Question

A star in the Milky Way that is about 35 percent of the way out from the center of the galaxy has an orbital distance of 17.5 thousand light years and an orbital velocity of 238 km/s. What is the mass of the galaxy inside this star's orbital radius? Enter in solar masses.

Answer 1

orbital speed, v = sqrt(G*M/r)

==> r = v^2*r/G

a) v = 238000 m/s

r = 17500*3*10^8*365*24*60*60

= 1.6556 *10^20 m


M = v^2*r/G

= (2.38*10^5)^2*1.6556*10^20/6.67*10^-11

= 1.406*10^41 kg
mass of the galaxy inside this star's orbital radius is 1.406*10^41 kg