The Paradox of Orbital Pursuit
Orbital rendezvous defies terrestrial intuition. To catch a spacecraft ahead of you, you must first slow down — dropping to a lower orbit where you travel faster in angular terms. To separate from a nearby vehicle, you thrust toward it. These paradoxes arise because orbital velocity and altitude are linked through Kepler's laws: higher orbits are slower, lower orbits are faster. Buzz Aldrin's 1963 doctoral thesis formalized these dynamics, providing the theoretical foundation for every crewed space mission since.
Phasing and Approach
Rendezvous begins long before the spacecraft are close. The chaser adjusts its orbit to create a differential angular rate that slowly closes the phase angle with the target. A spacecraft 20 km below the ISS catches up at roughly 7° per orbit — about 45 minutes per degree. Multiple phasing orbits may be needed, with burns at precisely calculated times to arrive at the target's altitude at the exact moment of phase alignment.
Proximity Operations
Within a few kilometers of the target, the physics shifts from Keplerian orbits to relative motion governed by the Clohessy-Wiltshire equations. In this linearized frame, the chaser follows elliptical relative trajectories that drift along the orbital direction. Station-keeping at a fixed relative position requires continuous thrust — there is no free parking in orbit. Approach corridors, hold points, and retreat paths are all pre-planned for safety.
Docking: The Final Meters
The last meters are the most critical. Relative velocity must drop below 0.1 m/s, lateral alignment must be within centimeters, and attitude angles within fractions of a degree. Modern systems use LIDAR, cameras, and laser reflectors for precision guidance. Soft-capture mechanisms — spring-loaded latches, inflatable bumpers, or magnetic systems — absorb residual kinetic energy before rigid structural latches complete the hard dock, creating a sealed pressurized tunnel between the vehicles.