Seeing the math would help me get a handle on this.
Orbital mechanics use conic sections. For instance for a flyby you would use a hyperbolic section, with an offset parameter determining where the object would pass by the target object at its closest (and if you set this parameter to zero, you get a collision).
With a nearly circular orbit like Luna's orbit, there are a lot of simplifications. I haven't done orbital mechanics since Theoretical Mechanics II, but if I recall, it's still pretty complicated. It's perhaps easier to just calculate the velocity of a circular orbit first (as it will depend on G, mass, and radius; so it will take into account whatever little changes are made to the mass of the object) and then use a brute force trajectory calculation.
Or you could go old school and use Kepler's equation, which is also brute force. Most kinematics in space are brute force.