Internal View of an O’Neill Cylinder	External View of an O’Neill Cylinder (Pair)

On the Tennis Court

What if you were to play tennis in outer space?

Imagine living in a space station and standing on a tennis court. Your feet remain firmly planted on the ground due to gravity. The court curves slightly upward on the left and right instead of being flat. It’s your serve and you strike the ball, visualizing its trajectory. May your ball land in the service box; otherwise you’ve committed a fault. The ball flies from your racket yet veers from the direction of your strike. What happened?

Welcome to the world of centrifugal gravity.

Becoming a Space Faring Civilization

In the future, humans may venture beyond planet Earth. Several reasons could drive us to do this. Reasons range from an expanding population requiring additional resources to escaping repression on Earth. Otherwise, why leave a ‘paradise’ home to which we had evolved to thrive within? This assumes we won’t ultimately destroy our paradise to become inhabitable. An unfortunate consequence of our technological capabilities is that we could make our world uninhabitable.

Existential risks abound. And let us hope none of these happen. We’d rather not destroy our Earth or society. Otherwise, we couldn’t enjoy playing sports such as tennis.

If a risk became reality, we would be forced to settle elsewhere. Alas, outer space is a deadly environment where we could not live without significant technological assistance. Other planets are also unsuitable for multitudes of reasons. Mars is the closest to being Earth-like—that we know of. Even there, we would need to build pressurized shelters with advanced life support systems. The costs to build a suitable infrastructure are extremely high, especially when considering the costs to deliver materials from Earth.

Alternatively, we could try a ‘live off the land’ approach as proposed by the Mars Society (Or also known as In Situ Resource Utilization.) Essentially, settlers could use local Martian resources and if required, one could mine additional resources from ‘nearby’ asteroids and our moon, where escaping Earth’s gravity wouldn’t be a factor.

Can we do this? Eventually yes but certainly not now.  It could take a century or centuries to build up the outer-space mining and manufacturing capability. Opinions vary, ranging from optimism by the Mars Society and the NSS to the less optimistic. For a sobering viewpoint, check out “A City on Mars.”

The Challenge of Non-Earth-Like Gravity

A big unknown for Mars settlement is to live in a lower gravity of one third of Earth’s. Experience with astronauts has shown that zero gravity can cause bone loss among other effects. And we do not yet know the impact of non Earth-like gravity. In particular, we do not know whether human procreation in partial or heavier gravity is possible. And without procreation, what future is there for tennis?

One prudent approach is to settle where gravity is similar to Earth’s. But few other planetary alternatives potentially exist. Being light years away, we do not know yet if other factors may rule out these alternatives. Besides, all of them have gravity differing considerably from Earth’s.

Why Would We Live in a Space Station?

If one rules out planetary possibilities, this leaves us with artificial possibilities. Since the early 20^th century, some theorists have suggested space stations. The type we will focus on here is the O’Neill cylinder,

Welcome to the O’Neill Cylinder

This animation will give you an idea of the interior of an O-Neill cylinder. Certainly looks like one can build a tennis court in it.

A pair of O’Neill cylinder consists of two counter-rotating cylinders. The cylinders would rotate in opposite directions. Without the counter rotation, it would be difficult to obtain the sunlight required for power. And without power we cannot sustain a tennis-playing culture. For now, we’ll ignore alternative power sources, such as nuclear reactors. Besides, we need a sufficiently large population of people for sustaining a long-term society.

Generally each cylinder would be 6.4 kilometers (4 mi) or 8.0 kilometers (5 mi) in diameter and 32 kilometers (20 mi) long, connected at each end by a rod via a bearing system. Their rotation would provide artificial gravity.

Among other things, the large dimensions are necessary for reasonable gravity generation.  To understand how gravity is generated, we’ll need to consider some physics. Sorry about that.

Remember Newton? He told us that force causes mass to accelerate. More precisely, the amount of force on an object equals an object’s mass multiplied by its acceleration. Acceleration is not just speeding up or slowing down. An acceleration can also be a change in the direction of motion.

