Newtons theory of gravity : satelite orbits and ellipses

AI Thread Summary
The discussion centers on the calculation of the orbital period (T) for two planets of mass m orbiting a star of mass M in the same circular orbit with radius r. The user initially presents an equation but realizes it leads to an incorrect answer. They specifically seek assistance in identifying the error in their calculations. Clarification is requested regarding the figure referenced, which illustrates the orbital setup. The focus remains on deriving the correct formula for T based on Newton's theory of gravity and orbital mechanics.
marshall104
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The figure shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radius r, but are always at opposite ends of a diameter.
This is the equation eq. I used:

mv^2/r=GMm/r^2+Gmm/(2r)^2

This is what I came up with but it is not the right answer. Where did I go wrong?

sqrt4pi^2/G(M+m)*r3/2

Any help would be great!
 
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marshall104 said:
The figure shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radius r, but are always at opposite ends of a diameter.
This is the equation eq. I used:

mv^2/r=GMm/r^2+Gmm/(2r)^2

This is what I came up with but it is not the right answer. Where did I go wrong?

sqrt4pi^2/G(M+m)*r3/2

Any help would be great!


What are you trying to find ?
 
marshall104 said:
The figure shows two planets of mass m orbiting a star of mass M.

What figure?

Zz.
 
I'm sorry. I'm trying to find T the orbital period
 
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