The Physics Behind Theoretical Artificial Gravity

Written by TKS Boston Student Amelia Settembre.

Artificial gravity has been one of the biggest question marks when considering actual, plausible space flight — and more specifically, improving it for the people. Of course, there are still a ton of issues with the current system, and our knowledge of artificial gravity is a far cry from futuristic shows like Star Trek and Battlestar Galactica. For a brief overview of artificial gravity, check out my other article on it here.

So now let’s take the next step deeper and look at some of the physics, both known and experimental, that physicists are analyzing this very moment to improve future space tech. In current gravity, the gravity of an object increases when the mass does. Unfortunately, when an astronaut is on a spaceship, there isn’t enough difference in mass for the craft to generate enough gravity to keep the astronaut on it.

Modern Artificial Gravity And Principles

Back in Einstein’s time, he proposed something called the equivalence principle, which basically stated that gravitational force is indistinguishable from a pseudo-force generated in an accelerated frame of reference. This meant that we didn’t need to have a massive, planet-sized spacecraft, we only need to have sufficient acceleration to simulate gravity.

As it turns out, there are three big types of acceleration:

  • Linear, which is like driving in a car.
  • Rotational, which is like spinning a bucket around with water in it.

Spinning water in a bucket is a great example of rotational acceleration.

  • Gravitational, which is like dropping a penny off the Empire State Building. Here, it accelerates due to gravity.

For humans, we can’t go above a certain amount of g-force. On Earth, the g-force we experience is around 1 g. That’s not very much. However, air force pilots often experience intense change in the g-force. The most g-force any human has managed to survive is 214g, which occurred during a car racing match.

On the Enterprise, travelling at warp one, a human would be subjected to around 4,000 g. Unless in the distant future they’re able to come up with some kind of reverse-accelerator to protect astronauts, it’s not going to bode very well — for anyone. Now that we’ve ruled that out, that doesn’t mean there aren’t any ideas for getting stable artificial gravity. One of the biggest questions regarding this is compensation.

In other forces, like electromagnetism, you could just put all the people into a conductive capsule and block out the extra electromagnetic waves. The remaining amount can be contained and pushed around within the capsule, making it safe for the crew.

This diagram represents the inner capacitor in which the electric field — kept with an opposite and equal charges — is arranged safely between two plates, making the capacitor safe and livable for all humans inside it.

Unfortunately, there’s no negative gravitational mass in the known universe, which does make it more difficult to determine how to reverse the effects of gravity. However, in theory, if there is indeed a particle such as the “graviton”, then it’s possible for there to be another exotic particle, perhaps dubbed the “anti-graviton”. Up until this point, there’s no proof that the known universe even contains any gravitons.

That’s the biggest issue experienced with gravity — unlike other forces (like electricity) which have positive and negative values — it only has one, and that’s the attractive quality it always has. All this means is scientists are either going to have to get incredibly theoretical, find new physics, or just use the acceleration methods we all know and love.

The most considered one of these acceleration methods concerning artificial gravity is rotation. By taking a spacecraft and rotating it quickly, artificial gravity can theoretically be generated, holding the contents of the spacecraft secure.

In this figure, the acceleration as relating to the center of the figure and the outside is mentioned, in which what changes is the acceleration in relation to the center of the circle [pictured on the left]. In the other image, when taking into account speed which increases, by using the acceleration in relation to the center of the figure and outside of the figure can help determine what the overall acceleration is.

As it turns out, physicists have designed formulas to calculate the exact acceleration of artificial gravity. In the formulas below, we’re assuming that there are two chambers in a spacecraft which are connected by a tunnel with a length of 2R. Here, let ‘v’ represent the frequency of the tunnel and ‘t’ can be the time period.

Remember that centripetal acceleration we talked about a little earlier with the circle figure? Well, it comes back into play here, as you’re trying to also solve for how it fits into the rotation of the artificial gravity chamber.

Before you reach the second half of the formula, add in ac=g, which helps figure out the calculations of the actual gravity (which is what you’re trying to determine in the first place). In this way, you can determine what the velocity ultimately has to be comfortable for the astronaut, which (above) would be equal to about 9.5 revolutions per minute 10 meters away from the axis of rotation.

So that’s how you calculate the basic rotating artificial gravity, which initially seems simple but isn’t as simple in the long run. However, that’s not saying that rotating artificial gravity is the only option: in fact, scientists are looking now into whether anti-matter or dark energy could provide insight into whether or not artificial gravity could be supported differently.

Is Anti-Gravity Plausible, Or Even Real?

