Lunar orbit problem

[Mission_CDR]

Let's say that you were orbiting the moon or some other body with no atmosphere at a constant altitude of 5 Km. and due to an uneven distribution of mass the center of gravity of the body is 6Km. away from the center of the body (measured distance)
If you orbited the body long enough for it to make 1/2 a rotation then wouldn't your new orbit have a periapsis of -1Km. and an apoapsis of 11Km. because the body should rotate on it's center of gravity causing the relative position of it and it's satalite (you) to change, right?

 

[ijuin]

Since you are always orbiting around the body's center of mass (barring perturbation by other bodies), I think that you would have the surface-intersecting orbit right from the beginning. The body would not need to rotate if your orbit begins as circular.