Homework help very

1. Apr 8, 2008

hobobobo

[SOLVED] Homework help very urgent!!!! plz help

The potential energy of an object due to its own gravity is of order
Potential Energy ~
GM2
r
where M is the body's mass and r is its radius. There is a factor in this equation that depends on the density distribution within the
object (e.g. 0.6 for a uniform sphere) - but for rough calculations we can ignore that.
Using preceeding approximation.

So I need to calculate the potential energy stored in the self-gravity of the sun, assuming a solar radius of
6.96μ108m and solar mass of 2.0μ1030kg.

I also need to calculate the total power radiated by the sun assuming the temperature of the stellar
photosphere is a 6000° K blackbody and estimate the lifetime of the sun if its energy source was purely locked-up gravitational
energy.

I'm stuck on all three of them since my physcis and math aren't strong, so can anyone please help me onto how to start off! Thanx!!!^^

2. Apr 8, 2008

Kurdt

Staff Emeritus
Do you have to derive the self gravitational potential energy from first principles or have you been given that formula or what?

You know part two is to do with black body radiation, so what equations do you know or can find that will help you there.

Part three will require you to work out how long it would take the sun at its current temperature to radiate away all that gravitational energy.

3. Apr 9, 2008

hobobobo

No deriving is invloved as far as I know. They just gave potential E = GM^2/r.

so a) calculate potential energy which uses the equation above, so i got that since solar radius is given as 6.96x10^8 m and solar mass is 2x10^30 kg.

But I'm stuck on of how to calculate the total power radiated from the sun assuming the T of the stellar photosphere is 6000 k blackbody. Do I use the blackbody equation for this? and if so what info do i need for the equation.

I also need to to estimate the lifetime of the sun if its energy is purely locked up in gravitational energy. What kind of equation will give you this?

Last edited: Apr 9, 2008
4. Apr 9, 2008

Dick

Look up the Stefan-Boltzmann law for the dependence of power radiated per unit of surface area. Use that together with the area of the sun to get the total rate of energy loss.

5. Apr 10, 2008

hobobobo

E= σT4 j/m^2s you mean this one right dick?

6. Apr 10, 2008

Dick

That's the one. I wouldn't call it 'E' though, it's not an 'energy', it's energy per meter^2 per second.

7. Apr 10, 2008

hobobobo

ok so I got 3.43x10^15 as my total power radiated by the sun assuming T=6000k. I calculated area of the sun by using pir^2 since solar radius which is 6.96x10^8 m. So this question wanted j so i moved things around. I sub in E by using the potential energy that I calculated from part a is that right?

8. Apr 10, 2008

Kurdt

Staff Emeritus
The sun is not a circle, so I'd reconsider the power radiated from it. What you need to do next is find how long it takes the sun to radiate the gravitational energy away.

9. Apr 10, 2008

hobobobo

oops haha 4pir^2 lol. So the rearranging and finding j is right? But i thought after all this i would just do lifetime = energy from part a divided by energy from part b, isn't that right?

10. Apr 10, 2008

Kurdt

Staff Emeritus
J? You're trying to find how long the sun will last if its powered by gravitational energy.

11. Apr 10, 2008

hobobobo

hmmm i followed what dick said about the boltzmann equation and then including the area of the sun so thats wrong then? well E=constant x T^4 x j x area of the sun which I got to be 1.71x10^68

Last edited: Apr 10, 2008
12. Apr 10, 2008

Kurdt

Staff Emeritus
Ok sorry, wasn't sure what point you were upto. Yes you multiply the surface area of the sun by the power per unit area, to find the total power radiated by it. Then you need to find the lifetime of the sun.

13. Apr 10, 2008

hobobobo

well lifetime of the sun I try calculating and it seems wrong came up with a number x 10^26 and that can't be right. I used this: lifetime = (energy) / (rate [energy/time] at which sun emits energy), is there another way to do it becuase this seems to be the only way.

14. Apr 10, 2008

Kurdt

Staff Emeritus
I'd check your calculations again. Specifically your calculation for the total power radiated by the sun. Remember it also helps us homework helpers if you post all the steps you use as we can quickly identify where you go wrong and how best to help you.

15. Apr 10, 2008

hobobobo

ok srry I'll post my steps:

So calculation for potential stored self stored gravity of sun as follows:

potential Energy = GM^2/r
= (6.67x10^-11m^3kg^-1s^-1)(2.0x10^30kg)^2/(6.96x10^8m)
=3.83x10^41m^2/s

Calculation of total power radiated by sun as follows:

E=(constant)(T^4)(j)(4pir^2)
=(5.67x10^-8 watt/m^2k^4)(6000^4k)(3.83x10^41m^2/s)(6.09x10^18m^2)
= 1.71x10^68

So are these right so far?

16. Apr 10, 2008

Kurdt

Staff Emeritus
The j in the Stefan-Boltzmann law is just part of the units (i.e. Joules per meter squared per second). Its not a variable. Also what are the units of potential energy?

17. Apr 10, 2008

hobobobo

m^2/s?......... because we have like m^3/m and kg^-1 and kg so they cancel out.

18. Apr 10, 2008

Kurdt

Staff Emeritus
The unit of energy is the Joule. Which is $J=\frac{Kgm^2}{s^2}$.

So could you see where you went wrong in your above calculation?

19. Apr 10, 2008

hobobobo

oohh? hmm I was following my sheet which says potential energy of an object due to its own gravity is of order Potential Energy = GM^2/r

20. Apr 10, 2008

Kurdt

Staff Emeritus
Potential energy is fine. Perhaps I was a bit misleading when I asked you to think about its units. Look again at my previous posts specifically post 14.