At perigee of an elliptic gravitational orbit a particle experiences an impulse S (cf. Exe...

At perigee of an elliptic gravitational orbit a particle experiences an impulse S (cf. Exercise 1) in the radial direction, sending the particle into another elliptic orbit. Determine the new semimajor axis, eccentricity, and orientation in terms of the old.

Exercise 1

Two particles move about each other in circular orbits under the influence of gravitational forces, with a period τ. Their motion is suddenly stopped at a given instant of time, and they are then released and allowed to fall into each other. Prove that they collide after a time .