The Sun rotates about the center of the Milky Way Galaxy at a distance of about 30,000 light years from the center (1 light year = 9.5x1015m).

Question

If it take about 200 million years to make one rotation, estimate the mass of our galaxy. Assume that the mass is concentrated mostly in a central uniform sphere. If all the stars had the mass of our Sun (about 2 x 1030kg) how many stars would there be in our galaxy?

Answer 1

We can model this as the sun rotating around the mass of the galaxy at the center. The gravitational force on the sun equals the centripetal force of the sun in its rotation about the galaxy center.

G x M_sun x M_galaxy / d² =M_sun x ω² x d where G is the gravitational constant M the masses, d the distance from the galaxy center to the sun, and ω is the angular velocity of the sun around the galaxy.

We need to change the units of all variables to the mks system.

M_sun = 2 x 10^30kg

G = 6.67408 × 10^-11 m³ kg^-1 s^-2

d = 30000 x 9.5 x 10¹⁵m

ω = 2 x pi radians / (200 x 10⁶ years x 365 day/year x 24 hrs/day x 3600 sec/ hour) = 1.99 x 10-15 rad/s

Put these variables into the first equation and solve for M_galaxy.

M_galaxy = ω² x d³ / G = (1.99 x 10^-15)² x (30000 x 9.5 x 10¹⁵)³ / 6.67408 × 10^-11

M_galaxy = 1.37 x 10¹⁶ x 1 x 10²⁶ = 1.4 x 10⁴² kg CHECK THE MATH!

# of stars = mass of galaxy divided by mass of sun = 1.37 x 10⁴² / 2 x 10³⁰ = 7 x 10¹¹ stars

This calculation assumed a circular orbit of the sun around the galaxy center.