The ISS crosses its own sky at 28,000 km/h, and a crew capsule has to arrive at the same place, at the same speed, gently enough to touch. The way it's done breaks your driving instincts — in orbit, you slow down to catch up.
You can't just point at it
On the ground, chasing something means aiming at it and going faster. In orbit that exact move fails: thrust toward a target ahead of you and you raise your orbit — and higher orbits are slower, so your target pulls further away. Orbital speed and altitude are locked together; you don't get to choose both. Every chase in space is really a negotiation with that rule, and pilots who trained on aircraft had to unlearn everything to fly it.
Slow down to catch up
The real technique is a game of lanes. A spacecraft launched behind the Station enters a lower orbit — the inside lane — where it naturally travels faster and gains ground on every lap. When the geometry is right, it raises its orbit in stages, timing each burn so that its climb ends just below and behind the target. That phasing is why crews typically spend hours circling the Earth before they ever see the Station out the window: a Dragon or Soyuz usually takes several orbits to close the gap, and the fastest profiles ever flown still take about three hours.
The last hundred meters
The endgame reverses all the drama. Two vehicles that are each moving at 7.66 kilometers per second approach each other at centimeters per second — final closing rates are about the speed of a minute hand. The capsule pauses at set hold points, waits for 'go' calls, and creeps in along a safety corridor until capture. Docking is the one moment in spaceflight where the right speed is almost zero, and it's why a rendezvous that began with a controlled explosion ends with a touch too gentle to crack an egg.
It starts on the launch pad
This is also the secret behind 'instantaneous launch windows'. A Station-bound rocket must launch at the exact moment the ISS's orbital plane sweeps over the pad — miss it by a minute and you're aiming at a plane the spacecraft can't afford the fuel to reach, so the launch waits for tomorrow. When a countdown you're watching holds and scrubs for the day, this geometry is often the reason: the chase is lost or won before the engines even light.