious about the other versions of the claim and about how my research had proceeded, then please do continue reading.

But if you have questions or concerns about the science or want to raise objections based on the science, then you can skip ahead to the section, More Details, which comprises most of this page.

Or you could simply continue reading and get both the history and the science.


A Brief Informal History

The Beginning

It all started with a cold email, but even that was presaged by a question posted on a Yahoo creation/evolution forum I used to participate on. A freshman college student posted a message asking some questions, but his questions were based on the assumption that the Sun burns through combustion on its surface. Of course, we corrected and educated him, but that got us started researching the subject; I had known since elementary school about the fusion reaction in the Sun's core, but it always helps to review the details.

On a side note, I got into a discussion about this with a creationist who proved to be very unhelpful. Thanks to the science films in elementary school and Wonderful World of Disney films about space (in cooperation with Dr. von Braun), I literally cannot remember a time when I didn't know at least basically how the sun shines (ie, by nuclear fusion in its core). I raised the question with this creationist of what other people think is happening and he "replied" with sarcastic remarks about what a stinking arrogant little genius I was thinking that I'm so superior to everybody else. What? You cannot have even the simplest discussion with people like that and sadly he was typical of so many creationists I have encountered.

Then in 2002 I received a cold email which included this claim:

As any good scientist will tell you, the Sun burns half of its mass every year. If you multiply the Sun's mass by millions (even though science says it is in the billions) the Sun will be so incredibly huge it will stretch out past Pluto. And if you say that the planets would stay close to the Sun as it shrank, then why don't the planets still move closer?
In the twenty years that I'd been following creation/evolution, that was the most outlandish and most obviously false claim I had ever seen.

I sent him a detailed response. While it may appear to be scathing, the only thing that would make it scathing is the complete and utter falsehood of the claim. My intention was for my response to be an exercise and demonstration in testing and verifying a claim, though I also used it as an opportunity to play with some "what would it take" thought experiments. I also did not assume my correspondant to be the source of the claim, so I asked him directly for his source. He was a fundamentalist Christian of high school age who had just gotten back from a retreat where one of the youth ministers had given him that claim.

It appears that a true fact had been included with the original claim, which is often done to make a claim look more "scientific". This true fact is that half the mass of the Sun is concentrated in the Sun's core, which comprises only 1.5% of the Sun's total volume, and it is only that half of the Sun's mass that will ever be involved in the fusion reaction that powers the sun and causes the mass loss (E = mc2). So these three factors seem to have been combined to produce this howler of a bogus claim:

  1. That true fact seems to have gotten corrupted into a claim that half the Sun's mass gets "burned" in a period of time, which somehow got identified as one year.
  2. The apparently common misconception that the Sun "burns" through combustion.
  3. The apparently common misconception that combustion destroys the mass of the fuel being burned, such that it somehow simply "goes away", ceasing to exist. That is contrary to what basic chemistry teaches us, that the atoms of the fuel are recombined into other compounds and escape as gasses, such that in combustion no mass is lost.
It is very difficult to determine whether that youth minister had been the one to mangle the claim up so badly or whether the damage had already been done long before he got hold of it, but it is very telling of the creationist community that such an obviously bogus claim would continue to be accepted and spread indiscriminately; I am thinking, of course, of what Jesus said of millstones and those who would mislead children (Matthew 18:6, Mark 9:42, Luke 17:2), which that youth minister should have been very aware of.

Hovind's Claim

The thing is, though, that in researching that response via Google, I came across Hovind's claim. First I found this item from his list in his site's article, Universe Is Not "Billions of Years" Old, which has been spammed far and wide across the Web on creationist websites -- I Google'd on Hovind's claim from his site and got 847 hits. That article has since been changed to Evidence from Space of a Young Earth and has had Hovind's name removed from it. That claim is:

The shrinking Sun limits the earth-Sun relationship to fewer than billions of years. The Sun is losing both mass and diameter. Changing the mass would upset the fine gravitational balance that keeps the earth at just the right distance for life to survive.

Hovind cites seven sources for this claim, all of them by young-earth creationists including his own seminar tapes, most of them difficult to find. Of the four sources that I could find they all covered the "diminishing diameter" part of the claim, but only Hovind's seminar tape covered the mass-loss part, leaving Hovind so far as the only source for this claim. I quoted from Hovind's seminar tape above, but here it is again:

All you got to do is step outside and look up. Obviously the Sun is burning. It's losing 5 million tons every second. You can't just keep losing 5 million tons a second, pretty soon you start to lose weight. And so the Sun is losing this mass -- 5 million tons every second -- which means it used to be larger. And it used to be more massive. If you increase the mass of the Sun, going backwards in time for several billion years, you start to create a problem with the gravitational balance between the earth and the Sun. It's going to suck the earth in and destroy everything.

(Hovind in his seminar tape video downloaded from his site circa 2003. From my transcription taken from the audio of video #7, "Questions and Answers", from 37 minutes 40 seconds to 39 minutes 54 seconds)

Now, it is a very daunting task to have to sit through hours upon hours of Kent Hovind nonsense (to describe it with extreme generosity), one that turns your stomach. So before I was able to get to that quote, I first found this other one which gave the rate. It was only much later that I finally stumbled across the quote from Hovind's seminar, so it was this one below from Southwest Radio Church that formed the basis of my research.

From a then-recent radio interview with Hovind on Southwest Radio Church (13 Sep 2002), he elaborated a bit more on the part of the claim regarding the loss of solar mass:

For instance, the Sun is burning, of course, and it's burning an enormous amount of fuel. It's losing about 5 million tons every second. Well, if the earth is billions of years old that creates a problem, because you couldn't go back 5 billion or 20 billion years like they say with the Sun constantly getting larger and larger and heavier and heavier. The Sun's gravity would of course become real great and would suck the earth in. Plus the Sun would be bigger and burn the earth up. It can't possibly be true that it's billions of years old.
(my transcription taken from the audio at http://www.swrc.com/ramfiles/sept1302.ram (link broken) at 8 minutes 53 seconds into the broadcast)

First I verified his numbers. I knew already that that "20 billion years" for the accepted age of the sun is totally bogus and longer than the age of the universe, but 5 billion years is about right. I simply chalked up that "20 billion years" as his having misspoken and ignored it from that point on. Even if Hovind had actually meant to say "20 billion years" thinking that it was right, all that would mean was that he didn't know what he was talking about. At any rate, this mistaken age of the sun has no bearing on the refutation of Hovind's claim, so it doesn't really matter.

I surveyed several scientific sites for the actual rates of mass loss due to fusion and most of them cited a rate of 4 million tons per second and some gave a rate of 4.2 million tons. So Hovind's figure was higher, but not by that much. Later in my analysis, I came to assume that it might include other ways in which the sun loses mass (eg, solar wind, which I discuss below in Aren't there any other ways for the sun to lose mass?). As it is, he would only say that he had gotten that rate from a book but wouldn't say which book, so we have no way to determine what the orginator of that published rate had included in it. In my analysis, I decided to use Hovind's higher rate, which still does his case no good.

Next I started doing the math, applying both the standard rate and Hovind's rate. What I found was that even Hovind's slightly exaggerated rate produced total solar mass loss that was insignificant when taken in context, when compared to the total mass of the Sun (See above).

But Wait, It Gets Worse

Then I posted my findings in that Yahoo forum I mentioned earlier and we had a lively discussion about it. We also figured out that since in the fusion of hydrogen (AKA "hydrogen burning") only 0.7% of the mass gets converted to energy (and hence lost) while 99.3% of it remains as helium (AKA "helium ash", since it's what's left by the "hydrogen burning"), then the absolutely most solar mass that could possibly be lost through fusion is only 0.7%, though since only half of the Sun's mass could ever possibly be involved, a more reasonable upper limit on solar mass lost through fusion would be 0.35%. Of course, only the hydrogen in the Sun could have been fused into helium, so unless the Sun had started out consisting purely of hydrogen the upper limit would be even lower; the Sun did not start out as pure hydrogen but rather about 71.1% hydrogen, so its upper limit is indeed lower, about 0.25%. The 0.036% calculated to have already been lost is only about one-seventh of that theoretical upper limit.

One creationist took great exception to that, though most of his problem seemed to be that he couldn't understand what we meant by "helium ash", in that the helium produced by the fusion reaction would metaphorically be the "ash" from "burning" the hydrogen. He even wrote a program to iterate through each second of 5 billion years and add up the mass lost, but it wouldn't work (it was in QuickBasic, which treated the loop iterator as floating-point so when the iterator got too big it would underflow and forever thereafter not increment). After he refused all our attempts to help him debug it (I'm a software engineer by profession), he finally accepted my suggestion that he use nested for-loops instead of one for-loop in order to avoid the underflow problem. Ironically, his resultant accumulated mass loss was lower than the one he had objected to in the first place, my straight-forward application of "rate times time."

But his greatest contribution was to complain that we'd have to get more information from Kent Hovind about this claim, though when I presented him with Hovind's email address, he refused to contact Hovind. So a little further down the line, I went ahead and wrote to Hovind myself. In addition to the solar-mass-loss question, my research had uncovered another troublesome question about Hovind. Remember that freshman college student who thought that the Sun burned like a fire? Well, I came across a couple sites that made it look like Hovind also believed the same.

On a site that was dedicated to quoting Hovind and examining his claims, http://www.oocities.org/kenthovind/quotes/sciencei.htm, "Quacky Quotes -- Basic Science I", there was this quote from Hovind's own "Truth Radio" show, 5 August 2003 at 37:50:

Listener's letter: [.....] It is said the Sun is a burning ball of gas, in other words fire. What is the one thing that fire needs to burn? Oxygen. How come that stars continue to burn if they have no oxygen to keep them burning? [.....]

Hovind: Excellent question, Andres. I'm sorry but I don't know that I have a positive answer. [....] As far as the oxygen required, I'll have to pass on that one too and do some more study on that one. I don't know that I could prove one way or the other. I think there are different types of burning though - some do not require oxygen. Sorry about that, Andres. I'll have to do some research and check back with you on that one.

And there was a rather odd fringe site, Cutting Edge Ministries, with a page entitled:

TITLE: EXACT ILLUMINIST TIMETABLE FOR PRODUCING ANTICHRIST HAS BEEN REVEALED TO CUTTING EDGE MINISTRIES!

Subtitle: We have been given the exact timetable for producing Antichrist, including the exact date he is planned to arise. We have also been given the precise occult thinking by which this timetable was produced. If God does not act to prevent the Illuminati from carrying out this Plan, Antichrist will likely arise as the Illuminati has scheduled.

Nobody ever expects the Illuminati!

Their entire argument was an "Illuminist conspiracy" to use the crashing of the Galileo probe into Jupiter to ignite that planet into a star by exploding its nuclear power reactor.

They quote a number of astronomers they contacted to find out what it would take for Jupiter to burn like a star. Each time they got the same answer, that Jupiter is just not massive enough to get a fusion reaction going in its core. And each time, that answer just went completely over their heads; they couldn't understand the answer ... until they asked Hovind:

We were still not sure exactly why Jupiter could not ignite, especially if it were hit with the huge atomic explosion of 1,750 Megatons, as occult sources are saying will occur when the 49.7 pounds of plutonium in the spacecraft Galileo is turned into the planet on December 6. After all, the largest thermonuclear explosion on earth was the Russian test of only 100 megatons in 1961. The answer we received from a Christian scientist, Dr. Kent Hovind, [www.drdino.com] explained the science to us so we could understand. In the NASA excerpt, quoted above, we learned that "most" of the mass of Jupiter is Hydrogen and Helium, a most explosive mix, if it is mixed with sufficient oxygen in order to burn this mixture. Dr. Hovind says Jupiter does not contain enough oxygen in order to sustain the type of continuous burning that would be needed to produce a star. Now, we understand and now it all makes sense. No matter how large the initial explosion might be, the lack of sufficient quantities of oxygen would snuff out any resulting fire rather quickly.

I wrote to the site asking about Hovind's reply to them, but they never responded.

BTW, Galileo carried 34 pounds of plutonium, not 49.7, 17 pounds in each of two General Purpose Heat Source — Radioisotope Thermoelectric Generators (GPHS-RTG. Each GPHS-RTG contained 18 pellets of plutonium oxide, which were designed to be fracture-proof in case of a launch accident or accidental re-entry. The primary safety concern was to keep the plutonium contained in case of an accident. There was never any risk of an atomic explosion because the matrix of the plutonium oxide kept the plutonium too diffuse to ever achieve critical mass. For some idea of what it would take to get plutonium to explode, review the basic design of Little Boy and of Fat Man. IOW, those people at Cutting Edge Ministries had absolutely no clue what they were talking about.

Trying to Get a Straight Answer from Hovind

In late 2003, I emailed Hovind asking him about this claim. After all, since he was the only known source for the claim, he should know the answers better than anybody else.

My questions were simply these:

  1. What did he come up with as the Sun's mass 5 billion years ago which would "suck the earth in"?
  2. How did he determine that mass?
  3. How did he determine that the mass he arrived at would be sufficient to "suck the earth in"?
  4. If he calculated that mass, then what method did he use (ie, what formula and/or algorithm)?
  5. If he got the entire claim from another source, then could he please cite that source?
  6. If he never bothered to determine that mass nor its effects, but instead just jumped to his conclusion without basing it on anything but an impressive-sounding large rate (5 million tons per second), then shouldn't he just admit it?
It was truly amazing how hard he worked to avoid answering my simple and highly pertinent questions. He even tried twice to pick a fight with me over my email name, DWise1. He only stopped doing that after I replied that its origin is actually quite mundane and I would gladly relay it to him. In the end, the closest he had come to answering any of those questions was to say that he had gotten that 5-million-tons-per-second rate from a book:
"Nearly any high school or college earth science book will give the sun's loss rate at about 5 million tons/sec. To complicate things it probably burned at a different (faster most likely) rate in the early stages when it was larger. I state in my seminar that it obviously used to have more mass and this puts a time limit on the earth sun relationship. There are scores of factors that limit the age of the earth to less than the billions some arbitrarily assign to it."

