Artificial Gravity

In most space ships in sci-fi movies, people stand on the ground or sit in chairs. This makes sense intuitively on two levels. For one, we all naturally spend almost all of our lives standing, sitting, and lying down. Space travel seems like just another method of transportation, so it feels like it should be similar to what it is like to travel in a car, bus, train, or plane. Secondly, it’s historically been really hard to depict weightlessness on a movie budget.

The Millennium Falcon is designed for walking.

But we know there isn’t a universal “down,” and we aren’t magically stuck to the ground. Instead, mass attracts other mass with a force called gravity, and we are stuck to the ground on Earth because the planet’s giant mass is pulling our relatively tiny masses toward its center. In space, we don’t have that. Instead, small objects orbit large masses like planets, moons, and stars, being pulled in the direction of all the nearest gravitational forces added together. This leads to “free fall,” also called “microgravity,” (or incorrectly, “zero gravity”) in which occupants of a spacecraft float in the air, pulled along the same currents of gravity as the ship they are inside. There is no up or down, no floor nor ceiling.

This leads us to the question, can we create artificial gravity like in the movies? The answer, which might surprise you, is yes. There are in fact several ways, one of which we might see in ten years or less.

The first is to use acceleration to mimic the effect of gravity on the surface of the Earth. The Earth pulls downward on us with an acceleration of 9.8 m/s², which means if we were freely falling, we would speed up another 9.8 meters per second every second. It is also called 1 g. But we are stopped from falling by the ground, which pushes us upward with the exact force needed to counter gravity, because the Earth is packed full of solid and liquid matter. In space, without this balance of gravity and ground, we could get the same effect by having the ship accelerate at 1 g. The back walls of the ship push on us with the same force as the surface of the Earth, becoming the floor. And there we have it, artificial gravity.

behold my awesome MS Paint skills

Accelerating a space ship at 1 g is really hard. Yes, we do several g’s to get rockets into space, but a rocket’s mass has to be over 90% fuel just to make it to low Earth orbit, so keeping up 1 g even for an hour is beyond us right now, much less the weeks it would take to visit anywhere farther than the moon. A more feasible approach is spin gravity.

Newton’s first law says an object in motion will keep its speed and direction unless acted upon by an outside force. If a force is applied parallel to the direction of motion, the speed will change. If the force is applied perpendicular to the motion, its direction will change. In order for something to move in a circle, a constant force must be pulling it toward the center. Thus, our second method of giving space ships artificial gravity is to make them spin.

The direction of gravity, “down,” is the direction opposite the direction our surroundings push us. The ground pushes us up, therefore on Earth, down is down. A rocket pushes us forward, therefore down is toward its tail. A rotating space station pulls us inward, therefore down is outward. This illusory sense of being pushed away from the center of something spinning is called centrifugal force. So if we set a space station spinning, we get artificial gravity pointing away from the axis of rotation, and can walk around on the rim of the wheel or curved side of the cylinder.

The first problem we’ll have to face is making a ship big enough that standing up won’t make you dizzy. If you’re in a ship with spin gravity, your head experiences less gravity than your feet, because it is closer to the center. The significance of the difference depends on what percentage of the radius your body takes up. The smaller the circle, the greater the difference in gravity between your head and your feet. I don’t know how big it would have to be not to make you sick, but I expect we wouldn’t want a diameter smaller than a 6-story building.

There is one more option, which is much more futuristic. It is, drum roll please, straight up old fashioned gravity. Just cram enough mass into the center of our ship that it has its own gravity. These types of space ships occur naturally, and we call them planets.

Which leads us to the downside of using this type of gravity: it’s really freakin’ hard to get your ship to move. According to Newton’s second law, the more mass something has, the more force is needed to accelerate it. We’re not going to sail Earth around the solar system by pointing a rocket engine at the ground and firing its exhaust into space. We can get around that problem by building our ship around a black hole. A black hole can give an Earth’s worth of gravity to a normal-sized ship, using a whole lot less mass.

Suppose you had a black hole the mass of the Earth, 6*10²⁴ kilograms. How far away from it do you think you would have to be in order to experience 1 g of gravity? The answer: exactly the radius of the Earth. Whether the mass of the Earth is the size of a planet or a marble, the strength of its gravity is the same at the same distance from its center. If we went inside the Earth, gravity would get weaker, because some of Earth’s mass would be above us. But if we got closer to an Earth-mass black hole, the gravity would get stronger, because all of that mass would still be below us. Thus, to have a small space ship with a black hole providing 1 g, much less mass is required.

How much mass? To answer that, we need to know how big our ship is going to be. The tidal force (head-to-foot difference) for a black hole scales differently from spin gravity, so our black hole ship will have to be bigger than 6 stories. Let’s say 10 stories, or 30 meters. Using Newton’s law of gravity (which doesn’t have a number), a radius of 15 meters, and 1 g of gravity, we calculate the mass of the black hole to be 30 trillion kilograms. That seems like a lot, but it is just the mass of a small mountain, 100 billion times less massive than the Earth.

This black hole would be the size of a proton, and give off 400 kilowatts of power in Hawking radiation, which you could use to power your ship’s life support, and have about the same acceleration as an ion thruster on a satellite of normal mass of about .00001 g. So a properly-sized black hole could supply a ship’s artificial gravity its power, and a small amount of thrust.

If we had the technology to make micro black holes, options would become available. The smaller a black hole, the more power it gives off. We could opt for a slow-accelerating ship with a black hole providing gravity, or we could use a much smaller black hole and accelerate at 1 g. Heck, we could even have two black holes in the same ship, one for gravity, and one for thrust. Or more, if we wanted to build a larger ship.

Artificial gravity may seem like pure science fiction, but as we have seen, there are ways to do it in real life, one of which, spin gravity, isn’t even that hard. Someday, perhaps even soon, we will have space stations we can walk around in, almost just like we do on Earth. They won’t look like the space planes or battleships we see in science fiction. Rather, they’ll be something new and unique, wheels and cannisters speeding through the solar system.

From 2001: A Space Odyssey