So I guess this isn’t about anti-gravity so much as it’s about anti-matter and its potential applications with regular gravity. Science right now talks about two really big ideas which encompass the definition of what mass is:

  • There’s the kind that accelerates. This can be seen in the equation by Isaac Newton, F = ma, and in Einstein’s equation E = mc².
  • The other kind is gravitational. This is found in Newton’s equation F = GmM/r² which talks about the gravitational mass.

However, when looking at antimatter, you have to question the interaction it’s going to have with the actual matter. Although with antimatter, we’ve been able to create it and destroy it, as well as calculate seen the interactions it has with non-gravitational forces. However, it’s relatively uncertain how it would behave with gravity, as we’ve never been able to test that before.

The ALPHA-G generator. It works by taking anti-protons and positrons which are forced to interact with one another at slow speeds, resulting in the creation of the neutral antihydrogen used in the experiment.

One project working diligently on finding a response to this is the ALPHA experiment at CERN. This experiment has the goal of analyzing neutral antimatter and applying it’s reaction to gravitational forces. To directly quote the ALPHA website surrounding the outcome,

"The gravitational mass of antihydrogen is more than 110 times its inertial mass, or that it falls upwards with a gravitational mass more than 65 times its inertial mass."

That’s pretty impressive, as well as not necessarily expected. However, it does still have the question with different types of matter as to what would happen if antimatter is applied to the regular Earth, especially different varieties of particles. We’re still far from an answer of artificial gravity with antimatter, but this is a step in the right direction. There’s still a final idea which may answer these questions once and for all, and that’s string theory.

String Theory And Quantum Gravity

So this is the final question, and as we’ve worked our way from most plausible to (now) least plausible, it’s time for an analysis of quantum gravity and the workings behind it. Quantum gravity is essentially the analysis of gravity which is taken when assuming that quantum physics indefinitely plays a role. It’s known to exist in the realm of theoretical physics, which just means that most of the information is derived entirely on paper, typically with mathematics backing it up.

However, because of how theoretical quantum gravity truly is, there isn’t just one theory about how it could work, there are quite a few:

  • Semi-classical quantum gravity. This is taken when looking at a curved background (so essentially non-Minkowskian), and although it isn’t completely a quantum theory, it was widely accepted in the 20th century as a major component in classic electromagnetic fields. It could possibly explain black hole radiation, and is currently one of the best theories we have.

In this image, the representation for field theory is represented, having the e+ and e- represent different particles which are combined to help form a string (y) with the other side of particles (-q and q)

  • String theory. By looking at quantum field theory, physicists determine that when quantum particles reach certain energies, they also reach different modes of oscillation which affect the charge of the fundamental string each is part of. Think of it as taking two pieces of twine and shaking them back and forth, only shaking one faster. The waves on it will be smaller, changing the frequency of energy output. The same goes for the fundamental strings.

In this image, the spin network illustrated in loop quantum gravity is pictured. Here, the operators quantify the energy frequencies pictured.

  • And last but not least, loop quantum gravity. This assumes that each energy frequency from the quantum operator is quantified, and the quanta are photons. When talking about gravity, the operators represent an area and volume of the space. From this, most physicists suggest that spacetime as an elementary granular quantum structure at the Planck scale.

These certainly aren’t all the theories (there are over a dozen more), but they’re some of the most prominent ones featured in considering quantum gravity. However, in the end, we still have many more possible ways of determining artificial gravity, and quantum gravity doesn’t quite seem like the best way to start, given that it’s so theoretical.

So What Does This Mean In The End? + TL;DR

Although scientists are working at making artificial gravity even better, there’s still an awful lot they don’t know and are still trying to understand. Gravity is one of the most mysterious forces in the known universe, and trying to sort through it naturally is going to take a bit of time. Who knows, maybe in a couple of centuries we’ll have figured out how to have artificial gravity a la the Enterprise! So to sum up:

  1. There’s a ton of physics involved in determining how much artificial gravity you’ll need to sustain a human, as well as determining how much you can logically create.
  2. Gravity is an incredibly confusing force, because it has no “opposite” reaction — the same way every other force does. This makes it more difficult to accept and channel properly.
  3. There are three kinds of acceleration which can be used, but rotational acceleration is used the most.
  4. The main varieties of potential artificial gravity that can be analyzed is rotating artificial gravity, antimatter artificial gravity, and string theory/quantum gravity.
  5. There’s still a lot we need to know, and although we’re working on it, in terms of successful artificial gravity, we don’t really have anything up in space yet.

Sometimes in order to truly get the gravity of a situation, one needs to take a step back and take a long look at everything in the picture — which is almost certainly more than meets the eye in artificial gravity.

Thank you for reading this article! I hope you enjoyed it and maybe learned something too ;)! If you’d like to connect, feel free to email me at or find me on LinkedIn under Amelia Settembre.