Explained: How Spaceships rendezvous with the ISS
To go slower, you must speed up. No, this isn’t some ancient Chinese proverb — it’s a core tenet of orbital mechanics. These two words side by side may strike fear in your heart but their meaning is simple. This is the field of science where we try to answer the question: how do we get a spaceship to change orbits? This is the same question scientists at NASA and SpaceX faced with the Dragon 2 spaceship. Rockets don’t just fly up vertically and intercept the International Space Station (ISS), they stalk it like prey, moving up orbits until they match that of the ISS and dock. Clearly, some sums needed to be done. Let’s understand how they went about it.
1: Each orbit has its own speed
A key place to start is that each orbit has its own speed. Think of them as lanes on the motorway/highway, except each lane has a different minimum speed limit. The lanes closest to the Earth have the highest speed and the lanes furthest out have the lowest speed.
Your natural reaction to this may rightly be, why? Well the force of gravity is stronger the closer you are to Earth. If you’re in a closer orbit, you need to travel really fast to avoid crashing down to the surface. But, if you’re further out you don’t want to go too fast against a weaker force of gravity or you’ll escape Earth all together. Balancing the two is a delicate dance. To get the intuition behind this, consider twirling a ball on the end of a string, you can imagine that with a short string the ball will be rotating much faster.
2: The Hohmann Transfer
The Hohmann transfer is the bread and butter of orbital mechanics. It is the most efficient way to move up orbits, so no surprise it was invented by a German. Perhaps more surprisingly it was inspired by the 1897 science-fiction book Two Planets and is still the best transfer we have.
Here’s the setup: we have the ISS travelling at around 8km/s in orbit 3 on our diagram. The Dragon 2 spaceship is in orbit 1, also known as a phasing orbit.
We take aim at the ISS’s higher orbit (3) and fire the thrusters once. This is important, we’re not continually firing them which is why the new elliptical orbit (2) path has this banana shape as we coast along. At some point it just touches orbit 3, when this happens the thrusters are fired for a second time. This gives it an extra boost and stops the spaceship from falling into orbit 2. We time this perfectly so that it coasts in just next to the ISS and can begin its docking procedure.
3: A mess of counter-intuition
This transfer does make sense but your intuition might trick you into thinking you understand what’s going on. I described changing orbits like changing lanes, and on the face of it, the Hohmann Transfer seems no different. There’s this idea that you accelerate a bit and now you’re in this new lane — but what was your speed again? We established before that higher orbits have slower speeds and our spaceship started in a lower phasing orbit. So what’s actually happened here is that we’ve hit the gas, to change into the slow lane…
What’s occurring is that the ISS’s higher orbit has more overall energy. As our spaceship travels between the two orbits, it’s losing speed energy but gaining gravitational potential energy (GPE). In fact it’s gaining so much GPE that it’s losing speed it had before it even fired its thrusters. The answer to why this happens is that it’s a weird byproduct of other more important rules that need to be followed when talking about orbiting. An orbit is really just free-fall with the centripetal force of Earth’s gravity holding you in place. But this force of gravity decreases the further away from the Earth you go. Coming back to centripetal force, its equation tells us that to achieve that same free-fall with less gravity, you need less speed.
Unfortunately for us, this entire setup is exclusive to orbits. Those astronauts have an excellent excuse for any speeding ticket: to go slower, you gotta speed up.
