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  Tension of two mass and a rod satellite

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Hi Guys :)


I need to prove that the tension for an artificial satellite consists of two points of mass m/2 connected by a light rigid rod of length that is

\(T=\frac{3}{4}\frac{Gmm'l}{a^3}-\frac{1}{4}\frac{Gm^2}{l^2}\)

The satellite is placed in a circular orbit of radius a>>l (from the middle point of the rod) around a planet of mass m'.
The rod is oriented such that it always points toward the center of the planet.
I think that the second term -

\(\frac{1}{4}\frac{Gm^2}{l^2}\)

might comes from the mass interaction according to the newton gravitation law -

\(F=G\frac{\frac{m}{2}\frac{m}{2}}{l^2}\)

But I don't know how to get the first term (Maybe it is related to the orbital angular velocity of a planet.) -
\(\omega = \frac{(GM)^\frac{1}{2}}{a^\frac{3}{2}}\)

Thanks!

asked Jul 31, 2021 in General Physics by anonymous [ no revision ]

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