Interception and rendezvous: An intuition-building approach to orbital dynamics

The problem of rendezvous, the meeting of spacecraft in orbit, is an important aspect of mission planning. We imagine a situation where a chaser craft, initially traveling on the same circular orbit as its target and separated from it by a known distance, must select an initial thrust vector that will allow it to meet the target (interception) followed by a second thrust vector that will allow it to match velocities with the target (rendezvous). The analysis presented here provides solutions to this problem in simple algebraic forms while offering many rich challenges that support intuition-building exercises for students across a range of skill levels. An html-javascript orbit calculator is made available with this manuscript as a supporting visual aid and can be used to test the analysis and explore the consequences of different orbital intercept solutions.