I commute by tube. Like most people on the London Underground, I do something to pass the time — usually a mix of doom-scrolling, listening to music, and reading. Recently, I've been re-working my way through The Expanse, James S.A. Corey's sprawling solar system sci-fi series, which is notable among other things for taking its physics unusually seriously.
In The Expanse, humanity has spread across the solar system. For a laws-of-physics-correct way of generating artificial gravity, stations like Ceres and Tycho spin to generate it — the centrifugal effect tries to fling you outward into space, and the hull becomes your floor. It works exactly like the real proposals for large rotating habitats that engineers (and sci-fi authors) have been dreaming up since the 1970s.
So there I was, trying to ignore the iconic demonic screeching of the Northern Line, and I started thinking: how would people get around inside these spin stations? In the books they refer to transit systems. A train, a tram, or something like that. And the moment I asked that question, it immediately brought up another — what would happen to gravity on board a carriage?
On a rotating station, your "gravity" comes entirely from the fact that the hull is constantly accelerating you inward. I.e. you're being flung outward, the hull pushes back, and that push feels like weight. The faster the station spins and/or the larger its radius, the stronger the gravity.
Now put a train on the inside of that hull, travelling around the circumference. The train runs along a circular track — either spinward (in the same direction the station rotates) or anti-spinward (against it). Because gravity here is really just due to spin — v² / r — the train's speed adds directly to or subtracts from the total velocity that generates your felt weight.
Travel spinward and you're moving faster relative to the inertial frame. Your effective centripetal acceleration goes up. You feel heavier — potentially significantly so. Travel anti-spinward and you're moving slower. Your effective gravity drops. Go fast enough anti-spinward and you could match the rim speed in reverse, achieving genuine weightlessness mid-journey.
Small side joke: While writing this with Claude, it suggested that "faster still, and "down" flips: you'd float up toward what was the ceiling and find yourself stuck there." Which I thought was hilarious. You wouldn't Gravity would just come back as you'd still be spinning in a circle, just in the other direction.
On top of the strange counter-acting or amplifying effect of speeding along inside the ring, any accelerating vehicle produces its own inertial force; the sensation of being pushed back into your seat as it pulls away, or thrown forward when it brakes. On Earth, these forces are small compared to normal gravity (usually a fraction of 1g), so they're noticeable but not dramatic. You lean a little, or bump someone on the tube and both of you pretend like nothing happened, but nothing falls over (unless too many pints were involved).
But on a low-gravity station, say, one designed for Martian gravity at a third of Earth's, the picture changes considerably. The same train acceleration that barely registers on Earth now represents a much larger fraction of your total felt weight. The gravity vector doesn't just shift slightly; it can swing by tens of degrees. During a vigorous anti-spinward departure, the combination of reduced radial gravity and a strong tangential shove from the train could tilt effective "down" far enough that standing passengers would struggle to stay upright. It could end up being like having a hallway tilt down to become a pit.
I found this fascinating in a very specific way, not just as a physics curiosity, but as a design problem. Whoever builds these transit systems will have to think carefully about top speed, acceleration rates, station spacing, and how to differ speeds between spinward vs. anti-spinward services, to maintain passenger comfort in a rotating reference frame. On top of that, navigating to find the quickest route somewhere could get interesting. If the speeds between the two services don't match, taking the longer route might sometimes get you someplace faster. It's a particularly strange and fun infrastructure engineering problem.
I wanted to see the numbers. How much does gravity actually change across a journey? What does the full profile look like: the ramp up during acceleration, the steady state at cruise, the swing back during braking? Does it matter much for a fast, large station, or only become uncomfortable on smaller, slower-spinning ones? Is it plausible that it might be a regular fact of life that travelling anti-spinward means enduring brief moments of weightlessness?
So I built a calculator. With some help from Claude. (Who, when writing this, gave me too much credit by saying that the physics are mine. No, Claude, physics belongs to us all.) What I found was that on Tycho station, with a particularly eagre transit system, that gets up to 75km/h, spin gravity almost disappears when traveling anti-spinward, and more than doubles when travelling spinward, with some funky gravity vectors along the way.
Want to see the graphs? The link is below, feel free to play around! You can adjust the station diameter, target gravity, train speed, acceleration, and stop spacing, and watch the felt-gravity profile update in real time for both spinward and anti-spinward journeys.