If a satellite is revolving around a plenet of mass `M` in an elliptical orbit of semi-major axis `a`. Show that the orbital speed of the satellite when it is a distance `r` from the focus will be given by
`upsilon^(2) = GM[(2)/(r ) - (1)/(a)]`

Answer

A

Explanation

Total mechanical energy of a satellite in an elliptical orbiot of semi major axis 'a' is `- (GMm)/(2a)`.
`E = K + U`
`:. -(Gmm)/(2a) = (1)/(2) m nu^(2) - (GMm)/(r )`
or `nu^(2) = GM [ (2)/(r ) - (1)/(a)]` Hence Proved.