Gravitational potential energy during core collapse from 0.01 to 20 km

[jess_vander]

I'm really stuck with this last question...im not quite sure where to start...any help would be greatly appreciated! for a) I am not sure what to use for the mass of the star and the radius..do i have to subtract the two radii?

When a massive star is at the end of its life, the inner core that is perhaps 2 solar masses shrinks in radius from a size of around 0.01 solar radii to a radius of just 20 km.

a) Calculate that the gravitational potential energy of the core EPOTENTIAL = −0.6GM2
R before and after the collapse.

b) The total energy of the star is conserved during this collapse: ETOTAL = EOTHER + EPOTENTIAL. This implies that the difference is liberated as other forms of energy. Calculate the amount of energy liberated.

c) How important is it to know the original radius of the core before collapse?

d) The liberated energy goes into heat, expanding the outer layers of the star at very high speed, neutrinos and light. Assume that just 0.1 percent of this energy emerges as light over a period of 100 days. Determine the luminosity of the star over this period.

e) Convert this luminosity to solar luminosities. For comparison the entire Milky Way galaxy has a luminosity of around 2 × 1010 Solar Luminosities.

 

[pervect]

It appears that they already gave you the equation for the Newtonian gravitational binding energy in your problem. (Though your post mangled it into near unintelligibility). So I presume that's what they want you to calculate for the first part of the problem.

http://en.wikipedia.org/w/index.php?title=Gravitational_binding_energy&oldid=380972925

$$U = -\frac{3}{5} \frac{G M^2}{R}$$

 

[qraal]

I'm really stuck with this last question...im not quite sure where to start...any help would be greatly appreciated! for a) I am not sure what to use for the mass of the star and the radius..do i have to subtract the two radii?

Read the question again. It's all there.

When a massive star is at the end of its life, the inner core that is perhaps 2 solar masses shrinks in radius from a size of around 0.01 solar radii to a radius of just 20 km.

So the mass of the core is what's relevant - everything outside it is going to go BLOOEY! in the supernova. So the core mass is 2 Solar Masses (you hopefully know what that is.) The core's initial radius is 0.01 Solar radii (another constant I hope you know) and the final radius is 20 km. So the core collapses from pretty big to very small.

a) Calculate that the gravitational potential energy of the core EPOTENTIAL = −0.6GM2
R before and after the collapse.

Well you know R before and R after so that's pretty straightforward.

b) The total energy of the star is conserved during this collapse: ETOTAL = EOTHER + EPOTENTIAL. This implies that the difference is liberated as other forms of energy. Calculate the amount of energy liberated.

Ignore the heat already in the star - it's tiny compared to the big bang of core collapse.

c) How important is it to know the original radius of the core before collapse?

In otherwords what happens if it's a bit different? The cheat answer is not much, but you need to prove that with maths. Vary the initial radius and see what happens.

d) The liberated energy goes into heat, expanding the outer layers of the star at very high speed, neutrinos and light. Assume that just 0.1 percent of this energy emerges as light over a period of 100 days. Determine the luminosity of the star over this period.

Oodles of energy and luminosity. Once again show it with maths.

e) Convert this luminosity to solar luminosities. For comparison the entire Milky Way galaxy has a luminosity of around 2 × 1010 Solar Luminosities.

Once again the cheat answer is that the two are comparable. But you need to do the work to show that obviously.