Compare his conduct to what he claimed that he would do. During his absence in federal prison, his website has been completely reorganized with some of his handful of articles (he depended primarily on speaking and would write down very little) completely renamed or removed. One, How would you answer critics who have written bad things about you?, appears to be missing but was mirrored at a site to which I just linked. Here's an excerpt with my emphasis added:

I will be the first to say that I have learned much from my critics and have changed things in my seminars over the years because of their legitimate gripes, corrections and suggestions. "Iron sharpeneth iron." (Prov. 27:17) These critics can be a man's best friend, if they don't distract you from the main job. God knows that I want to be accurate and would never purposely tell a lie to promote my point. I may not always be right, but if I am saying it in my seminar then I don't know it to be false. I work hard and research a lot to try to be right. I am certainly willing to be corrected by friend or foe. Even if it is proven that I am teaching something that is not correct, don't be fooled into thinking that one incorrect statement means everything else I say is wrong. Any third grader should know that.

Actual experience shows that what he claims there is simply not true. At the beginning of the article, in the one paragraph answer to the question, he states that he only responds to a written request once. The problem is that his single response avoids answering the question, so that when that is pointed out to him in a second correspondence he complains about having to "respond again" and still try to dodge the original question.

This Claim is Apparently Older than We Thought

In August 2003, a creationist created a site, questionevolution.com, in order to "put up some Evolution / Creation notes on the web". At some point, he stated that these notes were from a class about 20 years prior, a fact which for some reason did not click in my brain until just recently. He announced his new site on a forum I was participating on at the time, where he explicitly elicited comments and responses. Indeed, on his site

Any feedback that you care to give, pro or con, please pass it along. We will reply to each message, although sometimes it just may take a little time.

If you are providing additional questions that you would like for us to post, corrections to questions already posted, or ideas for web site enhancement, please provide as much information as possible. If you have any scientific evidence or references, please provide those as well. As we continue to develop this site we hope to begin to footnote every question and the reference will be vital as we start that process.

If you have negative feedback, please let us know. We even have an entire page set up for evolutionists to have their say, and your comments will either end up there or we will reply via e-mail.

A good and noble start, but he had made it truly believing that "The questions found on this site remain unanswered by the evolutionist" and hence no one would be able to answer any of them. Shortly after every single one of his claims had been answered and refuted, he fell victim to creationist dishonesty and removed all trace of those answers even while falsely continuing to ask for feedback. IOW, that's a deliberate lie [3].

Here is the claim that especially caught my eye, in his The Solar System section:

How big was the Sun 1 billion years ago?

The Sun loses 4 million tons of mass through fusion per second, and is shrinking by about 1% each century (5 feet per hour). This shrinking is responsible for a large amount of the energy that the Sun gives off.

As you can see, it is almost identical to Hovind's claim, except for citing 4 million tons per second instead of 5 million. So in my email response explaining what was wrong with that claim, I also asked him for the source of that claim, but he had no idea, only that it was in his notes from that class.

The thing that I missed the first time was when he had acquired that claim: twenty years before 2003, namely circa 1983. All of Hovind's presentations of the claim that I've seen postdate 2000, nearly two decades after the appearance of this instance. For that matter, Hovind didn't start his "Creation Science Evangelism ministry" until 1989, nearly a decade after the appearance of this instance of that claim. In fact, in 1983, Hovind was serving as assistant pastor and teacher at private Baptist schools.

All of that points to him not being the original source of this claim. It appears to have come from another creationist around 1980, when most of other bogus creationist claims were also being concocted or at least collected into books (I wouldn't doubt that many creationist claims date back many decades, likely back to the 1920's). Those claims keep circulating around in the creationist community like urban myths, making it nearly impossible to track them back to their originator. Hovind is notorious for reusing those old long-refuted claims, which also makes it difficult to figure out what he's made up himself and what's from other creationists. I've also seen a very corrupted version of this claim, that first email that started this entire investigation, one of the consequences of their "urban myth" distribution system.

So what really amazes me about this particular claim is that there is currently only one known vector for its spread, Hovind. I have never before seen a creationist claim die out as completely as this one had. That makes me very curious about it and its history. Though at this point, about all I can do is to go to libraries and browse through creationist books from around 1980. Of course, with budget constraints now most of those libraries are not open when I'm off work.


Footnote [3]:

This is yet another sordid tale of creationist dishonesty. This one is made all the more tragic by the fact that the creationist had naïvely started out truly believing his claims were true, but upon learning the real truth about them he was turned to the "The Dark Side", leading him to dishonesty and deliberate lying. Such is the corrupting influence of "creation science" on Christians' morality.

Back around 2003, a creationist created a "QuestionEvolution.com" website in which he posted several anti-evolution "questions" that he claimed "remain unanswered by the evolutionist", such as "why are there still monkeys?" I think that tells you everything you should need to know about him and his site. All his "questions" were the same tired old creationist crap claims that we've seen recycled endlessly for decades. The only thing that got me involved was that it contained the only other solar-mass-loss claim besides Hovind's.

Since he naïvely believed his "questions" to be unanswerable, on his site he explicitly asked for feedback, even negative feedback, and he explicitly promised to post it, including rebuttals. Then he actively sought out creation/evolution forums to advertise his site and to explicitly invite everyone, especially "evolutionists", to visit it and to provide feedback.

Be careful what you wish for ... . We came, we read, we rebutted. He was overwhelmed by the response and didn't know how to add it to his Rebuttal page, so one of the "evolutionists" HTML-ized the replies and posted them on his own site using the exact-same format as the QuestionEvolution.com site. True to his word, the creationist then posted a link to those rebuttals.

Then several months later he abruptly removed that link without notifying anybody. His excuse was that he was too busy and unqualified to verify the rebuttals, so he didn't want them on his site -- of course, the fact that he was too busy and unqualified to verify his own claims has never stopped him from keeping them on his site. When I pointed out that he knew for a fact that the statements on his home page (ie, "The questions found on this site remain unanswered by the evolutionist", "We even have an entire page set up for evolutionists to have their say, and your comments will either end up there or we will reply via e-mail.") were not true, he replied that it was his site so he'll post whatever he wants to. That does not change the fact that he is knowingly posting statements that he knows to be false and hence is deliberately lying.

Since then, the ISP for the rebuttal pages has gone out of business, but they have been archived and are available at http://www.geocities.ws/chastity403/questionevolution/index.html. The QuestionEvolution.com site is still at http://www.questionevolution.com/, but its appearance has been redone, though those same deliberate lies are still there.

Such are the wages of "creation science."


Other Instances of the Claim

So far, with one single exception, my only sources of this claim are Kent Hovind and the websites who copy Hovind's claims. And we will never know whether Hovind had concocted this claim all by himself or simply copied it from another creationist as he normally does, because he refuses to say.

That single exception is described immediately above in the sub-section, This Claim is Apparently Older than We Thought. The owner of QuestionEvolution.com created the site in 2003 in order to post lists of creationist claims from his notes from a class he had attended about 20 years prior, hence circa 1980. Again, from his site:

How big was the Sun 1 billion years ago?

The Sun loses 4 million tons of mass through fusion per second, and is shrinking by about 1% each century (5 feet per hour). This shrinking is responsible for a large amount of the energy that the Sun gives off.

While that claim is clearly based on the "shrinking sun" claim which originated in April 1980, it also includes mass loss due to fusion as a contributing factor. As such, it is the earliest instance of a solar-mass-loss claim that I have found. It is also a great rarity among creationist claims in that it was apparently quickly dropped and not used again for two decades when Hovind started using it again.

We could argue for there being a second exception, a second source for this claim outside of Hovind, but that might be stretching it. Recall that my initial research which led me to Hovind's claim was because of a cold email from a young creationist who asked me about this claim (see the beginning of the previous section):

As any good scientist will tell you, the Sun burns half of its mass every year. If you multiply the Sun's mass by millions (even though science says it is in the billions) the Sun will be so incredibly huge it will stretch out past Pluto. And if you say that the planets would stay close to the Sun as it shrank, then why don't the planets still move closer?
However, that claim had been so badly mangled by being passed along a long line of creationists that we cannot reconstruct its original form, let alone who had originated it.

So allow me to make a simple request of you:

If you are aware of a non-Hovind solar-mass-loss claim, please pass it on to me with as complete a bibliography as you can provide.
Please keep in mind that I am not asking for the "shrinking sun" claim, even though that claim seems to always be linked with this claim such that this solar-mass-loss claim is used to bolster the "shrinking sun" claim.

With your help, we can add more information to this last section.

Thank you.


More Details

Here I have tried to anticipate and address any questions and concerns that you might have or objections that you might want to raise. If your question/concern/objection is not addressed below, then please communicate it to me and I will address it in a direct response to you and may also add it to this page.

Here's the list I have so far:

If you have one that I don't mention, then please ask it through my "Contact me" link.


How does the Sun shine?

I apologize for this really basic question, but over the years I've had to learn the hard way that many people simply don't have some of the most basic scientific knowledge that I have taken for granted almost all my life. Therefore, I offer this section to ensure that we will be talking about the same thing in later sections.

This question has been pondered for much of human history. I discuss here three major explanations with an eye to how each one could cause the loss of mass.

  1. The sun is on fire or glowing like heated metal.
    Of course, I'm lumping several ancient ideas together here. Basically the resemblance between the sun and a fire as sources of heat and light has not been lost on the people of any era.

    This is worth mentioning because it seems to still be a point of confusion for much of the general public, especially among the scientifically illiterate. On a forum in October 2002, I witnessed a young college student insisting on the witness of his eyes that the surface of the sun is obviously burning like a fire and so some of its mass is being "burned up" on the surface and several things I have seen from Kent Hovind makes me suspect that he also believes the sun "burns" like a fire. Besides the misidentification of the incandescent solar surface as a "burning fire", the common misconceptions that student (and possibly Kent Hovind too) displayed are:

    1. What fire is.
      The fire of common experience is the release of energy from molecules' chemical bonds through rapid oxidation. That is not what is happening on the sun's surface.
    2. What fire requires.
      Anyone who's gone through fire fighting or safety training should know the "fire triangle": heat, fuel, air (i.e., an oxygen source). Looking at the sun's surface, the heat is there, whether the fuel is there is questionable (most fuels are molecules), and no source for oxygen.
    3. That the fuel that gets "burned away" in a fire is destroyed and ceases to exist in any form.
      Absolutely false! That misconception says that the fuel's mass has been destroyed and no longer exists, which may be consistent with what we think we observe, but that's not what's really happening. Rather, much of the fuel's mass has recombined with the oxygen to form gasses; what little does not recombine into gases remains as ash, atoms and molecules that were not involved in the chemical reactions of fire. If you were to measure all the air and fuel going into a fire and then measure all the gasses and ash produced, you would see the truth that every beginning chemistry student learns: every single atom of matter in a chemical reaction can be accounted for and still exists. No mass is lost in a fire.  [4]

    So when Hovind says that the sun is burning and that huge amounts of mass are being lost, most of his audience don't know enough to ask the pertinent question, "Where did that mass go?", and so they easily assume and accept the idea that most of the sun's mass just simply ceased to exist, which they "know" would happen in a fire -- they don't know any better, so they are easy to deceive.

    I suspect that even "science expert" Hovind thinks this is how the sun burns. I base this suspicion on the wording of his claims ("The sun is burning,(that's obvious to all) ... ") and on his reply about an "Illuminati conspiracy" to turn Jupiter into a second star by crashing the Galileo probe into Jupiter (2003 Sep 21) and exploding its plutonium reactor (Cutting Edge Ministries -- see more complete discussion below):

    "Dr. Hovind says Jupiter does not contain enough oxygen in order to sustain the type of continuous burning that would be needed to produce a star."
    "Dr." Hovind was clearly talking about combustion, not the fusion reaction that would need to be triggered in Jupiter's core in order to turn it into a second star. The real reason why that can't happen is because Jupiter would have to be at least 10 times more massive to be able to heat up its core enough to start a hydrogen-burning fusion reaction. That is exactly what the astronomers contacted by Cutting Edge Ministries had told them, but they simply could not understand the right answer.

  2. The sun is being heated by gravitational contraction.
    This idea was advanced in the 19th century and is known as the Kelvin–Helmholtz mechanism. As the sun's mass condenses about the core, the gasses' potential energy is released as heat. Of course, once the gravitational contraction stopped, the sun would lose this source of energy and would start to cool. Although this idea has been replaced by nuclear fusion, many creationists have tried to revive it, especially in connection with the "shrinking sun" claim.

    It should be obvious that this method involves absolutely no loss of mass.

    As it turns out, this energy source is real and it is responsible for raising the temperature of a protostar's core to the point where hydrogen fusion can begin. It is also what keeps the core hot enough to sustain the fusion reaction and even regulate it by establishing a hydrostatic equilibrium between gravitational contraction pressing inwards, heating up the core, and expansion outwards from thermal energy, cooling the core -- the fusion reaction of "hydrogen burning" is very sensitive to changes in temperature. Therefore, while gravitational contraction does contribute to sunshine, it does so only indirectly by enabling and sustaining the sun's fusion reaction, the real source of the sun's energy output.

  3. The sun gets its energy from a fusion reaction in its core.
    This idea was proposed in 1939 by Hans Bethe, which earned him the 1967 Nobel Prize for Physics. Under temperatures of millions of degrees in a star's core, lighter elements fuse together to form heavier elements, during which a small amount of the mass is converted to energy. More specifically, every second about 600 million tonnes of hydrogen is being fused into about 596 million tonnes of helium in the sun's core, during which about 4 million tonnes of matter is converted into energy. This process is commonly called "hydrogen burning" and the resultant helium is commonly referred to as "helium ash".

When the sun was forming, it got its energy from gravitational contraction. Then once the core heated up enough for nuclear fusion to start, radiative pressure from the fusion reaction slowed down and finally halted the gravitational contraction, placing the sun in hydrostatic equilibrium. Of course, all this happened before the sun became a main-sequence star, long before the earth could have been habitable. At present, the source of the sun's energy is the nuclear fusion reaction in its core.

Then when the hydrogen has effectively been used up in the core, the nuclear fusion reaction will slow down and gravitational contraction will predominate again. That will then drive the temperature of the core up to where it can start to "burn the helium" (ie, fuse the helium into carbon through the triple-alpha process) and start the sun's red giant phase in which the sun will no longer be a main-sequence star.

And the incandescence of the sun's surface helps to contribute to another form of mass loss from the sun's surface: solar wind. Though it turns out that this loss is small compared to the loss through nuclear fusion and doesn't contribute significantly to the sun's loss of mass (see below).

