# How do we know how much hydrogen the sun has?

1. Dec 14, 2006

### ranger

I've been hearing these talks that the sun will run out of hydrogen in 4.5 to 5 billion years from now. My question is, how did we arrive at this estimate. Is it based on the mass or something? It would be good if you can show me the mathematical calculations.

--thanks.

2. Dec 15, 2006

### marcus

this is not a cosmology question, it belongs more in general astronomy, or in astrophysics (the physics of stars)----but not to worry, ranger. the mods can easily move this thread into the appropriate subforum.

you are right that estimates of the remaining lifetime of the sun are based on mass.

we can easily tell the mass of the sun---it is about 2.0E30 kilograms
is it OK to write 2.0E30 instead of 2.0 x 1030?

and we can easily tell the wattage of the sun---it is about 3.8E26 watts.

we can tell the chemical make-up of the sun's outer layers by the spectral colors (different elements make different spectral lines) and the make-up is around 71 percent H and 26.5 percent He.

to a good approximation that percentage mix of H and He would also have been the ORIGINAL percentage mix the sun had when it condensed from gas.

I won't try to give you a complete answer. There are plenty of experts around who can do that. But I will just give a few hints for starters. The terminal event we are usually talking about is the RED GIANT stage which happens when the CORE (the central 10 percent or so, where it is hot and dense enough for fusion to occur) becomes DEPLETED OF HYDROGEN, so that the core no longer primarily fuses hydrogen and becomes crushed to a higher density and pressure where it starts to fuse HELIUM. this helium-fusing stage is associated with the enormous expansion of the star, forming what is called a "red giant". A star keeps doing stuff for millions of years after red giant, but that's the end as far as we are concerned because it doesnt support life on the inner planets.

So the question becomes, at the rate the sun is putting out energy (3.8E26 watts) how fast is it using up the hydrogen in its core? and how soon does the core become so depleted of hydrogen that it has to start fusing helium?

just as interesting trivia, the temperature in the core is 15 million kelvin,
and the density is 160 times that of water-----those are good conditions for fusion.

at the SURFACE of the sun it is no more than about 6000 kelvin, which is nothing compared with 15 million down in the core. Fusion is not going to happen except where it is really hot (the central 10 percent or so).

the sun as a whole is not going to "run out" of hydrogen, the outer layers will still be rich in hydrogen even when it goes red giant and expands to roast or engulf the inner planets.

Good luck, keep asking questions, you will probably get someone with expertise to provide formulas and stuff

Last edited: Dec 15, 2006
3. Dec 15, 2006

### ranger

I see that you mentioned the wattage of the sun several times. How did you get this? I'm assuming that the surface temperature and the area influence this? You also mentioned this figure, 3.8E26 for the wattage. What unit of time is it, mayb output per second?

thanks again.

4. Dec 16, 2006

### Staff: Mentor

You can measure the wattage directly with a solar cell: Divide the wattage you get from the cell by the cell's overall efficiency and multiply by the area of a sphere the size of earth's orbit (not sure how much the atmosphere absorbs, but it'll get you a good start. That should get you reasonably close. Or you can use the black-body radiation equation to calculate it.

And watts is a time-based unit: J/s

Last edited: Dec 16, 2006