The Science of Kerbal Space Program

Stable Orbits

In Kerbal

KSP uses conic approximations to calculate trajectories around planets, moons and the sun. By focusing on only two bodies, a computer can easily simulate gravitational forces between two bodies and map the trajectories. This is done by ignoring other sources of gravity when outside of a defined sphere of influence.

In practice, this allows one to easily calculate when would be ideal to launch a spacecraft from one planet and have it reach another planet. The angle required between the radii of the two planets is given by
$$γ=(v_2-v_1)-ω(t_2-t_1$$

Reality

Reality however is not so simple. The universe does not actually operate on spheres of influence, and there is a reason that the method is called patched conic approximations. For situations with more than two bodies, such as placing a satellite in orbit between the moon and Earth, n-body calculations are instead needed.

One important consequence of n-body calculations that is not observed in conic approximations are Lagrange points. Lagrange points are areas where the forces of gravity of two bodies produces the proper forces to allow an object to orbit that point. These points are located at the peaks and troughs of the graph of the potential energy surface of the two bodies. These points are places where the net gravitational force is zero.

A spacecraft can be made to orbit these points with a little bit of corrective action, since they are not stable orbits. Using these points, satellites and probes can be sent to unusual orbits for data collection and then be brought back to Earth with relative ease, as was done in the Genesis discovery mission. They are also useful for making fuel saving maneuvers, such as MUSES-A when MUSES-B failed its mission.