 #1
Barbequeman
 8
 1
 Homework Statement:

Consider three models of the mass distribution in the Milky Way. Model 1 has a constant circular velocity Vc. Model 2 places all the mass of the Milky Way at a single point at the centre of the Galaxy. Model 3 consists of a system in which the mass of the system is distributed in a sphere of constant density. In this model you can use Newton’s Theorem to compute the circular velocity.
The following rule about derivatives can be used. Suppose you have a function:
Question A. is
For each of the three models, write down the equation of the circular velocity as a function of radius. (Hints: For model 1 this should be trivial. For model 2 equate the gravitational and centrifugal forces. For model 3 follow a similar procedure to what you did for model 2, but considering the mass enclosed at a given radius.)
Question B. is
Therefore, for each of the three models, calculate dV/dR
 Relevant Equations:

V=V_0*R^n
then the derivative is given by:
dV/dR=V_0nR^n1
I attached a Jpeg with my attempted solution but I´m not sure if I´m on the right way... I hope for a correction in my calculations