(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

SUppose you have a galaxy with a spherically symmetric mass distribution with the mass density rho(r) = rho0 (r0/r)^5/3, where rho0 and r0 are constants. Derive the expression for M(r) the total mass interior to r, Then derive the rotation curve function.

2. Relevant equations

v^{2}= GM(r)/r

3. The attempt at a solution

I know that M(r) = the Integral from 0 to r of; 4/3 (pi) rho(r) r^2 dr

I know that rho(r) is proportional, or goes as 1/r^2

I also know that a rotation curve for a galaxy flattens out, so for this to be true then M(r) is proportional to r; thus I get the answer of

v^{2}= 4/3 (pi) G M(r)/ r

which should simplify to v^{2}= 4/3 (pi) G

But this doesnt seem right to me...perhaps Im messing up the part for the M(r) and the r...or maybe the rho and 1/r^2

Assistance if possible? THank you

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Rotation Curve for a Galaxy

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**