A satellite starts in a circular orbit of radius r ( = distance from the center

Question

A satellite starts in a circular orbit of radius r ( = distance from the center of the Earth). Its speed is v1. The gravitational force on the satellite is central, Fr = GMm/r2 where M is the mass of the Earth; the potential energy is GMm/r.
Suddenly, a burst of the rocket engine increases the speed of the satellite from v1 to v1+0.3 v1. Thereafter the satellite moves on an elliptical orbit, as shown.
Calculate the apogee ra (= greatest distance from the Earth). Express the answer in terms of the initial radius r. (Show your work please)

Explanation / Answer

The all forces are central hence law of consevation of angular momentum is always constant L = mvr = constant    here m = mass of the particle v = velocity , r radius of the orbit vr = constant vapehelion*ra   =   vperihelion* rp   ra   = (vperihelion / vapehelion ) *  rp      =    ( v1 /1.3 v1)*rp     =   0.769*rp Here rp   = ri   =   initial radius vperihelion   = initial velocity v1 vapehelion   =   final velocity 1.3 v1

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