So to recapitulate the mass-loss effects of these three ideas for how the sun shines:

  1. If the sun were powered by fire, which is a chemical reaction, then no mass would be lost [4]. Also, there would be questions raised by the lack of sufficient oxygen to sustain such a fire as well as the lack of the by-products of such a fire (H2 + O => H2O (AKA "water") -- basic high school chemistry: massH2 + massO = massH2O ).
  2. If the sun were powered by gravitational contraction, then again no mass would be lost.
  3. Since the sun is powered by the fusion of hydrogen (AKA "hydrogen burning"), there would be some mass lost: 0.7% of that hydrogen mass would be lost as energy with 99.3% of it remaining as helium (AKA "helium ash"). So while an enormous amount of hydrogen is being "burned", only a very small amount of that mass is lost as energy.
IOW, hydrogen fusion is the only method of powering the sun that we know of which would result in the loss of mass.


Footnote [4]:

"No mass is lost in a fire." Someone once told me on a forum that that statement is not strictly true. He stated that chemical bonds do contain some very small amount of mass and that the heat generated by the fire comes from the mass of those bonds being converted to energy.

I last had chemistry in high school, where this idea never came up and where we worked with the strict accounting of every single atom involved in a chemical reaction, among other topics. Therefore, I believe that this is a more advanced topic that is covered in university-level chemistry and I have no reason to doubt it. However, it is of no practical importance in this topic, since the mass of a chemical bond would be miniscule compared to that of the nuclei of the atoms being bound (the vast majority of an atom's mass is contained in its nucleus). An interesting experiment would be to repeat the calculations in the next section ("Where does that "5 million tons every second" figure come from?") using the amount of energy released by burning a given amount of fuel; i.e., is there a corollation between calories and E = mc2?

So this is an interesting fact to know, but it does not detract in any practical way from the original statement that no mass is lost in a fire.


Why do you talk specifically about hydrogen fusion? Are there other kinds? If so, then why exclude them?

Yes, there are indeed other kinds of thermonuclear fusion reactions which fuse elements other than hydrogen. But they don't come into play here because they only occur towards the end of a star's life-time, which for the sun won't be for another 5 billion years.

To put it simply, fusion reactions require a lot of energy, which in a star's case is the high pressure and temperature at its core. Another fact of life is that the heavier an element is (ie, the more protons and neutrons its nucleus contains), the more energy it requires in order to fuse into an even heavier element, which means that the core has to be even hotter. But because of hydrodynamic equilibrium which regulates the core's temperature, as long as a lighter element's fusion reaction is in progress, that will keep the core from getting hot enough for a heavier element to start to fuse. But when the lighter element is depleted, then the star will start to collapse, which will apply greater pressure on the core and heat it up enough to start the next heavier element to start to fuse, and so on.

As I said above about how the lighter elements being depleted which start the fusion reactions of the heavier elements, that only happens towards the end of a star's lifetime, when it has departed the Main Sequence. While a star is on the Main Sequence, the only fusion reaction is hydrogen fusing into helium. Our sun is currently in the middle of its time on the Main Sequence. All discussion how much mass the sun would have lost through fusion involves hydrogen fusion and no other kind of fusion. Any other kind of fusion would have absolutely no bearing on our sun for another 5 billion years.

If you don't understand why all that is, or what the Main Sequence is, then continue reading.


This question pertains to stellar evolution (which is of course very different from biological evolution, so don't fall for that old creationist switcheroo meant to confuse you). The word "evolution" dates back to around 1600, where it was used to describe a sequence of stages of development, and "turning out" or unfolding, as the basis of the word means. Thus you can use it to describe the sequence in which something like a star or a river will develope. Biological evolution only came along two centuries later.

Basically, there are certain stages of development that a star (such as our sun) will go through and each stage of development is marked by certain characteristics, which I will describe below as briefly as I can. The primary goal here is to identify those stages of development with an eye on what is powering the star in each stage. The important point here will be that while there are several kinds of fusion that can occur within a star, most of them happen only after the star leaves the Main Sequence. While the star is on the Main Sequence then it only uses hydrogen fusion. Our sun is about half-way through its time on the Main Sequence, so the only form of fusion that is applicable to Hovind's claim is hydrogen fusion.

I am going to keep this very brief, doing it more as an introductory overview. You can refer to the Wikipedia article on stellar evolution for more information. That article will cover the entire lifetime of stars and provide links to articles dealing specifically with each stage of development; in the discussion below I will link to those more specific articles.


Much of our understanding of stellar evolution comes from the Hertzsprung-Russell diagram which was created circa 1910. For decades astronomers had been doing an intensive survey of the sky collecting the spectra [5] of the light from many stars. They noticed that those spectra exhibited certain characteristic properties which led to their classifying those stars according to those properties, assigning almost random letters to each group (eg, A, B, F, G, K, M, O). When they tried plotting all those stars on a scatter graph with decreasing temperature on the horizontal axis and increasing absolute magnitude (AKA "brightness" or "luminosity") on the vertical axis, interesting patterns emerged. They found that stars of the same spectral class would not only group together on the chart, but those groups formed a downward sloping line across the graph with the hottest and brightest stars (class O) high on the left down to the coolest and dimmest stars (class M) low on the right. That line became the Main Sequence and the order of the spectral classes turned out to be O (white), B (blue-white), A (blue), F (green), G (yellow), K (orange), M (red) ("Oh Be A Fine Girl, Kiss Me" -- our sun is a class G star).

But then there were also the odd stars that did not fit on the Main Sequence. For example, clumped in the lower left of the graph were hot stars that were dim; these became known as "white dwarves". And clumped in the upper right were cool stars that were bright; these became known as "red giants". Later we came to recognize red giants and white dwarves to be the final stages of a star's life sequence, of its stellar evolution. And there are others, such as the super-giants of various colors along the top of the diagram and brown dwarves, etc.

As our understanding grew, the picture that emerged was that a new star would start to form as a protostar out of a nebula somewhere off of the Main Sequence. As it finished forming and started to fuse hydrogen into helium in its core, it would move onto a particular point on the Main Sequence, depending on its initial properties (primarily how massive it is), and it would then stay there for most of its lifetime fusing the hydrogen in its core into helium. Then as its supply of hydrogen ran out, it would become a red giant and leave the Main Sequence.

What would happen after that depends on how massive the star was to begin with. There is a sequence of a number of different fusion reactions that the star could progress through, provided it is massive enough to drive its core temperature up higher and higher to make each successive reaction possible -- as soon as its mass can no longer provide the required temperature, then it will progress no further. One scenario is for the star to start to fuse its helium core into carbon. If it's massive enough (more massive than the sun is), then it will "go nova" blowing off its outer layers leaving its carbon core as a white dwarf. If it's even more massive than that, it can fuse that carbon into ever heavier elements, though iron is the limit. Then it could end its life as a supernova leaving behind a number of possible exotic astronomical objects. If it goes nova or supernova, then it will create a planetary nebula which can provide the material out of which the next generation of protostars can form.

A side topic that all leads to is stellar nucleosynthesis through which the elements were formed in successive generations (called "populations") of stars through the fusion of successive elements starting with hydrogen. This idea was the source of Carl Sagan's poetic reference to everything being made out of "star stuff".


In more detail though still very greatly simplified, these are the basic stages of development a star will go through in its lifetime:

Giant Molecular Cloud (GMC)
A particular type of "nebula", the mass of a GMC is approximately 1,000 to 10,000,000 times that of the sun, but it covers a volume around 15 to 600 light-years in diameter. It contains dust and various elements, but mainly molecular hydrogen (H2). At this time, most if not all of the matter in a GMC comes from the novae and supernovae of older massive stars and will be the matter that will condense into a new star and its planetary system. Thus newer stars and planets are made out of recycyled "star dust."

Protostar

Protostars form out of GMCs, which in turn provide the protostar with its mass. Basically, part of the GMC will become denser and through gravity start to collapse the surrounding matter into a "dense core." There are various things that can cause this to happen as discussed in the Wikipedia article on star formation.

At first, gas pressure and magnetic pressure resist the force of gravity, but when enough mass has accumulated then the dense core starts to collapse under its own gravity as it continues to pull more mass in. Theoretically, this collapse starts in the center and propagates outward, leading to the formation of a protoplanetary disk.

Gravitational collapse causes the center of the dense core to heat up, first disassociating the molecular hydrogen and then stripping away the atoms' electrons. It's still not hot enough for hydrogen fusion, but deuterium fusion can start and produce helium-3 -- deuterium is an isotope of hydrogen with an extra neutron and helium-3 is an isotope of helium that's missing one neutron. This continues to heat up the core.

Matter continues to fall into the protostar making it both more massive and hotter. This is the stage where the Kelvin–Helmholtz mechanism uses gravitational collapse as the major contributer to the protostar's energy output. In a main-sequence star such as the sun, the star's energy output (ie, radiative pressure) counters its gravitational collapse such that they balance each other in hydrostatic equilibrium wherein radiative pressure outwards stops the gravitational collapse while that gravitational collapse keeps the core hot enough to maintain the core's fusion reaction that's generating the radiative pressure outwards. But the protostar is not at that point yet in that it does not have a powerful fusion reaction running yet, so matter continues to collapse into it, increasing its mass and its core temperature.

Pre-Main-Sequence Star
Once the core has heated up sufficiently, the hydrogen-burning fusion reaction starts up. This starts generating radiative pressure outwards which starts to slow down gravitational collapse. At first, the source of the new star's energy output will be a combination of fusion and of the Kelvin–Helmholtz mechanism, but then the fusion reaction eventually takes over as the primary source of the star's energy.

As the radiative pressure increases, the stellar wind starts up to push the surrounding dust away. In practical terms, this is what now makes the new star visible. The initial stellar wind appears to be very active as it pushes large amounts of matter away. This is the star's T Tauri stage. While it may appear to be expelling large amounts of matter from the star, in reality it is keeping more matter from infalling into the new star. That matter will contribute to the proto-planetary disk and to planet formation.

At this point, the star will have acquired nearly all of its initial mass. How much mass that is will determine what happens to the star from this point on throughout its entire lifetime. For example, a highly-massive protostar can skip this stage altogether, moving straight to the Main Sequence.

On the Hertzsprung–Russell diagram, the pre-main-sequence star moves onto the stellar birthline, which is a set of locations found above the Main Sequence where these newly visible stars reside and from where they will migrate down onto their place on the Main Sequence.

Main Sequence
With the hydrogen fusion reaction started, hydrostatic equilibrium establishes itself and the star evolves rapidly to a stable state that for all practical purposes it will remain in for the entire main-sequence phase of its life.

Again, the star's mass will determine many things about its time in the Main Sequence:

  • The more massive a star is, the hotter it will be and hence the further to the left end of the Main Sequence.
  • The less massive a star is, the cooler it will be and hence the further to the right end of the Main Sequence.
  • The more massive a star is, the larger and brighter it will be and hence it will be located further towards the top of the Main Sequence.
  • The less massive a star is, the smaller and dimmer it will be and hence it will be located further towards the bottom of the Main Sequence.
  • The more massive a star is, the more quickly it will burn up its hydrogen and the sooner it will "mature" and leave the Main Sequence.
  • The less massive a star is, the more slowly it will burn up its hydrogen and thus it will last longer and stay on the Main Sequence longer.
On those last two points, note that the hotter most massive class O stars will leave the Main Sequence after just a few million years while the cooler least massive class M stars can stay on the Main Sequence for hundreds of billions of years (the age of the universe is estimated to about 13 to 14 billion years). A mid-sized star like the sun (class G2) can last for about 10 billion years; our sun is estimated to be only half-way through its 10 billion years.

The two forms of hydrogen fusion are the proton–proton chain reaction (pp-chain) and the carbon–nitrogen–oxygen fusion reaction (CNO cycle). Follow the links for more detailed information Basically the proton–proton chain reaction has two hydrogen nuclei fusing to form a deuterium nucleus, which then fuses with another hydrogen nucleus to form a 3He isotope nucleus, which then fuses with another 3He nucleus to form one helium nucleus (4He) and two hydrogen nuclei. The CNO cycle is a catalytic reaction involving carbon, nitrogen, and oxygen nuclei that are used but in the end not changed in order to fuse four hydrogen nuclei into one helium nucleus; I won't even try to describe the process here, so follow that link and read it for yourself. The CNO cycle requires higher temperatures than the pp-chain reaction, so the CNO cycle predominates with stars more massive than 1.3 times the sun with the pp-chain reaction be more predominate in less massive stars. The sun uses both reactions though primarily the pp-chain reaction, however, as the sun's core is slowly becoming hotter, use of the CNO cycle is increasing.

After a star enters the Main Sequence, it doesn't just stay put, but rather it starts drifting to the left. As the hydrogen in its core fuses into helium, that helium builds up in the core. As a result, the core becomes ever hotter slowly over time. That causes the fusion reaction, which is very sensitive to temperature, to slowly increase, which in turn increases the star's energy output as well as its size. Hence, the longer the star stays on the Main Sequence, the hotter and brighter it becomes, which slowly shifts it to the left and up in the Main Sequence.

Mature stars
Eventually the star uses up the hydrogen in its core and the resultant changes move it off the Main Sequence. As the fusion reaction slows down for lack of fuel, the radiative pressure it was maintaining decreases and the hydrodynamic equilibrium the star had enjoyed for so long is no more. Gravitational collapse gains the upper hand again and continues to compress the core under the star's own weight until either atomic-level limits are reached (ie, electron degeneracy pressure) or the core has heated up enough for helium fusion to begin (the triple-alpha process[6] ).

Here yet again, what ends up happening depends on how massive the star is. The fates for lower-mass stars are few, while the fates for high-mass stars are more varied as well as being the stuff of entire series of Science Channel documentaries. Rather than engage in such a massive digression, I'll just describe basically what's going on and let you drill deeper in the side tracks that interest you.


So then very basically, what will happen when the star's core reaction runs out of hydrogen is that the radiative pressure that had been pushing against gravitational contraction will diminish and the star will begin to collapse, compressing the core, which increases the core's temperature. When the core gets hot enough, then the next heavier element, starting with helium, will start to fuse, which will restore the radiative pressure and establish hydrodynamic equilibrium again. However, since this is a hotter reaction, that radiative pressure will be greater and hence the star will be larger. Since the star is larger, its surface area will be far greater ( S = 4πR2 ). When the star's internal energy gets spread out over that far greater area, its surface temperature will be lower and hence the color will shift towards red. The general effect will be that the star will grow into a red giant, but what actually happens depends on different factors, the primary one being the star's mass.

