Gravitational Potential Energy of Envelope around star

[godzilla5002]

I am confused about this question:

A giant star has a radius of 200 Rsun, with core of mass 0.6 Msun surrounded by an extended envelope of mass 0.2 Msun.
(a) Estimate the gravitational potential energy of the envelope.



When it says the envelope, does this mean the 'shell' surrounding the interior, where you can use the conservation of mass equation of a shell => dm/dr = 4pi*p*r^2 and Plugging it into Gravitational potential energy equation: dU = -[G M(r)*dm]dr/r. In this case dm is the mass of envelope and M(r) is 0.6Msun and r would be 200Rsun. Not sure what dr would be, since it is the thickness of the envelope. Thanks

 

[Jhero]

for any help!

Hello there,

Thank you for your question. It seems like you are on the right track with your approach to solving this problem. However, there are a few things to consider when calculating the gravitational potential energy of the envelope.

Firstly, when we talk about the envelope of a star, we are referring to the outer layers of the star, including the outermost layer known as the photosphere. So in this case, the envelope would refer to the layers of the star beyond the core, not just the shell immediately surrounding it.

Secondly, the conservation of mass equation for a shell that you mentioned is used to calculate the mass contained within a spherical shell, not the thickness of the shell. In this case, we already have the mass of the envelope given to us (0.2 Msun), so we do not need to use this equation.

To calculate the gravitational potential energy of the envelope, we can use the equation you mentioned: dU = -[G M(r)*dm]/r. But instead of using the conservation of mass equation, we can simply use the mass of the envelope (0.2 Msun) and the radius of the giant star (200 Rsun) to calculate the potential energy at the surface of the envelope.

So the final equation would be: U = -[G * (0.6 Msun + 0.2 Msun) * 0.2 Msun]/200 Rsun. The thickness of the envelope is not needed in this calculation.

I hope this helps clarify the approach to solving this question. Please let me know if you have any further questions. Good luck!