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 `v^(2)=GM[2/r-1/a]`

Explanation

Total energy of the system is `E=-(GMm)/(2a)` which is conserved.
So KE+PE`=-(GMm)/(2a)`
At position r orbital speed of the satellite is V.
Then `KE=1/2 mV^(2)` and `PE=(-GMm)/r`
So
`1/2 mV^(2)-(GMm)/r=-(GMm)/(2a)`
`impliesV=sqrt(GM(2/r-1/q))`