What is the total energy of a system of two isothermal spheres?

[leonne]

Homework Statement

Suppose you start with two identical finite isothermal spheres, each with initial
mass Mi and initial circular velocity vi, that are at rest a distance d apart. What
is the total energy of this system? Hint: Consider the total energy for each one
in isolation from part (a), and then the potential energy between the two.

Homework Equations

E=v^2M/2

The Attempt at a Solution

So the total energy for each would be E=v^2M/2 ( from what i got from A) and then the potential to be u=-GM²/R
So would the total energy of the two equal GM²/2R From using the virial theorem E=-(k)=U/2

 

[drdoubleu89]

how did you get Etotal to be GM^2/2R?

 

[leonne]

well the virial theorem says e=-k=u/2 so well i made a mistake should be negative, total energy e=1/2 U= -Gm^2/2R
btw are you in the astrophysics class? If you asking about this problem and same with my other problem

 

[leonne]

but i am not sure if its right if u think of something else let me know

 

[drdoubleu89]

yes i am in the astrophysics class, i sent you a private message