Hail Mary Science
Spaceflight and relativity

Artificial gravity calculator

A spinning ship can simulate gravity. Choose the spin radius and the revolutions per minute and the calculator tells you how many g the crew feels.

Key formula

g = ω² · r · ω = 2π · rpm / 60

Try it

How to use the simulator

In a spinning ship, the floor constantly pushes everything resting on it toward the center, and the people inside feel that push as weight. This artificial gravity is g = ω² · r, where ω is the angular speed (radians per second) and r the spin radius. The simulator turns revolutions per minute into ω and tells you how many g you get.

Controls

  • Radius: 5 to 500 m, the distance from the spin axis to the living area.
  • Speed: 0.1 to 10 revolutions per minute.

Things to try

  1. With the Hail Mary's values (104 m and 2.95 rpm) you get almost exactly 1 g.
  2. Shrink the radius to 10 m and find the rpm that gives 1 g: about 9.5. Spinning that fast makes most people motion-sick, which is why realistic designs use large radii.
  3. Double the rpm at a fixed radius and check that gravity quadruples, because it depends on ω².

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Why spinning creates "weight"

A moving object tends to keep going in a straight line. Inside a spinning ring, the floor constantly pushes you toward the center to keep you on the circle. Your body feels that push the way it feels the ground on Earth, so you perceive it as weight.

The acceleration needed is ω² · r, where ω is the angular speed in radians per second and r the distance from the axis. Doubling the radius doubles the gravity. Doubling the rpm quadruples it.

Big radius, slow spin

With a small radius you have to spin very fast to get 1 g, and that has unpleasant side effects. When you turn your head or walk, the Coriolis force deflects things and upsets the inner ear, causing motion sickness. Centrifuge studies suggest most people tolerate about 2 rpm well, and that 4–6 rpm is reachable with adaptation.

There is also a gradient: your head is closer to the axis than your feet, so it feels less gravity. With a 10 m radius and a 1.8 m person, the difference is almost 20%. At 100 m it drops below 2%.

Worked example

Example: how fast to spin for 1 g?

  1. We want 9.81 m/s² with a 100 m radius. Solving: ω = √(9.81 / 100) ≈ 0.313 rad/s.
  2. In revolutions per minute: 0.313 · 60 / (2π) ≈ 3.0 rpm. One turn every 20 seconds.
  3. The ring floor moves at ω · r ≈ 31 m/s, about 113 km/h.
  4. With just a 10 m radius you would need about 9.5 rpm, too fast to be comfortable.

In Project Hail Mary

The novel's ship can split into two parts joined by cables and spin around its center to produce gravity during the trip. With the ship's values (104 m and 2.95 rpm) you get almost exactly 1 g.

This tool appears in:Chapter 8The Centrifuge and Xenonite

Frequently asked questions

Does any station have artificial gravity?

Not yet. The International Space Station doesn't spin, and its crew make up for the lack of gravity with about two hours of exercise a day. Small centrifuges and tether experiments have been tested, but no crewed station uses spin permanently.

Is artificial gravity the same as real gravity?

For the body it is very similar, but not identical: it changes with height inside the ring, and the Coriolis force appears when you move. With a very large radius those differences are small.

What is the Coriolis force?

An apparent effect in rotating systems: an object moving toward or away from the axis seems to drift sideways. On Earth it explains which way hurricanes spin.

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