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Question

If a satellite is revolving around a planet of mass M in an elliptical orbit of semi-major axis a. Show that the orbital speed of the satellite when it is at a distance r from the planet will be given by V2=GM[2r1a].

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Solution

In elliptical orbit , Total energy

E=GMm2a= constant

At position r, if V is orbital speed of satellite the

KE=12mv2,PE=GMmr

12mv2GHmr=GMm2a

V2=GM(2r1a)

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