Fusion doesn't stop with helium. There is a series of fusion reactions which produce ever heavier elements:

hydrogen (H) → helium (He) → carbon (C) → neon (Ne) → oxygen (O) → silicon (Si) → iron (Fe).
See the Key reactions section on Wikipedia's Stellar nucleosynthesis page. Each subsequent fusion reaction requires a higher temperature, for which the star needs to be ever more massive to attain. If the star is not massive enough to trigger the next higher fusion reaction, then that's as far as it will ever get. Therefore, only the most massive stars will be able work their way all the way up to producing iron, while the least massive stars won't even be able to get helium to fuse into carbon. A star with the mass of the sun will be able to fuse helium into carbon, but will unable to ignite carbon fusion.

But unlike in a Main Sequence star, fusion in a mature star doesn't happen only in the core. As the core heats up enough to start fusing helium, the layer around it also heats up to where it can start to fuse hydrogen. Such a layer is called a "shell". So as the core is burning helium, it's in a shell surrounding the core that the star is still burning hydrogen. And in a more massive mature star that can start to fuse carbon in its core, that core will have a shell that's burning helium and then another shell that's burning hydrogen. And a far more massive mature star could have a core that's fusing silicon into iron plus six shells, five of which have fusion reactions going and the outermost being hydrogen. And of course, the energy output of each of those fusing shells would add to the radiative pressure that would push the star's size out even more.

So what happens when the core runs out of fuel and the star isn't massive enough to get the next fusion reaction started? In general, the shells will continue their own fusion reactions until they also run out of fuel. When all the fuel has run out, then the star will again start to contract and will continue to do so until something stops it. There are many scenarios that could play out, all of which depend on various factors but still primarily they depend very heavily on the mass of the star. Normally, physical atomic-level limits will be reached (ie, electron degeneracy pressure) and the much smaller mature star will start cooling down as a white dwarf.

Of course, that all assumed a graceful decline into old age, but that is not always the case. Sometimes when a fusion reaction ignites in a shell, it causes an explosive expansion which expells upper layers from the star. It can also cause the core to undergo far greater compression due to implosion. Such events are called novae or supernovae. There are so many different scenarios and outcomes possible that I'll just let you follow through yourself. Otherwise I'd dig us into a digression so deep that we'd never find our way out (that was not intended to be an introduction to the subject of black holes, which is yet another possible fate for a very massive star).

For our purposes, we're only interested in the fate of our sun. It is not massive enough to become a supernova, but it should "explode" and eject its outer layers as it experiences "shell helium flashes" ("brief" and violent runaway helium fusion reactions) well into its post-retirement career as a red giant.


Now you can see that it is only a mature star that has left the Main Sequence which uses any form of fusion other than hydrogen fusion. While a star is on the Main Sequence, it is being powered by hydrogen fusion. Since the sun is in the middle of its time on the Main Sequence, it is only using hydrogen fusion.

This section's question is "Why do you talk specifically about hydrogen fusion? Are there other kinds? If so, then why exclude them?" The answer has just been given, since the sun is in the middle of its time on the Main Sequence, it is only using hydrogen fusion, so that is the only kind of fusion that we can consider here.

QED


Footnote [5]:

Stellar spectra -- see here for more details.

Everything we know about a star we get from its light. We can observe where it is in the sky, which includes observing its parallax and using trigonometry to determine how far away it is (up to a distance of about 100 light years, but the Hipparcos satellite in 1989 extended that to 1,000 and then the Hubble Space Telescope extended it to 10,000 light years out in 2014). We can observe how bright it appears to be (apparent magnitude) and deduce how bright it actually is (absolute magnitude).

And we can observe its spectrum. Basically, you place a prism to the eyepiece of the telescope (a gross oversimplification of the actual mechanism) and photograph the "rainbow" that's produced. Now, light is a band of frequencies of electromagnetic radiation, so each point along the visible spectrum is a distinct frequency of light corresponding to a particular color. Each element has a number of specific frequencies of light that it will absorb and emit, which correspond to particular quantum energy levels of its electrons. Therefore, in each star's spectrum we find Fraunhofer lines (named after their discoverer, Joseph von Fraunhofer) which tell us what elements are present in and about that star. Furthermore, when those lines are shifted from where they should be, either towards the blue or towards the red end of the spectrum, then that Doppler shift tells us both whether the star is moving towards us (ie, "blue-shifted") or away from us (ie, "red-shifted") and at what velocity.

So the stellar spectra that had been collected contained a great wealth of information which went into the creation of the Hertzsprung-Russell diagram circa 1910.

Footnote [6]:

The triple-alpha process.

Remember your nuclear warfare training. We were taught about dealing with three kinds of radiation named after the first three letters in the Greek alphabet:

  1. Alpha radiation -- Alpha particles, which are helium nuclei. Low energy, low penetration. Only dangerous if inhaled or ingested or allowed to lie on the skin for too long.
  2. Beta radiation -- Beta particles, which are electrons. Higher energy, deeper penetration. More damaging to living tissue.
  3. Gamma radiation -- A frequency of electromagnetic radiation (as are light, radio waves, and x-rays). It'll go right through you doing a lot of damage.

The triple-alpha process is so-named because it involves the fusion of three alpha particles (ie, 4He nuclei) into a carbon nucleus.


Your analysis of Hovind's rate may be well and good for that particular rate, but what about other rates?

That's a valid question, though another question would be how much effect changing the rate would have. But since that would involve diffential calculus, which may lose some of my readers, I will instead present a number of rates of mass loss along with the effects that those rates would have in the table below.

First, a brief description of each rate presented in the table, which will be discussed more fully elsewhere on this page (the last two do not involve an actual rate nor span of time):

Loss Rate of 4 million tonnes per second over the span of 5 billion years
This is the rate normally given in articles about the loss of solar mass through fusion. It is also the rate given in the oldest instance of this claim that I have found. And it is very close to our calculated rate of 4.28 million tonnes per second that we will calculate in one of the sections that follow.

Loss Rate of 5 million tonnes per second over the span of 5 billion years
This is the rate that Kent Hovind gave and it is the one that I used in the discussion above refuting his claim. While it is higher than the rate that's normally given, it is possible that his source had combined two different rates in one: mass loss due to fusion and mass loss due to solar wind. Unfortunately, we will never know that because Hovind refuses to divulge his source outside of saying that it is from a book.

Loss Rate of 6 million tonnes per second over the span of 5 billion years
I will offer this as a possible combined rate of mass loss due both to fusion and to solar wind.

Loss Rate of 7 million tonnes per second over the span of billion years
This is another possible combined rate of mass loss due both to fusion and to solar wind. I will present it as a blatant over-estimate. My purpose in presenting it will be to counter objections that the previous combined rate may be too low and to demonstrate that it does no better in supporting Hovind's claims.

Loss Rate of 5 million tonnes per second over the span of 10 billion years
Basically, this is Kent Hovind's rate over the entire span of the sun's time on the Main Sequence, after which it will start "burning" its helium (ie, fuse the helium into carbon through the triple-alpha process) as it enters its red giant phase.

As an alternative, you could treat it as 10 million tonnes per second over 5 billion years. In this capacity, it will be a much more blatant over-estimate, assuming that the 7-million-tonne rate wasn't enough to convince you.

The columns in the following table display values pertaining to each of the mass loss rates and times:

Time in billions of years
This is an input value. Since the formula for calculating the amount of mass lost is basically "rate × time equals distance", this is the time factor. Even though the accepted age of the sun is 4.5 billion years (4.5×109), I have chosen to use Hovind's inflated value of 5 billion years, yielding 10 billion years.

Similarly, when I calculate the effects of mass loss at the end of the sun's time on the Main Sequence, I take the estimate that we are half-way through that time and I again assume Hovind's inflated value, yielding 10 billion years (10×109) for the sun's entire time on the Main Sequence.

Loss rate in tonnes per second
This is an input value, the rate at which the sun is losing mass in tonnes per second. Although the claim as stated only includes mass loss due to the sun "burning its fuel" (ie, hydrogen fusion), there is another source of mass loss which is the solar wind. Whether I combine these two or only include loss due to fusion makes no difference in this table, since loss due to solar wind would be included implicitly. Mass loss is mass loss regardless of what's causing it.

Percent Mass Lost
This figure is obtained by dividing the total mass lost by the original mass of the ancient sun.

Total Mass Lost in tonnes
This is the "distance" value obtained by plugging the time factor input and the rate factor input into the "rate × time equals distance" formula. It is the total mass lost by taking the given rate over the given period of time. This value is then used to calculate the original mass of the ancient sun and the percent mass lost.

Original Mass of the ancient sun in tonnes
This is calculated by taking the current mass of the sun, 1.98855×1027 tonnes, and adding back to it the total mass lost. This value is then used to calculate the percent mass lost and the gravity ratio of the ancient sun.

The gravity of the Original Sun compared to the sun's current gravity
This is the ratio of the gravity of the ancient sun to the sun's current gravity. IOW, this is how many times stronger the ancient sun's gravity was. It is calculated by dividing the sun's ancient mass by its current mass.

According to Newton's Law of Universal Gravitation, the sun's gravity is directly proportional to its mass. Therefore, the ratio of the sun's ancient gravity to the its present gravity would equal the ratio of the sun's ancient and current masses.

This importance of this ratio is two-fold. First, it refutes Hovind's claim that the ancient sun's mass would be so immensely greater that it would have "sucked the earth in". Second, it can be used to calculate the effects of that greater gravity on the earth's orbit.

The original size in miles of the earth's orbit about the ancient sun
Since the average radius of the earth's orbit is inversely proportional to the sun's gravity, increasing the sun's gravity m times decreases the earth's orbit 1/m times. Therefore, I calculate this value by dividing the current size of the earth's orbit, 92,955,902 miles, by how many times stronger the original sun's gravity was.

How much the earth was "sucked in" by the ancient sun, in miles
This is simply the difference between the current and the ancient sizes of the earth's orbits. Its purpose is to show the effect that the ancient sun's greater gravity would really have on the earth's distance from the sun.

Please keep in mind that, since the earth's orbit is elliptical, the earth's distance from the varies throughout the year, being closest at one point and farthest out six months later. Given the earth's orbital eccentricity (0.0167086), the earth's distance from the sun varies from about 1.5 million miles closer in to 1.5 million miles farther out. That should give you some kind of context within which to evaluate the consequences of how much the earth would have actually been "sucked in" by the ancient sun's greater gravity.

Figures and Effects for Various Mass Loss Rates and Times
Time
(billions
of years)
Loss Rate
(tonnes/sec)
Percent Loss
(%)
Mass Lost
(tonnes)
Original Mass
(tonnes)
Gravity
(× Present)
Original Orbit
(million miles)
"Sucked in" by
(mi)
5 4 million 0.03172856 6.31138519×1023 1.98918114×1027 1.00031739 92.92640843 29,494
5 5 million 0.03965755 7.88923149×1023 1.98933892×1027 1.00039673 92.91903796 36,864
5 6 million 0.04758529 9.46707779×1023 1.98949671×1027 1.00047608 92.91166866 44,233
5 7 million 0.05551177 1.10449241×1024 1.98965449×1027 1.00055543 92.90430053 51,601
10 5 million 0.07928367 1.57784630×1024 1.99012785×1027 1.00079347 92.88220315 73,699

As we can see:

None of Kent Hovind's dire consequences for the ancient earth have any basis in reality. I very much want to see what his calculations were that led him to those conclusions, but he very strongly resisted all attempts to ask him. I very strongly suspect that he had never performed any calculations, not even the most basic calculations to determine how much mass would have been lost and how that compared to the sun's total mass. Rather, I think that even he just looked at that rate of mass lost per second, thought momentarily that there are a lot of seconds in 5 billion years, and then jumped to the conclusion he had decided upon from the beginning.

Furthermore, from his extreme evasiveness I strongly suspect that I was not the first to ask him about this claim and that he had learned from earlier contacts how bogus his claim is. But rather than drop his claim, he chose to continue to use it and bluff his way through any questions about it. IOW, he persisted in using a false claim that he knew to be false, which is also called "deliberate lying."


Where does Hovind's "5 million tons every second" figure come from?

        or stated more generally:

However are we supposed to know how much mass the sun loses every second?

Excellent questions and not just because I asked them. When I asked Kent Hovind where he had gotten his rate from, he just replied, "Nearly any high school or college earth science book will give the sun's loss rate at about 5 million tons/sec." -- actually, I had a different reason for asking him that, which I will discuss below. But that still begs the question of where those books had gotten that rate from. Actually, Hovind's rate is the highest rate that I've seen given, with most of the ones I've seen quoting about 4.6 million tons. And when we calculate it ourselves here, it will be a bit lower than that.

Believe it or not, we will use Einstein's equation that everybody knows from the titles of The Twilight Zone: E = mc2, energy equals mass times the speed of light squared. Or more specifically, we know the amount of energy and we know the speed of light, so we are able to solve for the mass that has to be converted to energy in order to account for the amount of energy we measured: m = E/(c2). In short, we know the speed of light, so we know c, and we measure the total energy output of the Sun per second, so we know E, so we plug those two values into the equation and get the value of m, the mass that is lost per second by having been converted to energy through the process of nuclear fusion.

Now let's do that math:

The sun's energy output per second is E = 3.846×1026 Joules
E = 3.846×1026 Joules = 3.846×1026 (kg × m2 / sec2)
c = 299,792,458 meters per second
c2 = 89,875,517,873,681,764 m2/sec2

Magnitude Calculation:

m = E/(c2) = 3.846×1026 / 8.9875517873681764×1016
         = 4,279,252,115.58

Units Calculation [7]:

(kg × m2 / sec2) / (m2/sec2)
         = kg × m2 / m2 × sec2 / sec2 = kg

Therefore, m = 4,279,252,115.58 kg = 4,279,252.11558 tonnes
        and the rate of mass loss is 4.28 million tonnes per second.

Published rates range from 4 million tons to 5 million tons, which I would assume are metric tons. The variation we see may be due to rounding off or to using different values for the sun's energy output per second. It might even be due to some writers converting from tonnes to short tons, as I would expect Hovind to do, but I do not deem that likely since I cannot imagine Hovind using any degree of rigor. In the final analysis, Hovind's rate of "5 million tons every second" is the highest that I have seen and another much older version of this claim (two decades earlier, the only other one I have seen so far) cites the rate as "4 million tons of mass through fusion per second." As we have already seen, Hovind's use of a higher rate does not benefit his claim at all.

On further reflection, I have come to wonder whether Hovind's higher rate mightn't be a combination of two rates. It could be possible that Hovind's source had combined a rate of 4 million tonnes lost per second through fusion and 1 million tonnes lost per second through the solar wind in order to come up with a total of 5 million tonnes lost per second. But since Hovind refused to divulge any of his sources or to discuss his claim, we will never know.


