Gravity. It’s what keeps us held to the surface of the Earth and provides a sense of up and down. When we venture into space and orbit the Earth, or some other world, the force of gravity precisely cancels out with the centrifugal force. The sudden and stark absence of any forces acting upon your body is known as weightlessness. Your body has literally entered a state of perpetual and stomach-churning free-fall. Most humans can adapt to this nausea after a few unpleasant hours, but many biological functions of our body are hardwired for gravity thanks to billions of years of evolution here on the Earth. the muscles used for standing posture and skeletal support are no longer used and thus atrophy losing up to 20% of their mass after a week. Astronauts on the International Space Station need to exercise for at least two hours every day to combat this muscle loss. But without gravity our bones also wither with astronauts losing 1 percent of their bone mass each month. The breakdown of bone within our body saturates our cells with calcium, leading to dangerous calcification of soft tissues. If we want to live in space for years or decades without severe medical interventions or genetic modification, some form of artificial gravity is going to be needed. In science fiction, artificial gravity is ubiquitous, mostly to save money on special effects. The explanation for this is usually something like gravity plating – a wholly fictional technology. But how could we do this for real? The simplest way to create artificial gravity in the real world is just to accelerate in a straight line. If you were inside a spacecraft that was not just moving but accelerating at 1g, your inertia – which is to say your resistance to motion – causes you to be pushed against the back wall with the same force as that which the Earth pulls you down right now as you watch this video. In fact, Einstein postulated that the effect is so similar that there is no experiment you could possibly do on board that spacecraft to distinguish between being in a gravitational field versus just accelerating. In other words, inertial mass and gravitational mass are equal, something famously known as the equivalence principle in general relativity. This sounds promising, but accelerating at 1g for months, years or decades would require engines with vastly greater sustainable thrust than any modern space vehicle. The N star ion thruster is probably the closest example we’ve ever built of such an engine. NASA’s Dawn spacecraft which visited Vesta and Ceres used three xenon ion thruster engines to sustain a record-breaking constant acceleration of just under 10 millionths of a G. It was an impressive technological feat but it is a long way of providing useful artificial gravity. Is there any other way of generating artificial gravity then? The only other proven physics to do this is rotation. When a car turns a corner you feel yourself pulled to the opposite side – that’s the centrifugal force. Another example is a fighter pilot pulling a hard turn causing a centrifugal force several times that of Earth’s gravity, or several G, so strong in fact that it can cause a human to black out. These forces are what physicists call fictional. Like the case of linear acceleration, they are just the products of our inertia. They are not fundamental like electromagnetism, for example. Your body’s matter will not change velocity unless acted upon by a force and so if the aircraft around you moves to one side you will not because of inertia, and so you find yourself slammed into the wall. But what if the wall wasn’t a wall, what if it was the floor? Take a giant merry-go-round and spin it fast enough and the occupants would feel pushed against the interior wall. If you did this in orbit, where there are no other net forces acting, that centrifugal force to the wall would mimic gravity. You could stand on the wall, feeling the same downward force but Earthlings enjoy. The idea of a spinning habitat in space is arguably the most plausible way in which humanity might mimic gravity. It’s an old idea too, toyed with in fictional tales such as Rendezvous with Rama, Babylon 5, Interstellar and The Expanse. There are quite a few different proposed concepts for achieving this with real-world physics but today we’ll focus on two foundational concepts that have been the most influential – the O’Neill Cylinder and the Stanford Torus. We’ll start with a cylinder concept, proposed by Princeton physicist Gerard O’Neill in his 1976 book, called The High Frontier Human Colonies in Space, O’Neill laid out a strategy for the colonization of space through asteroid and lunar mining, which included the construction of a five mile diameter spinning cylinder with a length of up to 20 miles. The inner wall of the cylinder would serve as the floor for the inhabitants providing up to 300 square miles of livable area – this is about the same land area as New York’s five boroughs. O’Neill wasn’t afraid to dream big describing a habitat for millions of people with a total mass of several billion tons. Today it costs about twenty thousand dollars per kilo to launch into low-Earth orbit, which means that the dry mass of the cylinder would cost about a hundred thousand trillion dollars in launch costs alone. That’s about a thousand times the world’s current