A galaxy has been found that is 5 kpc in radius and whose outer stars orbit the center with a period of 200 mi

Question

a galaxy has been found that is 5 kpc in radius and whose outer stars orbit the center with a period of 200 million years. what is the mass of teh galaxy? on what assumptions does this result depend on?

Answer 1

^^^^

^^^^

Peace for all!

Answer 2

It is just like 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.

T = SQRT [(4 • pi^2 • R^3) / (G*M)]

M = (4 • pi^2 • R^3) /(G*T^2)

T = period = 200x10^6 years = 6.3113852x10^15 seconds

R = radial distance from the center = 5kpc = 1.54284013x10^20 meters

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

M = 4*(pi^2)*(1.54284013x10^20)^3 / [(6.673x10^-11)(6.3113852x10^15)^2 ]

M = 4*(pi^2)*(1.54284013)^3 x10^39/ [(6.673)(6.3113852)^2]

M = 5.45x10^40 kgm

So that is the mass. These numbers (period and distance) are close to what the earth is with respect to the center of the milky way.