Footnote [7]:

Yes, that is correct. You can treat units as algebraic variables and solve for the units of your result. That was one of the cooler things I learned in physics. In fact, one of the more important functions of constants in physics (eg, G, the Constant of Gravitation: 6.674×10-11 m3×kg-1×s-2 ) is to make the units come out right.

A very practical use for this fact is in deriving conversion factors. At my first job as a software engineer, I was the go-to guy for conversion factors even though I kept trying to teach them how to do it themselves. Now mind you, these were exotic units (eg, binary angular measurement (BAM)) that you could not find in most reference books (nor could you find them on-line since in 1983 there was no such thing as "on-line"). The procedure is simple: you just set up an equation for the same value using different units and then solve for the unit you want to convert from; eg:

Derive the conversion factor for radians to degrees, given that a full 360° circle is 2π radians:
2π radians = 360°
1 radian = (360 / 2π)°
1 radian = (180 / π)°
QED
Conversion factor for converting from radians to degrees: multiply by 180/π
A more involved example would be to convert a value without actually deriving a conversion factor; eg:
Convert 7 days to seconds:
Strategy: repeatedly multiply the value being converted by 1, which does not change its value. Of course, 1 comes in a great many different forms.

7 days × 24 hours / day = 7 × 24 hours × day / day = 168 hours
168 hours × 60 minutes / hour = 168 × 60 minutes × hour/hour = 10,080 minutes
10,080 minutes × 60 seconds / minute = 10,080 × 60 seconds × minute/minute = 604,800 seconds
Ergo: 7 days = 604,800 seconds
QED

Or, if you will be doing this more than once, you could have created a conversion factor for converting from days to seconds:
1 day = 1 day × 24 hours / day × 60 minutes / hour × 60 seconds / minute
         = 1 × 24 × 60 × 60 × day/day × hour/hour × minute/minute × seconds
1 day = 86,400 seconds
QED
Conversion factor for converting from days to seconds: multiply by 86,400
Another example, this time involving exponents:
Convert the density of the sun's core from g/cm3 to kg/m3
1 kg = 1000 g
1 m = 100 cm
Density of Sun's core = 162.2 g/cm3
         = 162.2 × (g × 1 kg/1000 g) × (1/cm3 × (100 cm)3 / 1 m3)
         = 162.2 × (1 kg/1000 × g/g) × (1/cm3 × 1003 cm3 / 1 m3)
         = 162.2 × [ (1 kg / 1000) × (1,000,000 / 1 m3 × cm3/cm3 )]
         = 162.2 × [ (1,000,000 / 1000) kg/m3]
         = 162.2 × (1000 kg/m3)
         = 162,200 kg/m3
QED
Conversion factor for converting from g/cm3 to kg/m3: multiply by 1000
And now you have acquired a useful skill.


But if the rate were greater in the past, couldn't that provide the ginormous amount of mass loss this claim requires?

It may seem so at first, but, no, that still could not work. Even Hovind tried to argue for this with me in what was perhaps his only attempt to actually discuss his claim with me:

"Nearly any high school or college earth science book will give the sun's loss rate at about 5 million tons/sec. To complicate things it probably burned at a different (faster most likely) rate in the early stages when it was larger. I state in my seminar that it obviously used to have more mass and this puts a time limit on the earth sun relationship. There are scores of factors that limit the age of the earth to less than the billions some arbitrarily assign to it."

The problem for Hovind and this claim is that hydrogen fusion itself imposes a very real upper limit to the maximum amount of mass that could possibly be lost through hydrogen fusion regardless of how fast the reaction is: 0.7%. The reason is because when you fuse hydrogen, it becomes helium. The hydrogen doesn't just simply disappear, but rather it is replaced with an almost identical amount of helium. That means that even if every single hydrogen nucleus were to be used up through fusion, almost all of that "lost" hydrogen mass would still remain in the form of the helium nuclei that were generated by that fusion reaction. And that outcome would be exactly the same regardless of whether it had taken billions of years or it had happened instantaneously. The rate of fusion has absolutely no effect on this effect.

Why is that? Let's do the math yet again:

Consider the end result of hydrogen fusion: four hydrogen nuclei fuse to form one helium nucleus. We would expect that the atomic weight of a helium nucleus (its mass) would equal that of four hydrogen nuclei, but it doesn't. Instead, it is less. Some of the mass has been lost! Take the difference between the atomic weights of four hydrogen nuclei and that of one helium nucleus and you get the amount of mass that was lost as energy (and as a couple neutrinos, but they're practically devoid of mass so they don't really count).

Doing the math:

Hydrogen:
      Standard atomic weight 1.008

Helium:
      Standard atomic weight 4.002602

4H -> He
4 × 1.008 = 4.032

    4.032000
  - 4.002602
  ----------
    0.029398 
0.029398 / 4.032000 = 0.729 %

So fusing hydrogen into helium results in 0.729% (normally rounded off to 0.7%) of the original mass being lost as energy and 99.27% (normally rounded off to 99.3%) of the original mass remaining as helium (AKA "helium ash" when referring to hydrogen fusion as "burning hydrogen"). That will hold true regardless of how slowly or rapidly that fusion reaction runs. If the fusion reaction were to run 100 billion times faster, all that you would accomplish would be to use up the hydrogen that much faster and the resultant mass loss could never be more than 0.729%.

For that matter, it could never be even that much. That ideal maximum mass loss would require two ideal conditions, only one of which might possibly be met (but not by the sun):

  1. At the start of the fusion reaction, the entire star would have to consist entirely of hydrogen. This would have been possible for Population I stars when there was basically nothing but hydrogen in existence, but not for our sun which started out about 71.1% hydrogen.
  2. Every single hydrogen nucleus would have to have been consumed by the fusion reaction. I.e., all the star's hydrogen would have to have been fused into helium.

The need for the first condition may not be completely clear; the creationist I presented it to was completely unable to understand it (but then he also could never understand that fusing hydrogen produces helium). Obviously, any percentage of the star's total mass that isn't hydrogen will not experience any mass loss due to hydrogen fusion. So if the star started out 75% hydrogen, then the most mass it could lose would be 0.7% of 75%, which is 0.525%. If instead the star started out 100% hydrogen, then the most mass it could lose would be 0.7% of 100%, which is 0.7%. IOW, the only way to achieve maximum mass loss would be if the star started out consisting entirely of hydrogen. In the case of our sun, which started out 71.1% hydrogen, that figure would be an absolutely maximum mass loss of 0.5%, but it could only lose about half that at most because the second condition is impossible.

To evaluate the second condition given above, consider that a fusion reaction has certain requirements of temperature, density, and pressure. Those requirements can only be met in the star's core, where half the star's mass is contained in only 1.5% of its volume (using our sun as the model). Thus, at most only half the star's hydrogen can be involved in the fusion reaction, resulting in a maximum mass loss of 0.35%, assuming the unrealistic conditions that the core starts out consisting of pure hydrogen and that all the hydrogen in the core gets used up.

For stars such as the sun which did not start out as pure hydrogen, that percentage gets reduced further by the tendency for gravity to pull heavier nuclei (ie, the non-hydrogen nuclei which in the sun are mostly helium but also include very small amounts of oxygen, carbon, iron, neon, nitrogen, silicon, magnesium, and sulfer) down into the core, so the core starts out been poorer in hydrogen than the star's upper layers. Still using the sun as an example, as a protostar it started out 71.1% hydrogen, but now after 5 billion years its photosphere is 74.9% hydrogen, a higher concentration of hydrogen than the sun had started out with, because much of the photosphere's pre-existing heavier atoms, mainly helium, settled into the core due to gravity. As a result, the sun's core would have started out 67.3% hydrogen and the most mass that we could expect the sun to lose through hydrogen fusion would be 0.2454%.

We just calculated that, with the sun's core, half the sun's mass, having started 67.3% hydrogen, the absolute maximum mass loss would be 0.2454%. As calculated even earlier in "Let's Do the Math!", the sun has already lost 0.03965755% of its total mass, but it's about half-way through its estimated normal life-time (ie, before it enters its red giant phase) so we should expect a final main-sequence mass loss to be twice that or about 0.08%, which is about one-third of that maximum loss of 0.2454%. But as more and more of the core becomes helium, it becomes more and more difficult for enough hydrogen nuclei to be in close enough proximity to each other in order to fuse. So that 0.2454% is an ideal maximum that could never be attained.

Now, let's see what effect that 0.2454% loss would have.


Like the table in a preceding section, the following table shows what effect these two maximum mass-loss percentages would have on the sun's mass and gravity and on the size of the earth's orbit. Unlike that previous table which used the current sun's mass and the current size of the earth's orbit as its reference point, this table's reference point is the mass of the sun and the size of the earth's orbit when the sun's fusion reaction started. In order to arrive at values for that reference point, I am using the values arrived at in the row of the previous table representing a rate of 5 million tons per second taken over a period of 5 billion years.

In the table below, these are what the rows represent:

Mass Loss Percentage of 0.2454%
This is the maximum possible percentage of mass loss that the sun could experience were all the hydrogen originally available for the fusion reaction (ie, the hydrogen in its core at the time the fusion reaction started) fused into helium. This mass loss percentage is independent of how long the fusion reaction takes or at what rate it runs. This mass loss percentage is also an ideal maximum possible percentage that could not possibly be attained for several practical reasons as will be discussed in a later section. Basically, this is the worst that the sun could do and here are the effects of that.

Mass Loss Percentage of 0.729%
That is the percentage of mass lost when four hydrogen nuclei fuse into one helium nucleus. Therefore, it is the percentage of the mass lost for all the hydrogen that has been consumed in hydrogen fusion. If a protostar consisted entirely of hydrogen and every single nucleus of hydrogen was fused into helium without any loss through solar wind, then and only then would it be the maximum possible mass loss percentage of such a star.

In short, this is the theoretical uppermost limit of the percentage of a star's mass that it could possibly lose through hydrogen fusion, which would be the only form of fusion a sun-like star would use while on the Main Sequence. Of course, for several more practical reasons as discussed above and below, it would be impossible for any star to actually experience this level of mass loss through fusion. Therefore, this line is included in the table to demonstrate that anything even remotely approaching the consequences of "the sun burning its fuel" would be completely impossible and that hence Hovind's claim is absolutely bogus.

These are what the table's columns represent:

Original Solar Mass in tonnes
This is an input value which is a starting point representing an original mass of the sun. For this value, we take the original mass value from the table above for 5 million tons per second over 5 billion years.

We use the same value in both rows of this table.

Percent Mass Lost
This is an input value which represents the absolute maximum percentage of mass loss due to the properties of hydrogen fusion.

Total Mass Lost in tonnes
This is derived by taking the percent mass lost percentage of the original solar mass. This value is then subtracted from the original solar mass to yield the new solar mass when all the available hydrogen has been used up.

New Solar Mass in tonnes
This is calculated by subtracting the total mass lost from the original mass of the sun. This value is then used to calculate the gravity ratio of the new sun.

The gravity of the New Sun Compared to the Original Sun's Gravity
This is the ratio of the gravity of the new sun to the sun's original gravity. IOW, this is how many times stronger the sun's final gravity was -- since it is less than 1, it will in fact be weaker. It is calculated by dividing the sun's new mass by its original mass.

According to Newton's Law of Universal Gravitation, the sun's gravity is directly proportional to its mass. Therefore, the ratio of the sun's new gravity to the its original gravity would equal the ratio of the sun's new and original masses.

This ratio will be used to calculate the effects of that lesser gravity on the earth's orbit.

The original size in miles of the earth's orbit about the sun
This is an input value taken from the table above for 5 million tons per second over 5 billion years. It is used to calculate the new orbital size.

The new size in miles of the earth's orbit about the new sun
This is calculated from the original orbital size and the gravity ratio. Since the average radius of the earth's orbit is inversely proportional to the sun's gravity, decreasing the sun's gravity m times increases the earth's orbit 1/m times. Therefore, I calculate this value by dividing the original size of the earth's orbit by how many times stronger (actually weaker since it's less than 1) the new sun's gravity would be.

How much the earth would drift out away from the new sun, in miles
This is simply the difference between the new and the original sizes of the earth's orbits. Its purpose is to show the effect that the new sun's lesser gravity would have on the earth's distance from the sun.

Please keep in mind that, since the earth's orbit is elliptical, the earth's distance from the varies throughout the year, being closest at one point and farthest out six months later. Given the earth's orbital eccentricity (0.0167086), the earth's distance from the sun varies from about 1.5 million miles closer in to 1.5 million miles farther out. That should give you some kind of context within which to evaluate the consequences of how much the earth would drift away from the new sun.

Figures and Effects for Maximum Possible Mass Loss (Independent of Loss Rates and Time)
Original Solar Mass
(tonnes)
Percent Loss
(%)
Total Mass Lost
(tonnes)
New Solar Mass
(tonnes)
New Gravity
(new ÷ original)
Original Earth Orbit
(million miles)
New Orbit
(million miles)
Drifted out by
(mi)
1.98933892×1027 0.2454 4.88183772×1024 1.98445709×1027 0.997546 92.919038 93.14762223 228,087
1.98933892×1027 0.729 1.45022807×1025 1.97483664×1027 0.99271 92.919038 93.60139211 682,354

As we can see, even when we lose the impossible-to-actually-obtain, absolute-maximum amounts of mass loss due to fusion over the main-sequence life of the sun, the effects are still minimal and insignificant. Keep in mind that since the sun has lost about 0.04% of its mass in half its lifetime, then its total expected loss should be twice that, or about 0.08%. Thus that maximum possible loss of 0.245% is three times greater than what we expect to actually happen and the actual effects would be correspondingly less than those given above.


