When you think of proximity operations, you may immediately think of the Hill-Clohessy-Wilshire (HCW) equations (and have flashbacks to your senior-year astrodynamics class). But these equations are a simplified model of relative orbital motion and may not be sufficient for your use case.
Is your target in a circular orbit? Are you operating in very close proximity to the target? Are you in an orbit regime where drag is not important? Do the chaser and target vehicles have nearly matched force models (i.e., SRP)? If you answered ‘NO’ to any of these questions, you need more sophisticated tools for modeling your proximity operations!
While the HCW equations can be useful for understanding the basics of relative motion, real world proximity operations require full numerical propagation with full force models. Using Systems Tool Kit (STK) with the Astrogator module, prox ops can be modeled to a high level of fidelity and set into an accurate physics environment, which includes gravitational forces, atmospheric drag, solar radiation pressure, and other space environmental conditions. Astrogator also gives you the flexibility to design really interesting (and useful!) forced motion relative orbits, like the Teardrop, Follow-Sun, and Perch orbits, pictured below.
To learn more about modern methods and tools for rendezvous operations planning and designing relative orbits, check out this Tech Talk by Dr. Cody Short: