Loss in gravitational energy during condensation of star

[gaobo9109]

Homework Statement

A spherical star of uniform density p and radius R is formed by the condensation of the interstellar dust from large distance due to gravitational forces. Find the energy change that occurs at some intermediate stage as the radius increases from r to r+dr

Hence derive an expression for the total loss of the gravitational energy during the condensation

Homework Equations

The Attempt at a Solution

I don't quite understand this question. It mentions that the radius of star increases from r to r+dr, but the question ask for loss of gravitational potential energy during condensation. So does the star expand or contract? I don't know what the question is trying to ask. Can someone explain to me？ Thanks

 

[hikaru1221]

The notation dr always means an increment of r, though r is not necessarily increasing. If dr>0, r increases; if dr<0, r decreases. It would be clearer if the problem stated "as the radius CHANGES from r to r+dr", but both ways lead to the same result.

 

[merryjman]

Well, what I think they want you to do is work backwards. The system loses GPE as the dust coalesces, but by working backwards and pushing all that dust out to infinity you can find out the GPE gain from doing that. It's kind of like saying, "find the work done by a spring as someone compresses it to a new length X" when what they really want is the potential energy stored in the spring.