The backwards rule of orbits

You are chasing another spacecraft. It’s in the same circular orbit as you, a little way ahead, going the same speed. You want to close the gap and dock. Every instinct says the same thing: it’s ahead, so go faster. Fire your engine forward, speed up, reel it in. So you do — and the gap grows. You watch your target pull away as you climb above it and fall behind. This isn’t a glitch. It’s the law of orbits, and it runs exactly backwards from how chasing works on the ground.

Speed is set by altitude

Start with the one fact this whole lesson turns on: in orbit, how fast you go is decided by how high you are. Not by how hard you push. By your altitude.

The earlier module showed why an orbit is a fall that goes around — you move sideways fast enough that the ground curves away as fast as you drop. There’s a precise speed that makes that work at each height. Too slow and you spiral down. Too fast and you swing out. For a circle, exactly one speed fits each altitude.

And here’s the twist: that speed is higher the lower you are. The closer you are to Earth, the harder gravity pulls, so you have to move faster to keep missing the ground. A low orbit is a fast orbit. A high orbit is a slow one. This is Kepler’s old law, the one that governs every moon and planet: the closer in, the quicker the lap.

So the racetrack isn’t like a racetrack at all. On a track, the outer lane is longer but everyone can choose their speed. In orbit you don’t choose. Pick a lane — a height — and the lane sets your speed for you. The inner lanes are both shorter and faster. The outer lanes are both longer and slower. Both effects push the same way: low laps quickly, high laps slowly.

What firing your engine actually does

Now the part that breaks intuition. When you fire your engine forward in orbit, the burst of speed doesn’t just make you faster in place. It hands you extra energy, and that energy lifts you into a higher orbit.

Think of it as a trade. You spend a moment going faster, and the orbit converts that into altitude — you climb. But once you’ve climbed, the rule above takes over: you’re higher now, so your steady speed is lower than it was. You ended up in a slower lane. You pushed the gas pedal and came out moving slower around the planet, and trailing further back.

Fire backward — slow yourself for a moment — and the reverse happens. You lose energy, drop to a lower orbit, and down there the steady speed is higher. You hit the brake and came out moving faster around the planet, pulling ahead.

That’s the headline, the one worth keeping: in orbit, the gas pedal sends you up and back; the brake sends you down and forward.

The chase, done right

So how do you actually catch the craft ahead? You go the way that feels wrong.

Fire backward. Slow down. You drop into a lower orbit — a shorter, faster lane, running underneath your target. Down there you sweep around the planet quicker than it does. You’re not chasing it across the gap anymore; you’re racing ahead of it on an inside track, gaining a little every lap.

Watch the angle between you and the target close. When you’ve come around far enough that you’re sitting just below it — or just ahead and below — you fire forward. That raises you back up to its altitude. You arrive at its lane, at its height, now matched in speed and right alongside it. Dock.

You caught a craft that was ahead of you by slowing down first. The brake closed the gap. The gas pedal would have opened it.

A worked picture

Put numbers on the lanes. The space station orbits about 400 km up and laps the Earth in roughly 90 minutes. Drop to a lower lane — say a couple of hundred kilometres down — and the lap time falls below 90 minutes. Climb to a higher lane and it rises above 90. Lower is always quicker.

So picture your target one minute of arc ahead of you, both of you on the 90-minute lane. You brake. You sink to a lane that laps in, say, 88 minutes. Each lap, you complete the circle two minutes sooner than your target does. After several laps those saved minutes add up — you’ve crept all the way around the inside and surfaced ahead of where the target sits. Now you raise back up to the 90-minute lane, alongside it. The whole rendezvous was paid for by being lower and therefore faster, exactly as the law says. Real spacecraft dock this way, every time: drop low to catch up, climb back to meet.

On the whole

The reason this feels so wrong is that we carry a road-map of the world in our heads, and on the road, faster means you arrive sooner. In orbit that map quietly lies. Speed isn’t yours to spend freely; it’s a property of where you are, and trying to buy it directly buys you the opposite. The gas pedal is really an altitude pedal, and altitude pays back in slowness.

It’s a small, sharp lesson in how a system can run on rules that invert the ones we learned as children — not because the universe is being perverse, but because we’re applying a map drawn for a flat road to a curved fall around a planet. You live on the ground, where pushing forward means going forward, and that intuition has never once failed you down here. Lift it a few hundred kilometres and it breaks completely. The orbit was obeying a deeper rule the whole time; we just never had to meet it until we left the floor.