So here's the deal.
You are an alien on an alien planet orbitting the planet's sun in a circular orbit. You want to find the mass of your sun. You "triangulate" the center-to-center distance between your planet and sun to be 3.52E+10 meters. The period of motion of your planet (the length of your year) is 1.81E+7 seconds. You know G = 6.67E−11 Nm^2/kg^2. What is the mass of your sun?
Given: R = 3.52E+10 m, T = 1.81E+7 s, G = 6.67E−11 Nm^2/kg^2
Want: M (as opposed to m)
Equation: F = GmM/r^2, ?, ?
We have three unknowns, M, m, and F. With T, one could potentially solve for angular velocity (omega = 2PI(1/T)) and go from there.
Anyone up for some phun?