Question

find the velocity of a satellite travelling in an elliptical orbit, when it reaches point `C`, at the end of the semi-minor axis.

A. `V_(c)=Rsqrt(a/g)`
B. `V_(c)=R^(2)sqrt(g/a)`
C. `V_(c)=Rsqrt(g/a)`
D. `V_(c)=Rsqrt(g/(a^(2)))`

Answer 1

Correct Answer - C

From the property of an ellipse, we can show that `r=a` Total energy of the satellite in an elliptical orbit is,
`E=-(GMm)/(2a) :. 1/2mv_(e)^(2)-(GMm)/r=-(GMm)/(2a)`
or `1/2mv_(c)^(2)-(GMm)/a=-(GMm)/(2a)`
or `v_(c)=sqrt((GM)/a)` or `v_(c)=Rsqrt(g/a)l, (as GM=gR^(2))`