GDP. A more realistic plan would be to build most of the habitat in space through lunar or asteroid mining facilities, which of course necessitates that those industries exist firs. Even so, a space-based construct of this scale would be so expensive that likely only the very wealthiest members of society could afford to live above the clouds. You would notice a few things that are quite different on board. Tilt your head up and you could see the curvature of the cylinder and even see your cohabitants hanging upside down above you. Air pressure and gravity might be reduced compared to that of the Earth, in order to save upon the cost of spinning of the cylinder and material strength for the walls. And the artificial gravity generated by rotation would depend on your altitude, as you ascend towards the slanders rotational and the gravity would drop off until eventually reaching zero, perhaps giving you the chance to enjoy low gravity sports near the axis. The Stanford Torus was the product of a NASA sponsored summer workshop held at Stanford University in 1975 around about the same time that O’Neill published his book on the cylinder concept, indeed O’Neil was the technical director of the Stanford study too. “This is torus the concept that has evolved from the work of these teams of scientists and engineers. They believe the huge space colony could be built before the year 2000.” The torus is again a spinning structure to give the artificial gravity needed for comfortable living. Unlike the cylinder only about 1/2 of the interior wall is now usable land. This could be seen as an advantage since now you have a potentially natural-looking sky, rather than a mind-bending landscape of the cylinder imposes. The diameter of the torus is not grossly different from the cylinder and about one kilometer with an inner tube diameter of about a hundred meters or so. This gives a living area of about one third of that of Hell’s Kitchen, certainly far smaller than that of the cylinder. But the smaller design saves on materials, coming in at about 100 times less mass. Compared to the O’Neill Cylinder, this would decrease the overall cast by an order of magnitude, but it would raise the cost per square foot by about the same factor. Living on board one might enjoy joking a couple of laps of the three-mile rim or staring out to the warped horizon at your neighbors down the torus. When you need supplies you might venture down the torus spokes to a central hub which experiences far weaker centrifugal forces enabling low gravity manufacturing or easy docking with supply ships. When we retrospectively look at these designs they sadly remain as fantastical today as they did during their inception in the 1970s. Although we have access to better materials and reduced launch casts that sheer size of these structures means that they are far beyond our economic capabilities, or indeed our collective will in the foreseeable future. So why are both of these structures so large? Could we build a much smaller rotating structure today, enough for a few astronauts maybe – just to demonstrate a working example of artificial gravity. Putting aside the issue of shape, cylinder or torus, an architect has two basic dials that they can control in designing a centrifugal artificial gravity structure these are the rate of rotation, omega, and the radius of rotation, R. Clearly, to reduced costs, we would like to use the smallest R possible since surface area, and thus cost, should scale roughly linearly with this term. As we make R smaller we need to spin the habitat faster in order to recreate the required gravity. This is because the centripetal acceleration equals R multiplied by omega squared, thus making the habitat 4 times smaller in diameter requires a spin rate twice as fast. Even ignoring the effect on human occupants rapid spin rates are generally non-desirable, since they make docking with the station more challenging and require more energy to enter and exit the rotational frame. This raises the possibility of humans living in reduced gravity, perhaps equal to that of Mars, or even the Moon. Research by Harris et at have shown that accelerations below lunar, about 1/6 of a G, make it difficult for humans to have a sense of up and down and remain balanced, so this is likely to be a good lower limit. On the other side, anything above 1G is generally uncomfortable for humans with 4G leading to complete blackout for example – so putting these together gives us the following comfort zone for possible combinations of R and omega. Although a small rotational radius reduces the costs it also diminishes the usable living space and even head space onboard. Clearly, radii a less than typical human heights would be a poor choice causing the inhabitants to constantly crouch and experienced no downward force in their heads but strong forces at their feet. In other words they’d experience a tidal force of 1G. There isn’t much research about how much tidal acceleration humans find comfortable but a reasonable guess might be an order of magnitude less tidal acceleration than centripetal, which would constrain our to be at least 17 meters for average human height. A 17 meter radius habitat rotating a very fast rates would indeed mimic Earth-like gravity if the occupants were completely stationary