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Two satellites of masses m and 2 m are revolving around a planet of mass M with different speeds in orbits of radii r and 2 r respectively. The ratio of minimum and maximum forces on the planet due to satellites is 1x. Find the value of x.

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Detailed Solution

Fmin=GMmr2−GM2m(2r)2=GMm2r2 and Fmax=GMmr2+GM2m(2r)2=32GMmr2∴ FminFmax=13

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Two satellites of masses m and 2 m are revolving around a planet of mass M with different speeds in orbits of radii r and 2 r respectively. The ratio of minimum and maximum forces on the planet due to satellites is 1x. Find the value of x.