If a satellite is revolving around a planet of mass M in an elliptic orbit of semi-major axis a, show that the orbit al speed of the satellite when it is at a distance r from the focus will be given byv^(2)=GM(2/r-1/a)

If a satellite is revolving around a planet of mass M in an elliptic o

1.	If a satellite is revolving around a planet of mass M in an elliptic orbit of semi-major axis a, show that the orbit al speed of the satellite when it is at a distance r from the focus will be given byv^(2)=GM(2/r-1/a)
Answer» Solution :Total MECHANICAL energy of the system is `E = - (GMm)/(2a) ` which remains conserved. `implies KE + PE = -(GMm)/(2a)` At a position .R. orbital speed of the satellite is V. Then KE =`1/(2)mv^(2) ,PE =-(GMm)/r` So, `1/(2)mv^(2)-(GMm)/r=-(GMm)/(2a) ` (or ) `v^(2) = GM (2/r-1/a)`