A satellite is describing a circular orbit around a massive planet of radius R. The altitude of the satellite above the surface of planet is 3R and its speed is v_0. To place the satellite in an elliptical orbit which will bring it closer to the planet, its velocity is reduced from v_0 to βv_0., when β<1. The smallest permissible value of β if satellite is not to crash on the surface of planet is √(2/K), find K.
3. The attempt at a solution
I think the angular momentum shall be conserved.
[itex]16mR^2 v_o /4R = mR^2 \beta v_0 / R [/itex]
But this equation gives incorrect value of β.
I also tried using conservation of energy but the expression for β does not come out to be in the same format as asked in the question.