Estimating the mass of our galaxy, and the number of stars in our galaxy

[aj_17]

Homework Statement

The Sun rotates about the center of the Milky Way Galaxy at a distance of about 30000 light-years from the center
(1ly=9.5×10^15m).
Part A
If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere.
Part B
If all the stars had about the mass of our Sun (2×10^30kg), how many stars would there be in our Galaxy?

Relevant Equations

((4pi^2)r^3)/G*T^2)

A previous thread outlined the problem with a correct answer, however I don't understand where they got the formulas from. Here are the steps I've taken so far:
1. Convert 2*10^8 years to seconds = 6.3072*10^15 seconds (period,T)
2. The previous thread then went on to say you plug period and radius (which the thread said was 2.85*10^20, how is this found?) into the "formula":
((4pi^2)r^3)/G*T^2) How do you arrive at this formula?

 

[phyzguy]

1. Convert 2*10^8 years to seconds = 6.3072*10^15 seconds (period,T)

Looks OK.

2. The previous thread then went on to say you plug period and radius (which the thread said was 2.85*10^20, how is this found?)

You need to get into a consistent set of units. Since you will probably use G in MKS units, you need to convert the radius in light-years into meters.

into the "formula":((4pi^2)r^3)/G*T^2) How do you arrive at this formula?

It's from Kepler's third law.