# [stars] Nuclear Fuel usage rate

1. Sep 8, 2005

### vincentm

At which rate do Stars burn there fuel, I know there are different stars (giants,dwarfs etc...)

For instance i read that our sun fuses 655million tons of Hydrogen into 650 million tons of Helium. The other 5 million is converted into 400 million watts of energy in the process. How did they get this figure for our star. And what is the rate for others, and how do they get the rate(s) for those stars?

2. Sep 8, 2005

### Garth

Luminosity (power) of Sun = 3.8 1033 ergs/sec ~4 1023 kW

Mass required to be totally converted into energy per second = E/c2

Solar conversion mass/sec ~ 4 1033/1021 ~ 4 1012 gms/sec
~ 4 million tonnes/second

Garth

3. Sep 8, 2005

### Chronos

The sun converts about 600 million tons of hydrogen to 596 million tons of helium every second [the e/c^2 equivalent of 4 million tons of mass to energy every second]:

http://www.squ1.com/index.php?http://www.squ1.com/solar/the-sun.html
http://www.solarviews.com/eng/sun.htm

The basic way of computing this is to measure the average energy of sunlight striking the surface of the earth and factoring in the distance of earth to the sun. That allows you to estimate the energy output per square unit at the surface of the sun.

Last edited: Sep 8, 2005
4. Sep 8, 2005

### SpaceTiger

Staff Emeritus
The reason we know how much hydrogen is being burned at the center is that we believe the sun to be in approximate equilibrium. To put it another way, we expect that the amount of energy lost per unit time (by radiation --> the luminosity) should equal the amount of energy generated per unit time (by nuclear fusion). If this weren't the case, the temperature and physical size of the sun would be changing rapidly (by cosmic standards) with time.

In reality, the sun can't be in exact equilibrium because its chemical composition is changing; that is, hydrogen is being converted to helium. As a result, there is a slight change in its size and temperature with time, but it's very slow, having changed its size by only about 20% in its lifetime.

Last edited: Sep 9, 2005
5. Sep 8, 2005

### Staff: Mentor

Putting the mass consumption in perspective - it is in quasi-equilibrium, almost but not quite -

1.9891x1030 kg (~2x1030 kg)

as compared to a consumption rate of hydrogen - 6x108 tons (English or metric? - I don't have time to do the math at the moment)

and - http://hyperphysics.phy-astr.gsu.edu/hbase/solar/sun.html#c1

6. Sep 8, 2005

### Garth

Total solar mass 2x1030 kg being used up at 6 x1011 kg/sec will last ~ 3x1018 secs = 1011 years .
Actually the Sun will go Red Giant in about a tenth of this time, as only the core is available for fuel, so the total lifetime of the solar system as we know it will be 1010 years and the present age is 5x109 years, so we are half way through and have a little way to go!!

Garth

7. Sep 8, 2005

### vincentm

well, wow,Thanks guys. My maths classes won't be starting until the end of this month and i have lost all skills in algebra, so these equations are bit, out there for me. But i'm very sure this is the best way to explain these answers to me, i appreciate it.

8. Sep 8, 2005

### Garth

For other stars you simply exchange the Sun's mass and luminosity for that of the star in question. Note: large stars that convect deep down onto the core will use a greater percentage of their overall mass as fuel and therefore last somewhat longer than otherwise. As it is, larger stars are much more luminous, and therefore have shorter lifetimes, than our Sun. (Thank goodness our Sun isn't larger!)

Garth

Last edited: Sep 8, 2005
9. Sep 8, 2005

### vincentm

One more question, how is it, in star birth (or when once a star is "born") that it has so much hydrogen to burn? I do know that the Helium once it has been converted from hydrogen (because it is done in such high numbers) that this helps fight the inward pull of gravity from the core of the star? why does the core have such a gravitational force? Forgive me, im just trying to figure out how stars work. I'm currently reading Joseph Silk's book on the big bang theory and i'm at the part of star formation. but posting here helps as well.

ok that was more than one more question...

