posted by Sam on .
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.)
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.
So using Keplers third law,
T=4.2 x 10^8
r=4.8 x 10^20
solve for M, then divide by 2.0x10^31?
which would give 1.855 x 10^25 stars