About Space Station Rotation

Guess what? Rotation is a change in direction. This means rotation is also acceleration. It turns out that acceleration causes one to experience a fictitious force, where the term fictitious force is a physics term referring to a force resulting from acceleration, instead of a force which causes acceleration.

If you’ve ridden a Graviton at a carnival, you’ve certainly felt pushed against the inside wall of the ride. Nothing fictitious about that feeling! That force is centrifugal force. Similarly when an O’Neill cylinder spins, a centrifugal force pushes you against its inner wall. The force feels like and sort-of acts like gravity pulling you to the ground.

The strength of centrifugal force increases with the radial distance from the axis of spin and with the square of angular velocity. You probably know from experience that spinning at high speeds can make you throw up. So how fast can people spin comfortably? (See answer #13)

According to some research, a revolving speed of one revolution per minute (RPM) can be sustained comfortably. This means that in order to achieve a force sufficient for Earth-like gravity, one needs a larger radial distance. Hence the size of the station must increase, for example a cylinder diameter of 6.4 km.

Although living in an O’Neill cyclinder would be like living in gravity, there are some differences.

The Weird World of Spinning

When you walk on the Earth, you don’t notice a force pushing you sideways. It exists though, but it is too small to notice. Whenever something moves on a rotating surface the object experiences a coriolis force. Because the Earth rotates, this force affects ocean currents and cyclones. The preceding link shows the coriolis force as acting sideways when one is standing on a spinning disk. When standing on the inner surface the coriolis force direction will depend on spin direction and on which direction the object moves within the cylinder.

This means a sufficiently fast tennis ball will experience a coriolis force, unless the ball moves parallel to the spin axis. As the ball’s angle of direction (away from parallel) increases, the coriolis force increases for any given ball speed. When the ball moves perpendicular to the spin axis, it will experience the maximum possible coriolis force for any given ball speed. 

If the velocity is parallel to the rotation axis, the Coriolis force is zero. For example, on Earth, this situation occurs for a body at the equator moving north or south relative to the Earth’s surface. Within an O’Neill cylinder, the spin axis runs along the centre of the cylinder. If one places the tennis court to run along the side, to make longer sides parallel to the spin axis, the coriolis force becomes zero if the ball travels purely parallel along the side of the cylinder. Making the ball fly at an angle however causes a non-zero coriolis force.

Simulation

Here is a simulation of a ball sent flying from within a spinning cylinder. Left click to shoot the ball. Press escape to stop the simulation. To shift the position of start location use one of W, S, A or D keys. Try to shoot the ball. Notice how the ball deflects.

You can also use the Tom Lechner simulation to see some of the effects of throwing a ball along the wall.  A tennis court should be meshed in completely during play. Otherwise some balls may escape to inward within the cylinder, or otherwise bounce within the cylinder.

For a more detailed look at coriolis force, including direction, refer to a UBC physics note which also describes the right hand rule. In summary, use your right-hand thumb to point along the axis of rotation. By physics convention, the positive rotation axis would be spinning counter clockwise. The index finger points in the direction of the object (ball in this case) velocity. The middle finger would point in the direction opposite of the coriolis force (due to a negative sign in the mathematical derivation).

For a spinning cylinder spinning counter clockwise, hitting the ball towards the end results in a coriolis force pointing left, resulting in a leftwards deflection.

Would the Coriolis Force be Noticeable?

When we walk on Earth, we don’t notice the coriolis force due to our slow speed relative to the large size and spin rate of the Earth. Would the effects be noticeable while playing tennis in a ‘typical’ O’Neill space station?

I did a crude calculation to ascertain this. I used a cylinder spinning at 0.6 revolutions per minute and with a diameter of 6 kilometers. I considered a player hitting the ball from corner to corner in a standard doubles court. Furthermore this person sent the ball flying at 225 kilometers per hour.

The resulting acceleration from the coriolis force would be about 0.14 g (g being acceleration due to gravity on Earth). After one second the ball would have diverted from a straight line of travel by about 70 centimeters. This would be noticeable.

I imagine a player would also notice the force pushing sidewise upon them while running about on the court, but I haven’t done any calculations in order to assess this.

Peter Spasov. Last updated Saturday October 04, 2025