To recapitulate:

  1. Running the sun at a much more rapid rate of fusion would no effect on the total amount of mass lost. Only 0.7% of the hydrogen mass being fused is lost as energy with the remaining 99.3% remaining in place as helium, the by-product of hydrogen fusion. That establishes an absolute maximum upper limit to the total amount of mass that could be lost due to hydrogen fusion regardless of how rapid the rate of fusion is. All that you would accomplish by running a faster fusion reaction would be to use up hydrogen all that faster, which is what we see in more massive (and hence much hotter) stars who are short-lived because they are burning up their hydrogen much more rapidly than the sun does.
  2. The sun cannot even begin to approach that absolute maximum upper limit:
    • Only hydrogen can fuse into helium through hydrogen fusion. But only about 71.1% of the sun's original mass was hydrogen, so only 0.5% of the sun's mass could possibly be lost through hydrogen fusion.
    • Only the hydrogen in the sun's core could be involved in fusion. Since the core contains half the sun's mass, only half the sun's original hydrogen at a maximum could be involved in the fusion reaction, reducing the maximum possible mass loss for the sun to 0.25%.
    • However, half the sun's original hydrogen did not make it into the core, since some of the hydrogen was displaced by heavier nuclei, mostly pre-existing helium. Hence, the core started out being about 67.3% hydrogen, giving us a maximum possible mass loss of 0.245%
    • Practically speaking, we could never expect to fuse all of the hydrogen in the core. As more and more of the core becomes helium, it becomes more and more difficult for enough hydrogen nuclei to be in close enough proximity to each other in order to fuse. That 0.245% is an ideal upper limit that could never be attained.
  3. The effects of that maximum mass loss taken over the lifetime of the sun would still have minimal effects on the sun's gravity and on the size of the earth's orbit.

Bottom line: there are very real limits to how much mass can be lost through fusion regardless of how fast the fusion reaction is. Running that reaction faster does not buy this claim any more mass loss, at least none that could ever make any difference.


How can we assume a constant rate of mass loss?

One word: hydrostatic equilibrium.

Quick review and overview:

  • The sun is powered by a thermonuclear reaction in its core which fuses hydrogen nuclei into helium nuclei while at the same time converting a very small part of its mass into an enormous amount of energy.
  • That thermonuclear reaction requires very high temperatures. It is also very sensitive to temperature, such that the hotter it is the faster the reaction will run, and the cooler it is the slower it will run.
  • The sun is very massive and is in a constant state of gravitational collapse.
  • A result of that gravitational collapse is an increase of pressure and temperature in the sun's core.
  • The thermonuclear reaction generates radiative energy which exerts enormous pressure outward towards the sun's surface.
  • A result of that outward pressure is to stop the gravitational collapse, causing the core to be cooler.
  • These two forces, gravitational collapse and radiative pressure, balance against each other in hydrostatic equilibrium.

One of the effects of this balance, this hydrostatic equilibrium, is that it regulates the rate of the fusion reaction. Being a thermonuclear reaction, it is very sensitive to temperature -- I had seen the equations once and recall that the reaction's rate is directly proportional to the temperature raised to the fourth power (T4) -- , speeding up significantly as it gets hotter and slowing down significantly as it gets cooler. So as gravitational collapse begins to dominate over radiative pressure, it heats up the core, which speeds up the reaction, which increases the radiative pressure, which begins to dominate over the gravitational collapse, which cools down the core, which slows down the reaction, which decreases the radiative pressure and allows the gravitational collapse to begin to dominiate, etc.

To describe that process more clearly:

  • As the sun collapses under its own gravity, the core heats up.
  • As the core heats up, the thermonuclear reaction speeds up.
  • As the thermonuclear reaction speeds up, the radiative pressure increases.
  • As the radiative pressure increases, it counters the gravitational collapse, which decreases.
  • As the gravitational collapse decreases, the core cools down.
  • As the core cools down, the thermonuclear reaction slows down.
  • As the thermonuclear reaction slows down, the radiative pressure decreases.
  • As the radiative pressure decreases, it no longer counters the gravitational collapse as much, so the gravitational collapse increases.
  • As the sun collapses under its own gravity, the core heats up.
  • Etc.

Thus the rate of fusion oscillates, but it does so about a constant average rate.

But wait! There's more!

In addition to gravitational contraction and radiative pressure, there is a third factor that affects the temperature of the core and hence the rate of the thermonuclear reaction: increasing amounts of helium in the core.

Of course, it is quite obvious that the amount of helium in the core would increase, since that is what the fusion reaction is producing and where. But that accumulation of helium has the effect of making the core hotter, which in turn speeds up the thermonuclear reaction over time, causing the sun's energy output and size to slowly increase over time.

I've heard two different reasons explaining how the accumulation of helium is increasing the temperature of the core:

  1. Helium is opaque to the gamma radiation produced by the reaction, which makes the helium hotter as it absorbs the energy and that makes the core hotter.

  2. The helium produced takes up less space than the original hydrogen, causing the core to shrink and become denser and hence hotter. According to Wikipedia:
    The Sun is gradually becoming hotter during its time on the main sequence, because the helium atoms in the core occupy less volume than the hydrogen atoms that were fused. The core is therefore shrinking, allowing the outer layers of the Sun to move closer to the centre and experience a stronger gravitational force, according to the inverse-square law. This stronger force increases the pressure on the core, which is resisted by a gradual increase in the rate at which fusion occurs. This process speeds up as the core gradually becomes denser. It is estimated that the Sun has become 30% brighter in the last 4.5 billion years. At present, it is increasing in brightness by about 1% every 100 million years.

Whatever the reason for the gradual heating up of the core, the sun's energy output is increasing over time, which means that it is presently at its brightest. That means that the rate at which it is presently losing mass due to fusion is the highest rate so far. Which means that in the past the rate of mass loss due to fusion was lower. Which means that extrapolating the current rate back over time results in an overestimation of total mass loss; the actual amount of mass lost due to fusion would actually be less. Since the overestimated amount of mass lost has been demonstrated to be insignificant, the actual amount of mass lost, being even less, would be even less significant.


Aren't there any other ways for the sun to lose mass?

Yes, there certainly are. It's just that they don't contribute enough to make much of a difference, just a small fraction of the mass lost through fusion.

The only other way I can think of for the sun to lose mass is by that mass being ejected from the surface of the sun. For that, there are basically two mechanisms, each with its own rates of mass loss:

1. solar wind
The total number of particles carried away from the Sun by the solar wind is about 1.3 × 1036 per second. Thus, the total mass loss each year is about 2 to 3 times 10-14 solar masses (2.0×10-14 to 3.0×10-14), or about one million tonnes per second. This is equivalent to losing a mass equal to the Earth every 150 million years. However, only about 0.01% of the Sun's total mass has been lost through the solar wind, a fraction of what has been lost through fusion as we've already established.

1 million tonnes per second is one-fifth to one-quarter of the loss due to fusion, so it does not contribute much. Some sources cite lower rates while a number of sources cite a slightly higher rate of 1.5 million tonnes per second. I will factor it into a couple scenarios later in this section.

You will doubtless encounter references to T Tauri wind, so-named because of the behavior of T Tauri stars which expell large amounts of matter in their solar wind. You will also doubtless hear that our sun had also gone through that T Tauri stage early in its life. That has nothing to do with our discussion, because the T Tauri wind is the result of the ignition of a protostar's fusion reaction, whereupon the matter falling into the protostar is being forced away, that matter constituting the T Tauri wind. This stage ends by the time the star arrives on the Main Sequence, that time marking the start of the star's life, and the star's mass at that time is considered to be its initial mass. Since the claim under discussion only pertains to the sun's time on the Main Sequence, the T Tauri wind is irrelevant and can be safely ignored.

2. Coronal mass ejection
A coronal mass ejection (CME) is an unusually large release of plasma from the solar corona. These are single events which are associated with other solar events such as solar flares. The average mass ejected by a CME is 1.6×109 tonnes, though that estimate is only a lower limit. The frequency of ejections depends on the phase of the solar cycle and varies from about one every fifth day near the solar minimum to 3.5 per day near the solar maximum, though those are also lower limits.

Since we don't really get an average rate of mass ejection, I'll do a worst-case approximation so that we can get a grip on an upper limit that will never actually be reached. First, I'll double the average mass ejected in a CME, since that is a lower limit, to 3.2×109 tonnes. The most frequent occurance of a CME is during a solar maximum with about 3.5 CMEs per day on average -- that's compared with one every five days during a solar minimum. OK, let's get a rate of mass lost per second by CMEs based on the assumption of 3.5 CMEs occurring every single day for billions of years:

3.5 CMEs per day × 3.2×109 tonnes / CME
         = 11.2×109 tonnes / day
         = (11.2×109 tonnes / day) × (1 day / 86,400 seconds)
         = (11.2×109 tonnes / day) × (1/(8.64×104) day/seconds)
         = (11.2/8.64×10(9-4) tonnes / day) × (1 day / 86,400 seconds)
         = 1.296296×105 tonnes / second
         = 129.6296×103 tonnes / second
         = 129,629.6 tonnes / second
         = 0.1296296 million tonnes / second
So as big and impressive as CMEs appear to be, the mass loss attributed to them is very small compared to the losses due to fusion. We just went out of our way to over-inflate that rate grossly and yet even that gross overinflation turned out to be puny, about 1/39th of the loss due to fusion and a fifth of the loss due to solar wind.

So what happens when we add these rates to the mass-loss rate due to fusion? We already looked at that in the section, Your analysis of Hovind's rate may be well and good for that particular rate, but what about other rates?. The effects are still minimal.

Let's create an unrealistically bad worst case: 5 million tonnes per second due to fusion, plus 2 million tonnes per second due to solar wind and CMEs for a total of 7 million tonnes per second. Since we've already done those calculations in that prior section, here's that table again:

Figures and Effects for Various Mass Loss Rates and Times
Time
(billions
of years)
Loss Rate
(tonnes/sec)
Percent Loss
(%)
Mass Lost
(tonnes)
Original Mass
(tonnes)
Gravity
(× Present)
Original Orbit
(million miles)
"Sucked in" by
(mi)
5 4 million 0.03172856 6.31138519×1023 1.98918114×1027 1.00031739 92.92640843 29,494
5 5 million 0.03965755 7.88923149×1023 1.98933892×1027 1.00039673 92.91903796 36,864
5 6 million 0.04758529 9.46707779×1023 1.98949671×1027 1.00047608 92.91166866 44,233
5 7 million 0.05551177 1.10449241×1024 1.98965449×1027 1.00055543 92.90430053 51,601
10 5 million 0.07928367 1.57784630×1024 1.99012785×1027 1.00079347 92.88220315 73,699

As we can clearly see, adding mass loss rates due to solar wind and CMEs has practically no effect on the results. Their contribution is minimal.

However, it did occur to me that Kent Hovind's "inflated" rate of mass loss might not be so inflated after all. We calculated the rate due to fusion to be 4.28 million tonnes. It is possible that the 5-million-tonne rate may have been arrived at by also factoring in losses due to solar wind. Hovind's response as to the source of his rate was that he had gotten it from textbooks ("Nearly any high school or college earth science book will give the sun's loss rate at about 5 million tons/sec."), which does not tell us what those books had said about what had gone into that figure. It is possible that we've been incorporating the effects of solar wind and CMEs from the start. But who's to know since Hovind ain't talkin'.


Exactly how would changing the mass of the sun affect its size?

For Further Reading on the "Shrinking Sun" Claim:
THE SUN IS SHRINKING
The creationist article containing the original claim by Dr. Russell Akridge, IMPACT No. 82, Institute for Creation Research, April 1980.

The Legend of the Shrinking Sun -- A Case Study Comparing Professional Science and "Creation Science" in Action
A definitive refutation of the claim written in 1986 by Howard J. van Till, Professor of Physics and Astronomy at Calvin College Grand Rapids, Michigan, and a Calvinist at the time of the writing.
From: Perspectives on Science and Christian Faith 38.3:164-174 (9/1986)

Answers in Genesis Is the Sun Shrinking?
By Dr. Danny R. Faulkner, 06 June 2016. Basically abandons the "shrinking sun" claim and accepts the standard model of how the sun shines while not committing to the conventional age of the sun. He is an astronomer and a young-earth creationist, basically a professional creationist.

TalkOrigins Young-earth "proof" #1: The sun is shrinking at 5 feet/hour which limits the earth-sun relationship to less than 5 million years.
From How Good Are Those Young-Earth Arguments? A Close Look at Dr. Hovind's List of Young-Earth Arguments and Other Claims by Dave Matson, 1994-2002.

TalkOrigins Solar FAQ: Shrinkage
By Sverker Johansson, Copyright © 1998-2003

How Creationism Taught Me Real Science 35 Shrinking Sun on YouTube
This is part of a series of videos by Tony Reed. I just found this one and I include it for two reasons:
  1. I feel that it does a good job of covering and refuting both the basic "shrinking sun" claim and the "solar mass loss" claim.
  2. The premise of Tony Reed's entire series of videos reflects my own experience, that I have learned so much about science by researching and refuting creationist claims, all of which I have found to be false.
The more learning the more life!
This question is both very interesting and very difficult to answer. There are so many factors that interact with each other in ways that can be difficult to calculate and would certainly be beyond my ability to calculate and beyond the ability of many readers to follow. Therefore, we will look at what the various factors are, what effects each one would have, and how they would interact with each other. If nothing else, we should be able to get some kind of feeling for what would be going on.

I will also introduce another creationist claim here, "The Shrinking Sun", a real favorite among creationists since 1980 despite its having been soundly refuted around the same time. Both forms of the mass-loss claim that I've seen are tied directly to the "shrinking sun" claim apparently in order to support that claim, though I've seen the "shrinking sun" claim standing alone more often with no mention of mass loss. My reason for introducing this other claim here is because it ties in with our investigation of the effects of mass loss on the size of the sun and provides us with the opportunity to investigate what kind of mass loss would be needed to support this other claim.

While Hovind's claim is mostly just hand-waving and doesn't give any specific figures outside of "5 million tons each second", I did find an older formulation that appears to date from around 1983, long before Hovind's ministry had started:

How big was the Sun 1 billion years ago?

The Sun loses 4 million tons of mass through fusion per second, and is shrinking by about 1% each century (5 feet per hour). This shrinking is responsible for a large amount of the energy that the Sun gives off.
That shrinkage rate was taken from the original claim,
THE SUN IS SHRINKING, which states that the sun's diameter is supposed to be shrinking by 5 feet per hour and hence the radius is decreasing by 2.5 feet per hour.

Among other things, in this section I plan to examine how much the sun's volume would need to change to support such a shrinkage rate for the sun's radius as well as how much mass loss would be needed to account for such a loss of volume. I plan to approach those questions from both directions:

  1. How much volume and mass would need to be lost to support the sun's radius shrinking by 2.5 feet per hour.
  2. How much the loss of the actual amount of mass would affect the sun's volume and radius.


Here are some of the basic facts that we will need to consider:

1. Volume and radius are not directly proportional to each other.

Basically, you cannot assume that doubling the volume would double the radius or anything close to that, 'cause t'ain't so.

