Star Trek: Artificial Gravity

Star Trek the Next Generation (1987-1994) (Picture)

The artificial gravity on the Enterprise has always confused me a little bit. I want to know how they do it!

Where does gravity come from and how can it be simulated in outer space? As it turns out, there are many ways to artificially simulate gravity.

Where does gravity come from?

Gravity is the force that Sir Isaac Newton famously "discovered"after watching an apple fall from a tree. It is something we have come to take for granted. When we throw a ball up in the air we know it will come back down. We know gravity exists, but where does it come from?

Gravity is an intrinsic property of mass. All mass attracts other mass by a force called gravity. When I stand on the earth, it pulls me down, towards its center. But I also pull on it a little. Since the gravitational force a body exerts is proportional to its mass I pull the earth toward me a lot less than it pulls me toward it.

The expression for gravitational force is:

F = GMm/r²

where G is the gravitational constant, M is the mass of the larger object, m is the mass of the smaller object, and r is the distance between them.

If you were interested in the acceleration of an object on earth you would apply Newton's second law:

F = ma

This yields:

a = gravitational acceleration = GM/r²

The acceleration of all objects on earth is therefore the same. It is independent of their mass. This might seem weird, but it isn't. The reason this is not intuitive is because most objects on earth experience other forces while in motion, like air resistance. This is why a feather falls more slowly than a lead brick. If both were in a vacuum (no air molecules) then they would fall at the same rate.

One interesting thing about gravity (just something to think about) is that it is only attractive. There is no negative gravity - there would need to be negative mass to achieve negative gravity. Even antimatter is comprised of positive matter. The other forces, like electricity and magnetism, have attractive and repulsive properties. Why should gravity be only attractive? 

What is artificial gravity and why is it necessary?

In outer space people are no longer on a planet. Looking back at the equation for gravitational force we can see that the force depends on the distance between the two objects, and it drops off quickly as the distance increases because that dependency is squared. A spaceship in outer space barely feels the effects of a planet's gravity, unless it gets fairly close to a planet (or a star). Therefore there will be no preferred direction like there is on earth. Each direction will "pull" or not pull a person equally. That is why astronauts look like they are floating: there is no force to pull them to one place on a ship.

Astronauts in zero gravity training (Source)

On the Enterprise everybody stands upright. How do they simulate gravity on their ship? There are several possibilities; I explore a few of the most interesting ones below.

Rotational/centrifugal methods

The easiest way to simulate gravity is to provide another force that is about equal in magnitude. One way to do that is to rotate a space craft.

Have you ever been on the teacup ride at Disney Land, or taken a sharp curve while driving? In both cases you may have felt like the outside of the teacup or car applies a force to you to keep you in - either in the teacup or the car. This principle can be applied to simulate gravity.

A point on the edge of a rotating body has a linear velocity which we will call v. Objects with a velocity always wants to continue in a straight line. In order to keep that point (in this case, a person in a space craft) from flying outward in a straight line, a force directly in toward the center of the rotating body needs to be applied to the person. This force will appear to push the person in from the outside walls of the space craft, like gravity would.

Circular motion. The black arrows represent velocity and the blue arrows show the inward force required to keep the ball in a circular orbit. (Source)

Let's take an example of how this might be done.  Assume there is a hollow wheel with a radius of 10m. In order to simulate gravity the wheel will have to spin with a certain speed (v is the linear velocity and ω is the angular velocity):

acceleration = gravity = v²/r = ω ²r

Solving for ω we get that the wheel would have to rotate about 9.5 times per minute in order to simulate the gravity we feel on earth. This is definitely achievable.

The enterprise is not continually rotating, though, so it must simulate gravity in another way.

Linear acceleration

Gravity can also be simulated by a linear acceleration, like when you speed up in a car and feel like you are being thrown backward. The Enterprise does not appear to employ this method, either.

Mass

Gravity is an intrinsic property of mass, right? So why don't you just squash a lot onto the bottom of the Enterprise so it pulls people down and they can stand on the ship? Well this can also work in theory, though it will require a lot of mass. For kicks, let's coat the bottom of the Enterprise with matter from a neutron star.

Neutron stars have a density of about 4 x 10¹⁷ kg/m³ (Source)

If we estimate the mass to be applied about 5 meters below the people on the ship (lots of problems with this, but I'm going to ignore them) we can use:

gravity = GM/r²

M = gravity*r²/G ~ 3.67 x 10¹² kg

This is a lot of mass, but neutron stars are incredibly dense so it might not be a problem. This corresponds to about 10^-5 m³ of neutron star matter. This is not much at all, only about one tablespoon of neutron star!

Of course there would be lots of difficulties in procuring a sample of neutron star, but nevertheless it's fun to think that it could be used for something as interesting as simulating gravity on a space ship.

The idea of using incredibly dense matter to simulate gravity on a ship is a cool idea - and very exotic!