10. Sep 8, 2005

### Garth

The 'cosmic mix', the recipe of relative abundances for the average present day content of the universe is, ~ 3/4 hydrogen, 1/4 helium and 2% everything else. You can play with the numbers a little but that is basically it. Of the 2% (the Earth & us!) the most common elements are Oxygen, Carbon and Nitrogen (about 1% of total) then Neon and then Iron and Silicon, (the Earth) and then the rest. That is where the Hydrogen came from - it was there is the first place and was the major constituent out of which the Sun was formed. Where did it all come from? When you do the nucleo-synthesis equations for the Big Bang you find it creates 3/4 hydrogen 1/4 helium and very little of anything else, it came from the BB!
Asking questions is how you learn...
The gravitational force is so strong because the mass is so concentrated. Stars are fighting a balance between the immense pressures of dense plasma at a temperature of about 13,000,0000K and a gravitational vice that is threatening to squeeze them out of existence, literally into a black hole. What is it that prevents this collapse? The answer is the heat energy created by the nuclear fusion reactor in the stellar core. Once hydrogen is used up then the core contracts until helium fuses into beryllium and the other elements. Once they are used up - the end of the line being Iron then the star contracts into either a white dwarf, (up to 1.4 solar masses), or a neutron star (up to 2 ~3 solar masses) or a black hole.

I hope this helps, I expect you have just read all that in Silk's book!

Garth

Last edited: Sep 9, 2005
11. Sep 8, 2005

### vincentm

Thanks Garth, that helped alot.

12. Sep 8, 2005

### Orion1

Anyone interested in demonstating a calculation in how much more massive the sun would have to be in order to have reached 'Helium Flash' or the 'Red Giant' phase already?

13. Sep 9, 2005

### Garth

I tried to post the relevant equations in tex but it was all screwed up, nevertheless, the result is (and you can find the equations in any good undergrad astrophysics text book such as Carroll)
M = 1.31Msolar

Garth.

Last edited: Sep 9, 2005
14. Sep 10, 2005

### Chronos

Garth is well versed in these matters. He has my respect. Oh, I also agree with his comments [despite minor technical issues].

15. Sep 10, 2005

### Orion1

Solar Solution...

Mass-Luminosity relation:
$$\frac{t_1}{t_{\odot}} = \frac{m_1 L_{\odot}}{m_{\odot} L_1} = \frac{m_1}{m_1^{3.5}} = \frac{1}{m_1^{2.5}}$$

$$\frac{t_1}{t_\odot} = \frac{1}{m_1^{2.5}}$$

$$\boxed{m_s = \left( \frac{t_{\odot}}{t_1} \right)^{\frac{1}{2.5}} m_{\odot}}$$

$$t_{\odot} = 1 \cdot 10^{10} \; \text{years}$$ - Sol's lifetime
$$t_1 = 4.56 \cdot 10^9 \; \text{years}$$ - Sol's current age

$$\boxed{m_s = 1.369 \cdot m_{\odot}}$$

Last edited: Sep 10, 2005
16. Sep 10, 2005

### Garth

I worked it out for a star of just half the Sun's lifetime, exact estimates of our Sun's expected lifetime should be taken with caution.
Garth

17. Sep 10, 2005

### Orion1

Should 'Sol's current age', also be taken with equal caution?

18. Sep 11, 2005

### Garth

Well, your figure was the acepted age of the Earth from the age of the oldest meteorites and isotope ages of the oldest rocks - but those rocks are not the originals.
"Astrophysical Quantities" gives the Earth's age as 4.55 +/- 0.05 Gyr.
It gives the Sun's age simply as 5 Gyr. - a little older than the Earth. Solar models will also give an approximate age from the Sun's position across the Main Sequence line on the H-R diagram, but that also depends on the Sun's initial composition.

I think all we can be confident about is the first significant figure.

Garth

Last edited: Sep 11, 2005
19. Sep 11, 2005

### Chronos

Garth is being the consumate scientist allowing for the full error bars. The age of the earth is tightly constrained by a number of parameters [especially radioactive decay.] It is very logical to guess the sun is slightly older than earth, but not by more than about 10% [another fairly tight constraint].

20. Sep 11, 2005

### SpaceTiger

Staff Emeritus
Just a small thing -- iron is only the end of the line for massive stars. Stars like our sun will end up as white dwarfs composed mainly of carbon, nitrogen, and oxygen.