The formula for the volume V of a sphere with a radius R is:

V = (4/3) × π × R3
That means that changing the radius R causes the volume V to change by the cube of R; eg, double the radius of a sphere and you increase its volume eight-fold (ie, by a factor of 23, which is 8). More exactly, the rate at which volume changes by radius (ie, the derivative dV/dR) would be:
dV/dR = 4π × R2
That tells you the rate at which changing the radius will cause the volume to change.

We could solve for the radius R to see what the radius would need to be for a given volume V (do please join in and do the algebra along with me):

R = cuberoot(3/(4π) × V)
     = cuberoot(3/(4π)) × cuberoot(V)
That means that changing the volume V causes the radius R to change by the cube root of V; eg, double the volume of a sphere and you increase its radius by the cube root of 2, which is about 1.26 -- IOW, not by very much.

Similarly, the rate at which the radius changes by volume (ie, the derivative dR/dV) would be:

dR/dV = (cuberoot(3/(4π)) / 3) × V-2/3
     = (cuberoot(3/(4π)) / 3) × 1 / cuberoot(V2)
That tells you the rate at which changing the radius will cause the volume to change.

2. Changes in mass affect volume directly and radius indirectly.

Objects have a property called density (ρ, the Greek letter rho), which is given by the formula:
ρ = m / V, where m is mass and V is volume
In physics, we were taught two systems of units using the metric system: centimeter-gram-second (cgs) for small-scale systems and meter-kilogram-second (MKS) for large-scale systems. In cgs, density is given as grams per cubic centimeter (g/cm3), which is equivalent to grams per milliliter (g/ml). In MKS, it is given as kilograms per cubic meter (kg/m3). Since the sun is a large-scale system, I will use kg/m3 here.

Later in this section, we will be looking at the changes in volume as we change mass while keeping density the same, as well as to determine how much mass is contained in a particular volume. Therefore, we want to solve that formula for the volume V and again for the mass m:

V = m / ρ
m = V × ρ
As you can plainly see, there is a direct relationship between mass and volume, but not between mass and radius. In order to work out that relationship, we will need to substitute the formula for volume for V:
m = ρ × V
     = ρ × (4/3) × π × R3
And things start getting messy, especially if we start taking derivatives again.

Of course, when we start figuring out how much mass has to be lost to account for various changes in volume and radius, we will need to know what the density of the sun is. That's where it starts to get complicated, because the sun's density all depends on where in the sun you're looking. And that's because of the next basic fact.

3. The sun is a giant sphere of compressible gas.

This is the basic fact that will give us the most difficulty. Adding mass to a ball of compressible gas is not at all like adding the same proportion of mass to a ball of clay. Double the mass of a ball of clay and you double its volume, but double the mass of a giant sphere of compressible gas and the increase in its volume is less than double because the effect of greater gravity is to compress it even more. But then that heats up the core more, causing the fusion reaction to burn faster which causes the star to expand and ... . Well, as you can see, we have a number of different effects working counter to each other, complicating matters greatly.

In this section, I will try to get around this problem by holding some factors constant so we can see how the outcome varies for each individual factor, somewhat like working with partial derivatives in calculus.

4. The sun has many different densities depending on where in the sun you look.

This is a direct consequence of the sun being a sphere of compressible gas. The deeper you go into the sun, the denser it becomes until you reach the core where the sun is the densest. This is somewhat like the earth's atmosphere where the air is thickest (densest) at the planet's surface and then gets thinner and thinner as you ascend to ever higher altitudes until you reach the top of the atmosphere which consists of occasional air molecules.

Basically, the major layers of the sun and their densities are, starting at the core and moving outwards:

  • Core -- 162,200 kg/m3 (12.4 times the density of the earth)
  • Radiative Zone -- from 20,000 kg/m3 out to 200 kg/m3
  • Convective Zone -- 200 kg/m3
  • Photosphere (the sun's surface) -- 2×10-4 kg/m3
  • Corona -- particle density around 1015 to 1016 particles per m3
For comparison, the density of air at sea level is about 1.2 kg/m3 and effectively goes to zero about 20 miles up, pretty close to the density of the sun's photosphere. The top of the photosphere is the visible surface of the sun.

By dividing the mass of the sun by its volume, we arrive at an average density of 1408 kg/m3.

5. The sun's dimensions and related figures:

Equatorial radius 695,700 km
109 × Earth's
Equatorial circumference 4.379×106 km
109 × Earth's
Flattening 9×10-6
Surface area 6.09×1012 km2
12,000 × Earth's
Volume 1.41×1018 km3
1.41×1027 m3
1,300,000 × Earth's
Mass (1.98855±0.00025)×1030 kg
333,000 × Earth's
Average density 1.408 g/cm3
1408 kg/m3
0.255 × Earth's
Center density 162.2 g/cm3
1.622×105 kg/m3
12.4 × Earth's
Photosphere density 2×10-4 kg/m3
1 astronomical unit (AU) 149,600,000 km
92,956,000 miles
4.8481×10-6 pc
1.5813×10-5 ly


First let's look at the basic problem of predicting what increasing or decreasing the mass of a star would do. And since we're trying to predict/retrodict what the ancient sun with greater mass would be like, we'll discuss the effects of increasing the sun's mass.

If we increase the mass of the sun then a number of different things will happen, some of which will cause its size to increase and some that will cause its size to decrease. What we need to figure out is what the net effect will be:

  1. Increasing a body's mass would increase its gravity. This is a key effect in the case of the sun, or in the case of any star for that matter.

  2. Increasing the mass of a non-compressible body would increase its volume and hence its size. Of course, that's assuming that its density would remain constant, a necessary condition for being non-compressible.

    However, the sun is a compressible body, which means that we cannot depend on its density remaining constant. If the sun's density is allowed to increase, then its size can actually decrease.

  3. So, when the sun's gravity is increased because its mass has increased, that greater gravity will cause the sun to compress into a smaller volume. This will cause its core temperature to increase, which will increase the rate of its fusion reaction.

  4. Increasing the rate of the fusion reaction in the core will increase the radiative pressure pushing outwards towards the surface. This will cause the size of the sun to increase.

  5. That increased radiative pressure will reduce the sun's density, which in turn will slow down the fusion reaction which would in turn reduce that radiative pressure which would allow gravity to compress the sun, increasing density and speeding up the reaction, ... etc, etc, etc. In other words, the sun would reach a point of hydrostatic equilibrium what would maintain the sun at a fairly constant size or at least fluctuating slightly about a constant average.

  6. However, the increased gravity and increased radiative pressure due to the increased mass would cause that constant size to be different. Whether that different size would be greater or less is the question.

So the size of the sun does not depend directly on its mass, but rather on what that mass causes to happen. The greater gravity wants to compress the sun more and make it smaller while the greater radiative pressure wants to expand it more and make it larger. Where does the balance lie?

Astrophysicists have studied those processes and developed models that we could use to predict the outcome. But to keep things simple, let's look at stars of different masses and see what effect that has on their sizes.

In reading the following table, please remember that the mass of a star determines many things about it including its temperature (and hence its color and spectral class) and how long it will last before using up its hydrogen fuel (the hotter it burns, the faster it burns and the sooner it runs out of fuel).

Also, a caveat: I had found this table about two decades ago and have lost any record of where I had gotten it from. However, researching the same information from other sources should yield very close to the same results.

In reading the table, remember that the units of most of the columns are based directly on the sun, as indicated by "(sun)". So the mass of a class B5 star would be 6.5 times that of the sun's mass, while its radius would be 3.8 times the sun's radius, and it would 600 times brighter than the sun.

Spectal
class
Mass
(sun)
Radius
(sun)
Luminosity
(sun)
Surface
temperature
(degrees K)
Life time
(Ma)
Relative
abundance
(in %)
W>40201.000.00050<1negligible
O53218600,0004010.00002
B0167.416,0002810 
B56.53.860015.51000.1
A03.22.5609.9500 
A52.11.7208.510001
F01.751.467.42000 
F51.251.236.640003
G01.061.11.3610,000 
G2 Sun1115.812,000 
G50.920.90.85.515,0009
K00.80.80.44.920,000 
K50.690.70.14.130,00014
M00.480.60.02 3.575,000 
M50.20.30.0012.8200,00073

This table shows how so many properties of a star depend on its mass. We see that the more massive a star is, the hotter it is and the brighter it shines. We also see that the more massive a star is, the shorter its lifespan, which only makes sense as discussed above, that the hotter and brighter a star is the faster it burns through its fuel. Or in other words, because of the star's greater gravity, it compresses and heats up the core more causing the fusion reaction to run so much faster, which results in far greater energy generation, etc. We also see that the more massive stars are much less abundant. The majority of the stars, 73%, are the red stars, class M, which also last the longest (200 billion years compared to our sun's expected 12 billion-year lifespan).

But what we really want to know is whether more massive stars are bigger and by how much. I think that intuition would have told us that they would be bigger and indeed they are as we can see on this table. However, they are not that much bigger. They certainly are not proportional. Doubling the mass (eg, A5) only results in a 1.7 increase in radius. Six times the mass (eg, B5) and the radius is only about 4 times greater. Yes, the more massive the star the larger its radius is, but the radius' growth lags behind that of the mass.

At this point we should revisit the original claim, which was that the ancient sun would have been so incredibly much larger and more massive. We already found that the sun's mass 5 billion years ago would have been about 1.00039673 times what it currently is. So how much larger would it have been? From the table, we see that the ancient sun's mass would lie between 1 and 1.06 for a G0 star and that the G0 star's radius is 1.1. Using the ancient art of interpolation (which was drilled into us in the 1960's in order for us to use log and trig tables, but which has since been killed off by scientific calculators), I estimate that the ancient sun's radius would have been 1.0006612167 times larger. Which would have been about 460 km greater. I have a feeling that the periodic oscillations in the sun's size are far larger than that.


But radius is not the only way to measure the sun's size. There's also volume. That table did not include volume, but I used the table's data to calculate the volumes of the stars in units of the radius of the sun. Then I divided all of those volumes by the sun's volume to get another column of the ratio of each star's volume to the sun's volume. And to top it off, I calculated the density of each star relative to the sun's average density.

Here is that table:

Spectal
class
Mass
(sun)
Radius
(sun)
Volume
(sun radius)
Volume
(sun)
Average
Density
(sun)
W>402033510.32168000< 0.005
O5321824429.024558320.00549
B0167.41697.3983405.2240.0395
B56.53.8229.847354.8720.118
A03.22.565.449815.6250.205
A52.11.720.57954.9130.427
F01.751.411.49402.7440.638
F51.251.27.23821.7280.723
G01.061.15.57531.3310.796
G2 Sun114.188811
G50.920.93.05360.7291.26
K00.80.82.14470.5121.56
K50.690.71.43680.3432.01
M00.480.60.90480.2162.22
M50.20.30.11310.0277.41

At first, it may seem that the increase in volume is following the increase in mass, but it really isn't. Rather, what we do see is an exponential increase in volume because volume increases by the cube of the radius, so a small change in the radius can cause a large change in the volume.

Now turn your attention to average density, which I calculated by dividing the star's mass (relative to the sun's mass) by its volume (relative to the sun's volume). The more massive the star is, the lower its average density. Now that's interesting. It appears that while the increased mass increases gravity, the subsequent increase that that causes in the rate of the core's fusion reaction results in much stronger radiative pressure pushing outwards. It would appear that in that hydrostatic equilibrium balancing gravitational collapse and radiative pressure, radiative pressure turns out to be the stronger force. The greater gravity from the increased mass results in far greater radiative pressure which balloons the volume of the star out so much that the star's overall density decreases.

I believe that this answers our questions about the size of the ancient sun; ie, what the sun was like 5 billion years ago. Using Kent Hovind's rate of mass loss, we determined that 5 billion years ago the ancient sun's mass would have been 1.00039673 times its current mass. Based on that ancient mass, we interpolated the ancient sun's radius to have been about 1.0006612167 times larger (ie, 460 km greater in 5 billion years (3.44×10-8 feet per hour) as opposed to creationists's claim of 2.5 feet per hour). That would have made the ancient sun's volume slightly greater, about 1.001985 times greater. That in turn would have made the ancient sun's average density slightly less, about 0.998415 times what it is now which would have been about 1405.7682 kg/m3.

Yet again, we find that the sun 5 billion years ago would have been only very slightly different in size than it currently is.


That last section only dealt with how the loss of mass would affect the sun's size, such that the sun would become smaller over time, but by a very low proportion of the mass lost. We found that the size of the sun is directly dependent on the sun's hydrostatic equilibrium and how the radiative pressure from the core's fusion reaction balances against gravitational collapse. Radiative pressure is directly dependent on how fast the fusion reaction is, which is directly dependent on the temperature of the core, which is caused by for the force of gravity compressing the core, which is caused by the sun's mass. We also found that the effects of radiative pressure seem to be greater than the force of gravity. The overall effect appears to be for the sun to be slowly shrinking over time, albeit at a vastly slower rate than creationists claim; ie, at about 3.44×10-8 feet per hour as opposed to creationists's claim of 2.5 feet per hour.

But gravitational collapse due to mass is not the only factor affecting the temperature of the core and hence the rate of the fusion reaction (and hence the amount of radiative pressure and hence the size of the sun). The accumulation of helium, the by-product of the fusion reaction, in the core is slowing increasing its temperature, as we have already discussed. This is causing a slow increase in radiative pressure unrelated to mass. At the same time, there's less mass to generate gravity and hence there's less gravity to counter the increase in radiative pressure. As a result, the sun is slowing growing over time with its radius increasing by about an inch a year.

So the ancient sun was actually smaller than the present-day sun is.


Now for the fun project: exploring the volume/mass-loss requirements of creationist claims. In this section, our goal will be to examine the sheer scales involved in dealing with solar volume and mass and therefore what volume and mass creationist claims would actually entail.

First, let's quickly review the relationship between mass, volume, and density:

Where m is mass, V is volume, and ρ (the Greek letter, rho) is density:
ρ = m / V

V = m / ρ

m = ρ×V

Also remember that in the metric system, density is often given as grams per cubic centimeter (g/cm3), which is equivalent to grams per milliliter (g/ml). It is also given as kilograms per cubic meter (kg/m3), which is what I will usually use here. However, in some sections below where we're dealing with mass in tonnes I will use units that I've invented (though Google reveals unit conversion pages that include it): metric tons per cubic kilometer (tonnes/km3).

