# Can centrifugal force actually overcome the health problems of microgravity?

Microgravity has a negative health effect which exercises cannot completely remedy. Rotation of spacecraft and the resulting centrifugal force have been suggested as a source of pseudo-gravity. But does that centrifugal force actually have the same (health-beneficial) effect on the human body as real gravity has? I seem to remember having read somewhere that "the body knows the difference".

A completely unrelated question about why a centrifuge isn't used on the space station has nothing to do with my question at all as it and its answers don't address nor even mention my question of whether there is a difference in health benefit between centrifugal force and gravity. Also, I'm thinking of something much, much more vast, more like an O'Neill cylinder or Niven's Ringworld.

• The answer would be based on speculation anyway. There are no experiences with training in a centifuge placed in an orbit during months. – Uwe Nov 17 '18 at 22:02
• @Uwe First, the question has the "interstellar-travel" tag. I'm not asking about "in orbit", but about interstellar travel. Second, as in many questions on this site, we haven't yet done what we are talking about, so an educated guess using physics facts about centrifugal force as it compares to gravity is fine. – user28089 Nov 17 '18 at 22:11
• There is no difference between microgravity in an orbit to microgravity in interstellar travel. Besides that, there isn't any experience in manned interstellar travel. Unmanned spaceships like Pioneer and Voyager are about leaving our solar system but the next stars are still very, very far away. – Uwe Nov 17 '18 at 22:46
• The size of the spaceship/habitat makes a vast difference.It would help to get a coherent answer if you could give an idea of what you have in mind. – Steve Linton Nov 18 '18 at 0:27
• @SteveLinton I thought I did. A huge rotating space vessel. – user28089 Nov 18 '18 at 0:32

First, I want to get out of the way that the equivalence principle, which is well supported by experiment, contends that gravity and acceleration are one in the same: "pseudo"-gravity caused by acceleration is equivalent to "real" gravity. So, there is no physical difference between walking in a spacecraft accelerating at 9.81 m/s2 and walking on the surface of the Earth. Therefore, there can be no difference in the biological effects. The body cannot know the difference.

But you asked about a rotating space station. A rotating station isn't exactly the same as a uniformly accelerating spacecraft. In a rotating station, a centripetal acceleration is constantly applied to keep going around the circle. In the rotating reference frame, this centripetal acceleration appears as centrifugal force, which acts as a replacement for gravity. By the equivalence principle, the effect of the centripetal acceleration (or centrifugal force) is identical to a gravitational force. However, the necessary centripetal acceleration to keep you going in a circle depends on your distance from the rotation axis. Because of this, any movement that changes your distance from the axis (say, bending over) will result in observation of the Coriolis force in the rotating frame. For small rotating space stations, the Coriolis force will cause dizziness, motion sickness and weird trajectories for dropped and thrown objects (presumably affecting O'Neill cylinder baseball).

The only physical difference between the rotating cylinder and real gravity is the Coriolis effect. So, any biological differences between real gravity and artificial gravity must be caused by the Coriolis effect. (I'm assuming that the rate of rotation of the cylinder is nearly uniform so that the Euler force is nearly zero).

The Coriolis acceleration depends only on the rate of rotation of the cylinder and your velocity, $$\mathbf{a_\mathrm{Coriolis}}=2 \mathbf{v} \times \mathbf{\Omega}$$, where $$\mathbf{\Omega}$$ is the angular velocity. On the other hand, as the radius of your cylinder gets larger, the rate of rotation required to attain Earth-like artificial gravity is reduced, because the apparent acceleration is $$|a_\mathrm{centrifugal}| = \omega^2 r$$, where $$r$$ is the radius of the cylinder. So, the bigger the radius of the cylinder, the less the Coriolis effect for a fixed centrifugal acceleration (for instance, 9.81 m/s2).

The question of how big the cylinder has to be to not cause dizziness has been addressed on WorldBuilding. It looks like it needs to be at least a few hundred meters in radius for 1 g acceleration. There may be other subtle biological effects at smaller Coriolis effects that we don't yet know about, but our bodies are made to move around, so at some point the small Coriolis effects must become negligible. As the size of the cylinder increases, the "artificial" gravity comes closer and closer to being physically equivalent to Earth's gravity. Indeed, the Earth itself has some Coriolis acceleration due to $$\Omega = 2 \pi / \mathrm{day}$$.

A nice discussion of the topic of artificial gravity is provided by Theodore Hall.

Edit: As pointed out by BlueCoder, the gradient of the effective gravitational field of a spinning structure on the one-kilometer-scale would be significantly larger than on Earth and could also be perceptible. This is described in the Theodore Hall link above as a "head-to-foot acceleration gradient". Too large a gradient gives "sensations of heaviness in the feet and lightness in the head". For a fixed effective gravitational acceleration, this gradient would be inversely proportional to the radius of the floor of the habitat.

• Excellent answer, yay for math! Since the OP specified a scenario far from the Sun, there wouldn't be a problem with frequent "sunrises" and "sunsets" near windows, but I wonder, for a few hundred meter radius at 1 g, how fast would the stars appear to move if one was lucky enough to be near a window? – uhoh Nov 18 '18 at 2:36
• This Space Exploration answer has some awesome gifs showing the Coriolis effect on darts thrown in a centrifuge: space.stackexchange.com/a/5626/19079 – WaterMolecule Nov 19 '18 at 0:27
• @WaterMolecule Isn't there another difference? On earth, the gravity gradient is very small i.e. gravity is about 9.81 wherever you are (-0.3% on Everest according to quora.com/…). However, in rotating station with a radius of, let's say, 100m, just being one meter nearer to the center would give you 1% less gravity..so your head feels less gravity than on Everest :) I don't think it would really change the answer, but who knows.. maybe it's worth mentioning :) – BlueCoder Nov 19 '18 at 10:06
• @uhoh if station diameter is 500m and your eye is 1m away from one 35cm diameter window, stars will cross the window diameter in 1.7 second. – qq jkztd Nov 20 '18 at 13:42
• @uhoh funny fact, if you want the stars to appear moving like the sun does seen from earth (one rotation each 24h), you need a circular station 3'720'000km in diameter, which is roughly 2.7 times sun's diameter. – qq jkztd Nov 20 '18 at 14:45