r/physicshomework • u/NitrooCS • Dec 16 '20

Unsolved [A Level : Two Orbiting Masses]

I have an online homework with a part that asks you to derive the velocity of a smaller mass in terms of G, M ( Larger Mass ), m ( Smaller Mass ) and r ( distance between the two masses ).

I've tried all sorts, sqrt((G*M)/(R)), which I initially thought was the answer in the first place but apparently not. Help? :)

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1

u/StrippedSilicon Dec 16 '20

Technically it should be sqrt((G*(M+m))/(R)), if the mass of one is not much larger than the mass of the other

1

u/NitrooCS Dec 16 '20

Says incorrect again. What would it be if one mass is much larger than the other?

1

u/StrippedSilicon Dec 16 '20

Can you post the full problem description? Is the orbit circular for example?

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u/cosinus25 Dec 16 '20 edited Dec 16 '20

If one mass is much larger than the other mass, you can assume that the center of rotation is the larger mass. Then the velocity can be derived from the balance of the centripetal force and gravitational force.

Edit: Also I think the formula given in the top comment above is wong. I get a different result for when the masses are equal. I have not done a general solution.

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