Density can be a very handy tool. Have you ever wondered how the park guides know how much a particular boulder weighs? Did they ever put it on a scale to weigh it? No, nor did they ever need to. If they know the boulder's size (volume) and they know its density, then from that they can calculate its mass and hence its weight by using the formula above:

m = ρ×V
Similarly, if you need to know how much space will be taken up by a given mass of a given density, then you simply use the formula above:
V = m / ρ
And, of course, if you know the mass and the volume and need to calculate its density, then you simply use the formula above that defines density:
ρ = m / V

Now, there are a few simplifying assumptions that we are going to make here:

1. Assume that density remains constant; ie, that the sun is not compressible.

Yes, we had just gone through a whole discussion about how the sun is composed of compressible gas and about how changing the mass will, through a slightly complex chain of effects, affect both the sun's volume and density. Even though we know that it's not correct, let us assume that the sun is not compressible. The only purpose in doing so is to make the calculations easier and more accessible as we explore the enormity of solar mass and volume.

But considering how it takes a lot of mass to change the size of the sun appreciably, many times more than the total amount of mass lost so far in the sun's 5 billion years, the much smaller amounts that we will be talking about shouldn't really bring the sun's compressibility into play. IOW, this assumption shouldn't throw us off that much. Rather, it will be Assumption #3 that will do that.

2. Assume that mass loss is the only factor affecting changes in volume.

While the solar-mass-loss claim seems to always be used to support the "shrinking sun" claim, this page does not deal with that claim itself. However, I am using that claim's claimed "shrinkage rate" for the sun's diameter as being five feet per hour just as an actual example claim. My purpose in doing so is so that we can examine what the loss in volume would have to be and how much could the loss of solar mass contribute to that loss.

However, that claim's main "explanation" for that "shrinkage" is gravitational collapse. It assumes that the sun has not yet reached hydrodynamic equilibrium. A consequence of that belief is that a portion of the sun's radiant energy comes from that gravitational collapse through the Kelvin–Helmholtz mechanism. And a further consequence of that is that the mass lost would be much lower since a much lower proportion of the sun's energy output would be due to fusion.

Bottom line is that:

  1. The "shrinking sun" claim is false, as even some creationists will now admit (eg, Answers in Genesis, Is the Sun Shrinking?, astronomer Dr. Danny R. Faulkner, 06 June 2016). As such, their "explanation" of on-going gravitational collapse can safely be ignored.
  2. Trying to take into account volume change due to gravitational collapse would over-complicate our calculations unnecessarily.
  3. The sun is in a state of hydrodynamic equilibrium and hence its volume is fairly constant (though fluctuating slightly).
  4. Changes in the sun's volume are due to mass loss and to the gradual heating up of the core due to helium accumulation.
  5. The effects of the gradual heating up of the sun's core is very gradual and so has no bearing on our little exercise here.
So for our purposes here we're just going to assume that the only factor affecting changes in volume will be mass loss.

3. Assume that we can take that mass out of any region in the sun.

To quote a fundamentalist friend, "That is just plain wrong!" And it is indeed not correct. But I'm doing it here because the goal of this section is to get a feeling for the vast scope that we're dealing with.

Naturally, we would expect the volume lost due to fusion to be felt in the sun's core where that fusion reaction is taking place, therefore that volume loss would be in accordance with the much higher density at the sun's core. We would also expect the volume lost due to solar wind et al. to be felt at the sun's surface in the photosphere where the density is very much lower. And we will indeed examine that scenario.

But then we will examine the effects of mass loss on volume in various parts of the sun, just for fun and for our edification.

4. Assume Kent Hovind's rate of mass loss, but split it up appropriately.

Well, a little more than that. Above in Where does Hovind's "5 million tons every second" figure come from?, we found that the amount of mass lost per second due to hydrogen fusion is nearly 4.3 million tonnes. And in Aren't there any other ways for the sun to lose mass? we found that solar wind and coronal mass ejections (CMEs) could account for the loss of upwards to one million tonnes per second.

Therefore, I will start out by applying the 4.3 million tonne figure to the core, because that is where that mass is actually being lost, and the one million tonne figure to the photosphere, because that is where that mass is actually being lost. And then I'll combine them again and apply them to each region of the sun just to get some perspective.

Furthermore, since the "shrinking sun" rate for the sun's diameter was 5 feet per hour, we will work within a time frame of one hour. So, also assuming the mass-loss rates we had obtained in sections above (the sum of which was rounded down in Kent Hovind's mass-loss rate), the values we will be working with will be:

Claimed "rate of shrinkage" of Sun's radius 2.5 feet/hour
0.762 m/hour
7.62×10-4 km/hour
Sun's current radius 695,700 km
Sun's radius one hour from now as claimed 695699.999238 km
Sun's current volume 1.410440010854×1018 km3
Sun's volume one hour from now as claimed 1.410440006219×1018 km3
Sun's volume lost in one hour as claimed 4,634,563,584 km3
3.2859×10-07 %
Mass loss (total) 5.3 million tonnes/sec (5.3×106)
19.08 billion tonnes/hour (19.08×109)
Mass loss (due to fusion) 4.3 million tonnes/sec (4.3×106)
15.48 billion tonnes/hour (15.48×109)
Mass loss (solar wind) 1 million tonnes/sec (1×106)
3.6 billion tonnes/hour (3.6×109)
Average density 1.408 g/cm3
1.408×103 kg/m3
1.408×109 tonnes/km3
Core density 162.2 g/cm3
1.622×105 kg/m3
1.622×1011 tonnes/km3
Photosphere density 2×10-4 kg/m3
200 tonnes/km3

Now let's get started!


First, let's see what volumes would be lost in the core and in the photosphere by the two processes for mass loss: hydrogen fusion in the core and solar wind and CMEs in the photosphere. Remember that this is the most realistic scenario, barring the fact that we're not taking compressibility into account. We will employ the formula:

V = m / ρ

Now let's see what the effects on that mass loss would be on the sun's volume:

  • Volume loss at the sun's core due to fusion
  • The sun's fusion reaction occurs in the sun's core, whose density is 1.622×1011 tonnes/km3. Our calculated rate of mass loss due to fusion is 4.3×106 tonnes/sec (4.3 million), which works out to be 15.48×109 tonnes/hour (15.48 billion in the USA). Applying our formula, that would mean that a volume of 0.095437731196 km3 was lost in one hour in the core.

    That's less than one-tenth of a cubic kilometer, about 1/48,561,124,892 (one 48-trillionth) of the required hourly volume loss. IOW, practically no volume loss experienced.

  • Volume loss at the sun's surface due to solar wind et al.
  • Things work out a bit differently in the photosphere, thanks to the density being much less: 200 tonnes/km3. At a rate of one million tonnes per second, solar wind et al. result in a loss of 3.6×109 tonnes/hour (3.6 billion). Applying our formula, that would mean that a volume of 18 million km3 was lost in one hour from the sun's surface.

    That's a much healthier looking slice, but will it be enough?

  • Combined volume loss due to both fusion and solar wind (et al.)
  • The volume loss due to fusion, less than one-tenth cubic km, is so small that it contributes virtually nothing to the volume loss due to solar wind et al., 18 million km3, and would get dropped by many calculators. But here it is nonetheless: 18,000,000.0954 km3.

    So how does that compare to the loss of volume expected from the claimed radius shrinkage of 2.5 feet per hour? That came to 4,634,563,584 km3, which is about 257.475 times greater than 18,000,000.0954 (BTW, the effects of adding the miniscule volume loss in the core just get lost in rounding off). That falls far short of what the "shrinking sun" claim would need.

    We divided the rate of mass loss into different rates for different regions of the sun with different densities in order to account for different processes for mass loss. That is to say that a total rate of 5.3 million tonnes per second was divided into 4.3 million tonnes per second for the core, which is where loss due to hydrogen fusion occurs, and one million tonnes per second for the photosphere, which is where loss due to solar wind, coronal mass ejections (CMEs), et al. occur.

    Our results do not come anywhere close to what they would need to be if they were to offer any support for creationist claims about the sun shrinking. The enormous size of the sun and the enormous amount of volume that we are trying to account for (4,634,563,584 km3) are just too great.


    Now what would happen if we take the entire mass loss and apply it to the densities of various parts of the sun, including the sun's average density? I'll even be generous and add the two rates together rather than going with Hovind's lower rate. So we'll use the rate of 5.3×106 tonnes/sec (5.3 million) which yields an hourly rate of 19.08×109 tonnes/hour (19.08 billion). Now let's apply that to the different densities:

  • Average Density: 1.408×109 tonnes/km3
  • Using the sun's average density, a mass loss of 5.3 tonnes would result in a volume loss of 13.55 km3. That is 1/342,034,213 of the required hourly volume loss of 4,634,563,584 km3. That falls very far short.

  • Core Density: 1.622×1011 tonnes/km3
  • The results are far worse when we apply the mass loss to the core density. Using the sun's core density, a mass loss of 5.3 tonnes would result in a volume loss of 0.1176 km3. That is 1/39,398,648,497 of the required hourly volume loss of 4,634,563,584 km3.

  • Photosphere Density: 200 tonnes/km3
  • The best chance this claimed volume loss had is with the lowest-density region, the photosphere. Using the density of the sun's photosphere, a mass loss of 5.3 tonnes would result in a volume loss of 95.4×106 km3 (95.4 million km3). However, that is still only 1/48 of the required hourly volume loss of 4,634,563,584 km3. Still no cigar, not even close.

    This time we took the total rate of mass loss and applied it to three different densities even though it makes no practical sense to do so. What we found in each case was that the resultant volume loss still fell far short of what the claim would require.


    Now let's take the opposite approach. We know what volume the claim needs for the sun to lose in one hour's time, so how much mass would need to be lost? To calculate that, we will use this formula:

    m = ρ×V

    Given that a shrinkage of the sun's diameter by 5 feet per hour, that would result in the sun's volume decreasing by 4,634,563,584 km3 in one hour. We also use our modified Hovind rate of mass loss of 5.3 million tonnes/second which is greater than his own rate (5 million tonnes per second) and which translates to an hourly rate of 19.08 billion tonnes/hour (19.08×109).

    Now let's see what the various densities will yield:

  • Average Density: 1.408×109 tonnes/km3
  • In order to lose 4,634,563,584 km3 in volume at the sun's average density, we'd have to lose a mass of 6.53×1018 tonnes in one hour. That is 342 million times more than the actual mass-loss rate of 19.08 million tonnes per hour. At the actual rate of 19.08 million tonnes per hour, it would take us 39,016 years to lose enough mass to yield that required hourly volume loss of 4,634,563,584 km3. Complete failure to deliver.

  • Core Density: 1.622×1011 tonnes/km3
  • Of course, using the core density yields far worse results. In order to lose 4,634,563,584 km3 in volume in one hour at the sun's core density, we'd have to lose a mass of 7.52×1020 tonnes in one hour. That is 39 billion (109) times more than the actual mass-loss rate of 19.08 million tonnes per hour. At the actual rate of 19.08 million tonnes per hour, it would take us 4.5 million years to lose enough mass to yield that required hourly volume loss of 4,634,563,584 km3. Abysmal failure.

  • Photosphere Density: 200 tonnes/km3
  • Again, our best chances are with the region that has the lowest density, the phososphere, but even this will let us down. In order to lose 4,634,563,584 km3 in volume in one hour at the density of the sun's photosphere, we'd have to lose a mass of 926.9×109 tonnes in one hour. That is 48.58 times more than the actual mass-loss rate of 19.08 million tonnes per hour. At the actual rate of 19.08 million tonnes per hour, it would take us 48.6 hours to lose enough mass to yield that required hourly volume loss of 4,634,563,584 km3. Again, not even close.

    This time we applied the amount of volume loss that the claim requires, 4,634,563,584 km3, and applied it to three different densities to see how much mass loss that would require. In each case, we found the necessary amount of mass loss to vastly exceed the actual amount lost. Yet again, we fail to find any support for the claim.


    Finally, let's look at the effect that the current rate of mass loss would have on the radius of the sun. We will do this by taking the formula for volume and solving it for the radius, as we had done above:

    V = (4/3) × π × R3

    R3 = V / ((4/3) × π)

    R3 = 3V / 4π

    R = cuberoot(3V / 4π)

    Next we need a formula for determining the change in the radius (ΔR) for a given change in volume (ΔV). However, trying to approach the problem algebraically turned out to be difficult, because our ΔR not only depends on the ΔV, but it also depends on the original radius, R0. Plus, ΔR did not want to factor out neatly to one side.

    This is the approach I came up with:

    1. We started with an original radius, R0, which we used to calculate the original volume, V0.

    V0 = (4/3) × π × R03

    2. We subtract the volume lost, ΔV, from V0 to calculate the new volume, V1.

    V1 = V0 - ΔV

    3. We then use V1 to calculate the new radius, R1.

    R1 = cuberoot(3V1 / 4π)

    4. We finally subtract R1 from R0 to obtain ΔR.

    ΔR = R0 - R1

    ...And Bob's your uncle. (ie, QEF)

    OK, we have the procedure and we have a batch of ΔV's from a previous section, so let's turn to! As you will recall, those ΔV's are the volumes lost by applying the mass lost in one hour, 19.08×109 tonnes/hour (19.08 billion), to different densities.

    Here is a table containing the ΔV's and their corresponding ΔR's:

    Density
    Type
    Density
    (tonnes/km3)
    Original Radius
    (km)
    ΔV
    (km3)
    New Radius
    (km)
    ΔR
    (km)
    Average 1.408×109 695700 13.55 695699.9999999990 0 (effectively)
    Core 1.622×1011 695700 0.1176 695699.9999999990 0 (effectively)
    Photosphere 200 695700 95.4×106 695699.999984 15.6858×10-6
    (15.6858 millimeters)

    It seems odd that the average and core density calculations yielded the same new radius. I think that the difference between the two were so small that it disappeared from Excel's floating-point operations; that is a common problem with computer floating-point operations, that the floating-point format has a set limit on its precision, on the detail in which the quantity is expressed in terms of the number of digits that are used.

    Whatever the cause, it does not change what we do discover, which is that the loss of volume due to the loss of mass per hour is so miniscule as to have virtually no effect on the sun's radius.


    OK, I think that we have discussed the subject as thoroughly as possible. And every approach we take and every which way we look at it, Hovind's solar-mass-loss claim is completely bogus.

    As I said in the beginning, if you think there's something that I haven't mentioned or discussed but I should have, then do please by all means tell me about it through my "Contact me" link. And if you have any questions or objections to anything on this page, then again do please by all means tell me about it through my "Contact me" link.


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    First uploaded on 2002 May 20.
    Updated on 2017 April 18.