Can we induce artificial gravity in space?

“My contract doesn’t cover bloody space walks”.

The bleating below of the hanger’s alarms began to wane as the cabin initialised its depressurisation. Taylor’s heavy panting was funnelling through Ripley’s communication unit, clearly acclimatised to the harshness of space. As the door opened, the transit line began its journey towards its docking destination: Sevastopol Station. Mid-way into their journey down the line, an vigorous explosion tore the lower segment of the station from the rest of its body and headed straight for Ripley and her crew. Moments later, with the transit line severed and Ripley separated from her crew, she somehow finds herself conveniently gripped onto a ledge just outside the station’s hanger. Pulling herself in, she manages to float towards the lever located on the near wall which seals the hanger doors and pressurises the room. And then she falls to the ground.

Alien Isolation does an amazing job at capturing the retro-futurism exhibited in the original film. The cutscene which I detailed that occurs in the opening stages of the game however captured my attention. The explosive fireball in space or the sound travelling through its empty void are well known flaws that are accepted in the culture of science fiction. But it is not they which cause my concern – rather, it was the final action. The scene seems to imply that upon pressurisation, gravity to the hanger was restored. Artificial gravity is not something new to this genre, but I have never seen it portrayed in this way before. Let’s dig a little further.

The process of pressurisation is a fundamentally important one for any space station – both in fiction and reality. Since empty space has very little matter in it, it is a near perfect vacuum, meaning that its pressure is nearly zero. In juxtaposition, any space station (or ship)  will need to be filled with a number of gases to allow its occupants to breathe. A good example is that of the International Space Station (ISS) which uses a composition that is very close to Earth’s, offering benefits of comfort to the crew and a reduced risk of fires breaking out on board. Of more importance is the air pressure, which is at a comfortable 101.3 kPa or 1 atmosphere (the same as at sea level). Now due to the difference in air pressure of the station and the vacuum, when the barrier (door) is removed, the molecules naturally diffuse into the region of lower pressure. Simply put, when the hanger in the game was opened (and the room was exposed to empty space) any air molecules would have quickly rushed out into space.

 

We can thank the second law of thermodynamics for this process. A good way to think about the second law is that energy has a tendency to go from more concentrated to less concentrated. It spreads out and gets diluted. Looking at the picture below, the dark purple blob indicates a higher concentration of pressure. Therefore as soon as the central valve opens, entropy dictates that the air molecules on the left side will flow to the right because the pressure is lower there. After some time the pressures will be equal and no more air will flow through the valve since they are in equilibrium. The total energy has not changed over this process, however the entropy has increased in the process.

Now let us switch over to the gravity side of things. The first thing we have to clear up is a big misconception; that there is no gravity in space! I’m going to jump into the theory again but I promise that the maths is relatively easy!

Newton’s theory of gravitation introduced the idea that a vector field surrounds any mass. Now a vector is simply any quantity that has both a magnitude and direction. In this particular case he was referring to the gravitational field which surrounds the Earth and ultimately determines how another object within this field will behave. We can determine the strength of this field vector as a function of distance by equating the force that an object some distance away would experience (Newton’s second law) with the Law of Universal Gravitation:

Now that we have derived an equation describing the strength of the field vector at any point around Earth we simply need to determine the direction of the vector; but that’s easy, from our everyday experience we know that it is towards the centre of the Earth.

It therefore becomes clear that gravity extends out into space (and for quite a distance for that matter). So perhaps a better question would be one along the lines of why such an astronaut in orbit doesn’t just plummet back towards the Earth. The answer, funnily enough, is that the astronaut does fall down towards the Earth. They are in constant free fall, hence why it looks as if they are floating. But the reason why they never reach the ground (and subsequently stay in orbit) is because of their very large horizontal velocity.

