Question: A satellite in an attractive potential of V(r) =-k/r has an elliptical orbit: r = p/(1+ecostheta)(Where the eccentricty, e
a) Show that after the rocket firing the new orbit parameter pnew= pold(1+r *Impulse(Im)/lold) Where r is the apsidal distance and lold is the angular momentum before the rocket firing.
b) Find the ratio of the required rocket impulses Im(rmin)/Im(rmax) where Im(rmax) is the required impulse when the rocket is fired at apogee(highest point of the elliptical orbit) and Im (rmin) if the rocket is fired at the perigee point of the original elliptical orbit.
c) The satellite at apogee or perigee has exactly the same energy and angular momentum should the answers in part(b) equal 1.0? If your result is not, explain why it is not?