If the true distance to the center of our galaxy is found to be 7 kpc and the orbital velocity of the sun is 2

Question

if the true distance to the center of our galaxy is found to be 7 kpc and the orbital velocity of the sun is 220 km/s, what is the minimum mass of the galaxy?

this is a home work question, but i cant seem to find it, im not good at this astronomy stuff, please show me the answer and where i can find it!!!

Answer 1

You can treat this just llike a satellite in orbit around the earth (assuming no dark matter, etc so that all you have in the way of mass is this galaxy).  See the reference for a good overview of the subject.

The equation to use is:

v^2 = (G • M) / R

Solve for M:

M = R*v^2 / G

v = orbital velocity of sun = 220 km/s = 2.2x10^5 m/s

G = gravitational constant = 6.673x10^-11 m^3 kg^-1 s^-2

One Parsec = 3.08568025x10^16  meters

One kpc = 3.08568025 x10^19 meters

R = 7 kpc = 2.159976175x10^20 meters

Just carry out the math:

M = (2.159976175x10^20)( 2.2x10^5)^2 /  6.673x10^-11

M = [ (2.159976175)( 2.2)^2 /  (6.673)] x 10^41

M = 1.567x10^41 kgm