- #1
CaptainEvil
- 91
- 0
Orbital Speed of a Star - Please Help!
Calculate \Omega(r) and v(r) for the following density models:
(a) all the mass M is at the center of the galaxy;
(b) a constant density adding up to a mass M(R0) at the Sun’s orbit and no mass beyond.
M(r) = v(r)2r/G
a) Using the above eqn, I can rewrite for v(r) = \sqrt{}GM(r)/r but since all the mass M is in the center, it is constant, and M(r) = M so
v(r) = \sqrt{}GM/r and \Omega(r) = v(r)/r
b) For a constant density, radius would extend from 0 to R0 and mass would increase from 0 to M(R0). So I'm thinking I have to integrate my equation from part (a) to account for this summation. But I'm a bit lost and don't know how to get it done.
Any help please?
Homework Statement
Calculate \Omega(r) and v(r) for the following density models:
(a) all the mass M is at the center of the galaxy;
(b) a constant density adding up to a mass M(R0) at the Sun’s orbit and no mass beyond.
Homework Equations
M(r) = v(r)2r/G
The Attempt at a Solution
a) Using the above eqn, I can rewrite for v(r) = \sqrt{}GM(r)/r but since all the mass M is in the center, it is constant, and M(r) = M so
v(r) = \sqrt{}GM/r and \Omega(r) = v(r)/r
b) For a constant density, radius would extend from 0 to R0 and mass would increase from 0 to M(R0). So I'm thinking I have to integrate my equation from part (a) to account for this summation. But I'm a bit lost and don't know how to get it done.
Any help please?
