A point mass is orbiting a significant mass `M` lying at the focus of the elleptical orbit having major and minor axes given by `2a` and `2b` respectively. Let `r` be the distance between the mass `M` and the point of major axis. The velocity of the particle can be given as

Options

A. `(ab)/(2r) sqrt((GM)/(a^(3)))`
B. `(ab)/rsqrt((GM)/(b^(3)))`
C. `(ab)/rsqrt((GM)/(a^(3)))`
D. `(2ab)/rsqrt((GM)/(((a+b)/2)^(2)))`

Answer

A

Explanation

on stopping, the satellite will fall along the radius `r` of the orbit which can be regarded as a limiting case of an ellipse with semi-major axis `r/2` Using kepler's third law `T^(2)propr^(3)`
time of fall `(T')/2=T/(2sqrt(8))=(sqrt(2)T)/8`