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Hermes
2006-Jul-18, 04:03 AM
Given:

Earth mass = 5.976 x 10^24 kg.

Sun mass = 1.989 x 10^30 kg = approx 332,831 earth masses

The sun converts 4.26 million tonnes of mass to energy every second. Therefore over the course of 4.5 billion years it has shed
4,260,000*3600*24*365.25*4,500,000,000 tonnes = 604.959192*10^24kg
which is approx 101 earth masses and approx 0.03 solar masses.

My question is: If so little solar mass has been shed in 4.5Billion years through nuclear burning and presuming that CME's etc are negligible compared to this process, how is it that the projected lifetime of the sun on the main sequence before ultimately becoming a red giant and white dwarf is only another 5 billion years.

Unless something takes of exponentially in the future, I cannot reason it out.
Also, it would seem that with such a small percentage of the hydrogen converted at present, doubling this assuming no exponential runaway would indicate that in about 5 billion years the sun will still only have converted less than 1 percent of its mass to energy, yet it will be be off the main sequence and on its way to the knackers yard.

Have I made an error?. Is there some physical process that can explain the seeming sensitivity between small change in mass yet large change in solar character?.

Romanus
2006-Jul-18, 04:29 AM
1.) Don't look at the mass conversion; look at the Sun's *luminosity*, which is a direct result of that mass conversion. To sustain the Sun's energy output requires that level of fusion burning.

2.) Only the hydrogen in the Sun's core fuses (for now), and only a small amount of that; stellar fusion is woefully inefficient. But, it works.

3.) The energy conversion is only a small part of the equation; much more important is the mass of hydrogen itself that must be fused to helium, not the mass defect of the reaction. That will indeed consume the Sun's hydrogen over the main sequence, not the E=mc^2 reaction in isolation.

Ronald Brak
2006-Jul-18, 04:48 AM
I was going to mention what Romanus put in his third point. When hydrogen is fused into helium only a tiny amount of mass is lost as energy (4%?). So for each unit of mass turned into energy you get a heapa lota hydrogen converted to helium.

kzb
2006-Jul-18, 11:50 AM
The mass loss in fusing hydrogen to helium is less than about 0.7%, if I remember correctly, not 4%.

Anyway, I think there's a mistake in your calculation, there is a factor of 1000 to convert tonne to kg which you have not included. Now, I'm assuming you've got the mass of the sun correct -and in the correct units- at 1.989 E+30 kg.

That being the case, I get the fusion mass loss to 0.03% (that's PERCENT, not a proportion) to date, assuming a constant rate (which BTW is probably not justified as the sun has been constantly heating up over time).

Now I don't have the proportion of hydrogen in the sun as it was, or is now,to hand, so I can't calculate exactly what proportion of its hydrogen it has "burned". But since the sun is mainly hydrogen, clearly it's only a small fraction of the total hydrogen, perhaps very approximately 1/15.

I think the life-time descrepancy is due to the fact that only hydrogen in the CORE is fused, at least while the sun is on the main sequence, and also there will be a lower cut-off in hydrogen core concentration, below which the sun is not sustainable in its present form. The proportion of hydrogen is decreasing and that of helium is increasing over time. So at some point it will be choking on its own ash.

Tim Thompson
2006-Jul-18, 02:38 PM
My question is: If so little solar mass has been shed in 4.5 Billion years through nuclear burning and presuming that CME's etc are negligible compared to this process, how is it that the projected lifetime of the sun on the main sequence before ultimately becoming a red giant and white dwarf is only another 5 billion years.
It's because the process you are looking at has nothing to do with solar (or stellar) evolution. You have to look at the detailed physics of the stellar interior.

For the sun (or any sun like star), transport of material in the deep interior of the star is very inefficient. So, as hydrogen is fused into helium in the core, no fresh hydrogen comes in to take its place. As hydrogen gets used up & replaced by helium, the hydrogen fusion rate naturally goes down, which means that internal heat production goes down, which means that the core contracts under its own weight, and the pressure of all that stuff above it. Eventually, hydrogen fusion in the core essentially stops, because there is no more hydrogen left to fuse. So now we have a star with a small, dense, helium core.

But around the outside of that core, in a spherical shell, it is hot enough for hydrogen fusion. So now we get hydrogen fusion not in the core, but in a shell around the core. And the core is far hotter than it was before. That greatly changes the thermal stability of the stellar interior, and forces the star to expand into a red giant. Helium ash from the hydrogen fusing shell rains down on the helium core, making it more massive, and heating it up. If the core temperature reaches about 100,000,000 Kelvins, then the helium will very suddenly start fusing, in an event known as the helium flash.

The helium flash forces the core to rapidly expand, which cools the hydrogen fusing shell and shuts off hydrogen fusion there. Now we have helium fusion in the core, no hydrogen fusion, and the star shrinks again. This process also instigates ferocious stellar winds, which will blow away about 1/2 of the suns mass. The blown away mass will become a planetary nebula, and the 1/2 solar mass that's left behind will become a helium/carbon white dwarf (when helium fuses, it fuses into carbon).

For more massive stars the process goes through a few repeats and winds up with a more massive white dwarf, or in the case of a star more than about 8 or so solar masses, a supernova. A star about 5 solar masses will blow away about 80% of its mass as stellar winds, which become the planetary nebula.

That's the short story. The whole story is too long & complicated to put here. Try my pages on Solar Fusion & Neutrinos (http://www.tim-thompson.com/fusion.html), or maybe even better, The Hertzsprung Russell Diagram and Stellar Evolution (http://www.tim-thompson.com/hr.html). They link to other pages, and suggest books. Hopefully at least most of the links are still good, I have not checked lately.

Hermes
2006-Jul-19, 12:17 AM
[QUOTE=kzb]
Anyway, I think there's a mistake in your calculation, there is a factor of 1000 to convert tonne to kg which you have not included. QUOTE]

I did include this, note I I express tonnes on left and Kgs on the right. I added 3 zeroes.

I like Tim Thompsons explanation. Because even though the Sun is still 75% hydrogen it would seem to have heaps left over 5 billion years from now to continue fusion unless the core was not refreshing.

Cheers

kzb
2006-Jul-19, 05:49 PM
I'm agreeing with Tim Thompson's explanation, but he put it so much better than me. As for the calc, I agree you would have got the right answer, if only you'd put 0.03 PERCENT of the solar mass, and not "0.03 solar masses".

I got to thinking, IF stars did burn ALL their hydrogen before going bang, we wouldn't be here. Most of the first generation stars would still be around, and the ones that had expired wouldn't have contributed any hydrogen for the second generation stars to burn.

Earth couldn't have formed around a first gen star as there aren't enough metals (that's astronomers' metals I'm referring to).

sol88
2006-Jul-21, 01:42 AM
Hi hermes.

After reading Tim's excellent site regarding stellar evolution, you may like to have a read of the site that he is debunking HERE (http://www.electric-cosmos.org/sun.htm)

You can then make your own mind reagarding Nuclear burning and solar lifetime/s.

makes for a very interesting point of view!

Sol