Question: calculating orbit using another orbit A satellite which is moving around a planet of mass $M$ in a circular orbit of radius $R$ is given a sudden thrust into the center of the planet, so that it deviates an angle $a$.
Find the latus-rectum $l$ and the eccentricity $e$ of the new orbit.
As a hint: a force directed inward does not change the angular momentum, and therefore does not change the semi-major axis nor the period. It's not clear which angle you're talking about, but knowing that the semi-major axis did not change should let you set the problem up as a simple geometry problem.