If a satellite is revolving around a planet of mass M in an elliptic orbit of semi-major axis a, show that the orbital 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 orbital 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. `KE + PE = - (GMm)/(2a)` At a position Y 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)`