Estimate gravitational energy from supernova

[henrco]

Homework Statement

Suppose that a 15 M(solar masses) star finally runs out of nuclear fuel in its core and undergoes a Type II supernova explosion. You are going to analyse the energy budget, calculating all the quantities in Joules.

a) Estimate the amount of gravitational energy that would be liberated by the collapse of the core (say) 1.4 M(solar masses) to the size of neutron star.

Homework Equations

[/B]
PE = - GM/r

The Attempt at a Solution

To calculate the gravitational PE. I believe the correct formula would be PE = -GM/r
With: M = (15-1.4)M(solar masses)

I'm not given the radius. Since it's a type II supernova, the radius would be around 10-15km.

Is there a way I can accurately calculate the radius?
Or since the question is asking for an estimate do I take an estimated radius based on it been a type II supernova, so a midpoint between 10-15km?

Any help guidance very welcome.

 

[haruspex]

Homework Statement

Suppose that a 15 M(solar masses) star finally runs out of nuclear fuel in its core and undergoes a Type II supernova explosion. You are going to analyse the energy budget, calculating all the quantities in Joules.

a) Estimate the amount of gravitational energy that would be liberated by the collapse of the core (say) 1.4 M(solar masses) to the size of neutron star.

Homework Equations

[/B]
PE = - GM/r

The Attempt at a Solution

To calculate the gravitational PE. I believe the correct formula would be PE = -GM/r
With: M = (15-1.4)M(solar masses)

I'm not given the radius. Since it's a type II supernova, the radius would be around 10-15km.

Is there a way I can accurately calculate the radius?
Or since the question is asking for an estimate do I take an estimated radius based on it been a type II supernova, so a midpoint between 10-15km?

Any help guidance very welcome.

Mass within it at different initial and final radii will release different quantities of GPE. Consider a thin shell at initial radius r. What radius does it collapse to?
(I don't know whether you are supposed to take initial distribution as uniform; maybe you know.)

 

[henrco]

The thin shell would collapse to (r - width of shell), assuming that the entire shell burns off.
I am to assume initial distribution as uniform.

I understand that the GPE will will be different an initial and final radii. However I don't understand.

1) Is there a way of working out what the radius is? Can it be derived from the information provided. If so, could you please help me with that.

 

[haruspex]

The thin shell would collapse to (r - width of shell), assuming that the entire shell burns off.
I am to assume initial distribution as uniform.

I understand that the GPE will will be different an initial and final radii. However I don't understand.

1) Is there a way of working out what the radius is? Can it be derived from the information provided. If so, could you please help me with that.

The final distribution is certainly uniform, and you say you are given that the initial distribution is uniform. So the sphere is compressed from one uniform density to another. (You need to figure out what those densities are. I do not know how to do that.)
If the ratio of the densities is D, what is the ratio of the radius of the 1.4M core before collapse to its radius after collapse?
For a shell radius r within the core before collapse, what is its radius after collapse?