Gravitation and Newton's Synthesis Problem

[Brooke143]

1. The problem statement, all variables and given/known data
Our sun rotates about the cneter of the galaxy (m = 4*10^41kg) at a distance of about 3*10^4 light years ( 1ly=(3*10^8m/s)*(3.16*10^7 s/y) what is the period of our orbital motion about the center of the galaxy?


2. Relevant equations
Okay so I believe you would use g(m1)(Ms)/(r1^2)= m1(4pie^2r1/t1^2) but i dont understand
what do i put in for ms and m1 and r1 i assume r1 is the (3*10^4) and m1 is the (m = 4*10^41kg) but then what is Ms any help would be great thanks

[HallsofIvy]

I think you have m1 and Ms reversed. In calculating solar orbits, Ms would be the mass of the sun in the center and m1 the mass of the planet- with the result that the mass of the planet cancels and the answer depends only on the mass of the sun.


But the sun is orbiting the center of galaxy so "m1" is now the mass of the sum, which cancels out and "Ms" is the mass of the galaxy.