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?
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this sounds more like someone's homework than phun
you are given a circular orbit which is pretty good; that makes things easy. I don't think Newton's law of universal gravitation is the right way to go on this one. this was just a quick google search so ill just hook you up here. Apparently:
the orbital period of something in a circular orbit is: T=(2pi)(r^3/(G*M))^(1/2). where M's the mass of the thing you are orbiting. You should be able to algebrate that and solve for what you need.
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The equation F = GmM/r^2 can be set to solve for M, rendering M = Fr^2/Gm. F is equal to the centripetal force, and Fcentripetal = (OMEGA)^2(r). Angular velocity, or OMEGA, equals 2PI/T. Solving for OMEGA and plugging into the equation for M gives us M = [(OMEGA)^2*(r)^3]/G.
Turns out the mass of that sun equals 6.55x10^29 kg.
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Can you like, permanently break the forums?