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Is there any way to determine the orbital velocity of a point around another stationary point, if I don't know the mass of either of the points but know the force that gravity exerts and the distance between them. I'd like to know at what velocity I should push the non-stationary point perpendicular to the stationary point, so that it will maintain a circular orbit.

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It sounds and looks like a school problem. If the orbit is circular, write the expression of the acceleration (normal component only, assume v=cte). a=V^2/R Then use Newton's 2nd law: f=m*a and ....work out the answer

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The masses are unknown in the OP's problem. There is probably not enough information. –  Emilio Pisanty Jul 19 '12 at 10:59
    
I ended up just giving my points a mass. And solving the problem using Kepler's Laws. –  Sina Ghaffari Jul 19 '12 at 14:56

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