Rendezvous & Proximity Operations

Getting two spacecraft to meet

Rendezvous uses a sequence of phasing and transfer maneuvers to catch a target. Key concepts:

Clohessy-Wiltshire (CW) equations

Relative motion of a chaser near a target in a circular reference orbit. Linearised equations describe R-bar, V-bar, and H-bar motion — ideal for the final ~10 km of approach.

Phasing

If the chaser is behind the target by Δθ in the same orbit, it needs to either drop to a lower (faster) orbit or climb higher (slower) and re-match. Time to close = phase angle ÷ rate difference.

Final approach

1. Far field (100 km → 1 km) — direct transfer on V-bar or R-bar.
2. Close approach (1 km → 100 m) — driven by safe abort trajectories (natural motion circle).
3. Berthing or docking — free drift plus attitude control.

Typical Δv costs

• First rendezvous (Gemini-class): ~200 m/s
• Modern autonomous docking: ~50-100 m/s
• ISS soft-capture braking: on the order of metres-per-second

Look up "passive abort" and "AAA — Automated Approach Algorithm" for how modern vehicles make this safe.