How to Solve the Two-Body Problem
Learn the fundamentals of orbital mechanics by deriving the equations of motion for a two-body system
Orbital mechanics can be an intimidating topic for any person. While it can get complicated and intensive, the fundamentals are quite intuitive. Let’s start with what is orbital mechanics? Orbital mechanics, or astrodynamics, is the study of the motion spacecraft and natural bodies under the influence of gravity from one or more large natural bodies. The field is broad and encompasses many niche topics, some of which include determining where an object is in space, attitude dynamics, and maneuvers.
If you are just getting into astrodynamics or are curious to learn more, the best place to start is the two-body problem, or 2BP. The two-body problem is an astrodynamics model that considers only two masses. One is usually a celestial body, and the other is usually a spacecraft, whose motion is of interest. The 2BP is considered a low-fidelity model, meaning a model that does not have good accuracy compared to the real world, but it can be used as a building block to create higher fidelity models. Such models include other forces affecting a spacecraft such as other natural bodies (other planets, moons, etc.), solar radiation, oblateness and aerodynamic drag (if its orbit is touching an atmosphere).
