Question

A star of mass 2.0 1031 kg that is 4.8 1020 m from the center of a galaxy revolves around that center once every 4.2 108 years. Assuming that this star is essentially at the edge of the galaxy, each of the stars in the galaxy has a mass equal to that of this star, and the stars are distributed uniformly in a sphere about the galactic center, estimate the number of stars in the galaxy. (Do not round your answer to an order of magnitude.)
stars

Answer 1

Use ^ in front of exponents please.

Express the galactic mass in terms of the number of equal-size stars, N.

Set the centripetal force equal to the gravitational frce on the edge star, and sziolve for N.

Answer 2

So using Keplers third law,
T^2=(4pi^2/GM)r^3
T=4.2 x 10^8
r=4.8 x 10^20
G=6.67 x10^-11
solve for M, then divide by 2.0x10^31?
which would give 1.855 x 10^25 stars