What Is the Total Kinetic Energy in Equilibrium?

[leonne]

Homework Statement

If the mass distribution is in equilibrium, what is the total kinetic energy? What
is the total energy

Homework Equations

The Attempt at a Solution

In the first part I was suppose to find the total potential with given
M(r)=Mr^3/(r^2+a2^)^3/2
p(r)=3Ma^2/4pie(r^2+a^2)^5/2
In my notes they have it as total kinetic =3/2 M o² o is velocity dispersion of stars
but not sure what to do with that

Edit looking at the last part of the problem I would need to use the total kinetic forum they give also what I get for the total kinetics, I guess ill have to figure out how to find kinetic from potential any hints on this part? Going to try to figure it out later i know potential would equal to kinetic if there is no external force, but i don't think i can use that in this problem

 

[leonne]

ok i think i figured it out after looking at notes notice that virial theorem is e=-k=u/2 so i am guessing how i derivated potential i just make it k=2pies G instead of u=-4pie G right?

 

[leonne]

ok seems like something is wrong the next part was to find velocity using the kinetic energy formula i got and k=3/2M o^2 (o is the radial velocity) so after going the calculation notice the formula i figured out is not right because the units i got for velocity is cm^2.2/s the formula i got for k is pie/2 G 3(M)²a² pie/32 but I am pretty sure the formula should be right looking at the virial theorem any hints? thxs