Question

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

Answer 1

In elliptical orbit, total energy
`E=-(GMm)/(2a)=` constant
At position `r`,if `v` is orbital speed of satellite the
`KE=1/2mv^(2)` and `PE =(GMm)/r`
`:. 1/2mv^(2)-(GMm)/r=-(GMm)/(2a)impliesv^(2)=GM(2/r-1/a)`