The best way to visualise this is with Newton’s cannonball analogy. Newton pondered that if one were to build a tower that was tall enough to reach the space beyond Earth’s atmosphere, and from it fire a cannonball, then with enough velocity a stable orbit should be achieved. Analysing the images below, the first case is one where the ball would just be dropped from the tower. The second would give it some horizontal velocity, but not enough. The force due to gravity would eventually bring it crashing back to the surface. The third however represents the case in which the velocity is just great enough such that the cannonball travels to the side faster than it falls towards the Earth. Essentially it will end up following the curvature of our planet, and since there is no atmosphere to slow the cannonball it will continue following this path indefinitely. Any velocity greater than this will lead to an elliptical orbit.

In hindsight, it is obvious that the idea of pressurisation and the feeling of weightlessness are independent. But before we write off the scene in which Ripley collapses to the ground after gravity has been ‘turned on’, let us analyse the use of artificial gravity in another famous piece of science fiction, this time from Hollywood.

Stanley Kubrick’s ‘2001: A Space Odyssey’ is a masterpiece. I mean who doesn’t get chills when the artificial intelligence, HAL, responds to Dave’s request to open the doors with “I’m sorry Dave, I’m afraid I can’t do that”. Nevertheless, the movie is great not only for its fearful portrayal of A.I. but also for its scientific accuracy regarding artificial gravity. The centrifuge (or rotating deck) that is located on one end of the Discovery One spaceship allows the astronauts on board to simulate gravity. Let’s have a look at how.

The feeling of weightlessness in orbit is achieved because there is no normal force (or contact force) pushing back against the force of gravity. On Earth the ground serves this purpose, however in orbit you remain at a fixed radius meaning that your direction of motion is always perpendicular to the centre of the Earth. The interesting thing is that you can feel weight even in the absence of gravity. The only thing you need is some force to stop you from travelling in your direction of motion.

The genius behind the centrifuge idea is that you can have a rotating cabin (whether or not you are in a gravitational field) which will try to fling you towards the edges, but obviously the edge of the cabin will push up against you (as you to it). Imagine a doughnut (or donut) that has had its insides removed. Also imagine that you are the size of an ant and that you live inside this hollowed out doughnut. Now the genius is that the floor should actually line the side of the doughnut (so that you would be upright if it were to be turned on its side and rolled). Now replace that idea with a real centrifuge (that spins) and you can produce an apparent weight. This video does a great job to highlight the point:

The physics behind this idea is also quite simple – simple enough to do right now. What you would want to do is equate Newtons second law with the centripetal force. Note that a centripetal force is just a force that makes a body follow a curved path. For objects in orbit the centripetal force would be the gravitational force of the Earth, but another analogy is the swinging of a ball connected to a string (or a bola). If you swing the ball overhead while keeping your arm in the same position then the tension in the rope acts as the centripetal force.

 From the equations we see a dependence on angular velocity w (velocity of rotation) and the distance from the centre:

Note that in this particular case g is apparent gravity that an astronaut would feel. Also note that as R approaches zero (say you climbed towards the centre of the centrifuge) then g also approaches zero… so at the centre you would feel weightless again!

The brilliant thing about this equation is that you can set any value for g that you want. If you were to remain at the edge (fixed radius, R) then changing the rate at which the centrifuge spins will (angular velocity, w) would allow you to set any value of gravity. For example if you wanted to maintain a value of 1g and the radius of your centrifuge is 10 metres, then:

This works out to be around 3 rpm (revolutions per minute).

Interstellar manages to pull off the same trick quite nicely here:

So after all that, we have finally come up with a mechanism to produce a sort of artificial gravity anywhere in space. All you need is a bit of angular velocity and you are good to go. But it doesn’t look good for Ripley over in Sevastopol station. The station itself is actually a very large satellite in orbit around a gas giant, KG-348. The sort of artificial gravity depicted there seems to come about from some sort of vague notion about manipulating space and fields and…. hold up, this sounds quite familiar. And familiar it is. With all the buzz around gravitational waves lately perhaps we should look towards Einstein’s greatest theory instead of Newton’s reliable but much simpler model.

Could General Relativity, a geometric (and field?) theory about space-time and gravity, lead to the possibility of inducing artificial gravity by manipulating fields directly, no spinning required?

Stay tuned.