Why a spacecraft can gain on a target by slowing down
In orbit, speed and position are linked by gravity. A spacecraft moving in a circular orbit closer to Earth must travel faster to keep from falling inward—but it also has a shorter route around the planet. It completes each lap sooner than a spacecraft in a higher orbit. That difference in lap time lets it steadily close a gap that would be hard to erase by simply chasing from behind.
To move downward, a craft briefly fires its engine opposite its direction of travel. This retrograde burn removes orbital energy: the craft loses speed, and gravity pulls it onto a lower, usually elliptical path. Near the low point of that path, another carefully timed burn can make the orbit circular at the new altitude.
Catching up is not the same as docking
Once the lower-orbiting craft has gained the right amount of orbital position, it must raise its orbit to meet the target. That takes another engine burn. The goal is not merely to reach the same place, but to arrive there with nearly the same velocity; otherwise, the spacecraft would streak past rather than rendezvous.
Mission planners therefore choose the lower orbit and timing to balance two needs: gaining ground quickly enough, and approaching gently enough for a safe meeting. The apparent detour turns orbital mechanics into a patient pursuit: the pursuer first changes its route around Earth, then uses that altered timing to meet the spacecraft ahead.
