Here are the initial steps for reducing a 2 dimensional elastic collision down to a 1 dimensional elastic collision:
Here is an example problem of the additional steps for solving a 1 dimensional elastic collision:
Here is my own depiction of the dynamic gravitational forces on a rocket performing a planetary flyby:
This shows the way in which a gravitational interaction can be modeled similar to a collision with the center of mass at the more massive body (gravitational collisions are a more complicated process as linear and angular momentum as well as gravitational kinetic energy may or may not be conserved all depending on the specific parameters, perhaps aerobraking or rocket propulsion are taken into account, and other effects such as magnetic forces and light or plasma radiation play an effect too depending on the circumstances):
Here is an artist's depiction of the longterm gravitational trajectories that asteroids tend to take as they interact with planets and moons:
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