Ok, firstly - the orbital period is not given by the area of the orbit. It is given by the semimajor axis, by T = 2 * pi * sqrt(a^3 / GM). So if you start off

Ok, firstly - the orbital period is not given by the area of the orbit. It is given by the semimajor axis, by T = 2 * pi * sqrt(a^3 / GM). So if you start off in a perfectly circular orbit, then you need to lower your perigee by the same distance as you raise your apogee, in order to maintain the same orbital period and meet up with what you jumped off. The angle of impulse is easy in this case. It's perpendicular to the direction of travel. (For a circular starting orbit, and for a small impulse).