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 by v^(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 by v^(2) = GM((2)/(r)-(1)/(a)).
Answer» Solution :Total mechanical ENERGY of the system is `E = -(GMm)/(2A)` which remains conserved `rArr 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))`.