Using the Clohessy-Wiltshire equations, this paper shows that close-proximity orbital rendezvous follows drifting-ellipse trajectories, derives a roughly 40 m line-of-sight range, and reproduces the Apollo 11 TPI burn within 1.6% of the flight plan.
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The Delicate Dance of Orbital Rendezvous
Using the Clohessy-Wiltshire equations, this paper shows that close-proximity orbital rendezvous follows drifting-ellipse trajectories, derives a roughly 40 m line-of-sight range, and reproduces the Apollo 11 TPI burn within 1.6% of the flight plan.