inside, but any movement inside and they would feel an additional force that we do not notice here on the Earth – the Coriolis effect. Artificial gravity of a centrifuge is not the same as that of linear acceleration, recall that Einstein argued that linear acceleration is indistinguishable from gravitational acceleration but this is not true for a centrifuge. There is no equivalence principle here and the occupants of an O’Neill cylinder, or Stanford Torus, could indeed design experiments to realize this. The acceleration felt by a crew equals the following, where the first tterm is the centripetal acceleration upon the crew, and the second term is the Coriolis acceleration and that last titerm there is linear acceleration. If the station isn’t linearly accelerating then we just have those first two terms. If you are perfectly stationary r dot, which is velocity, goes to zero and thus you indeed experience a perfect reproduction of gravity. But any movement – r dot – in a direction perpendicular to the rotation vector, described by omega here, will cause this second term to depart from zero and thus you would feel an acceleration normal to both of those ingredient vectors. That’s the Coriolis effect. Like the centrifugal force, this is what physicists would refer to as a fictional force – purely a product of living in a rotating frame of reference. Imagine a cannonball floating around the center of a rotating O’Neill Cylinder. Let’s give it a slight push so it starts to move down towards the edge of the cylinder. If we were watching this happen from the outside of the cylinder, through a window say, it would seem to travel in a straight line – which of course makes perfect sense. But now consider the same motion from the perspective of a person on the inner surface of the cylinder from their perspective the cannonball does not travel in a straight line but rather curves. That is purely a result of their rotating frame of reference though, and that curving is caused by the Coriolis effect. This effect even plays out here on Earth, affecting the path of winds in its spinning atmosphere or affecting the path of a thrown ball on a merry-go-round. The Coriolis effect actually has two different components on the inhabitants of a rotating cylinder or torus. The first is what feels like an apparent change in downward surface gravity, the vertical Coriolis if you will, and the second is a tipping effect and these deserve separate discussions. The direction of the Coriolis acceleration depends on the direction in which you move and the direction of the rotational axis, which is presumably fixed. More specifically, the Coriolis acceleration equals the cross-product of your velocity vector and the habitat’s rotation vector, meaning that it always pushes in a direction perpendicular to both vectors. So what does this mean? Well consider inside the habitat you have three directions of possible motion. If you move along the same direction as the rotation axis you would feel no Coriolis effect at all. So traveling hundreds of meters from one end of an O’Neill cylinder to the other is perfectly safe. For the Stanford torus case, this means that walking to either side of the torus corridor admittedly a smaller distance has zero Coriolis. This leaves us with two other directions that must experience Coriolis – one radial and one tangential. The tangential direction is probably the least concerning and leads to an apparent change in downward gravity. For example, if you walk along the O’Neill cylinder in a prograde sense, you effectively increase your overall rate of rotation, pushing you down harder into the floor and making you feel heavier. Walking the retrograde does the opposite and causes you to lose weight. In the case of the Stanford torus, this change in gravity happens when traveling along the three mile circumference instead. Now if we want to downsize these designs the question becomes how much change in surface gravity is comfortable. Research by Neste et al. in 2014 on human subjects show that people are not even able to perceive vertical changes in acceleration less than about 5% of surface gravity. The maximum tolerance is less well studied but certainly for a 1G system a 25% increase in gravity would start to become uncomfortable, based on centrifuge experiments by Cohen et al. If we take this as a maximum threshold, it leads to the following modified comfort zone when choosing R and omega. With motion along the rotational axis and tangential direction discussed, let’s finally turn to the issue of radial motion. In both the cylinder and torus, or indeed any centrifugal system for artificial gravity, this equates to the act of jumping up and down or equivalently ascending and descending to different decks. During these actions there is a slight change in the centripetal force itself, but by far the most destabilizing aspect for human occupants would be a tipping effect caused by the Coriolis acceleration. Dr Theodore Hall developed a nice way to visualize this by imagining dropping or throwing a ball vertically rather than landing at your feet it would curve to the side. In extreme cases, one can even throw a ball behind you and catch it in front as it whips around due to the Coriolis. This tipping acceleration has the effect of creating a perceived incline in the floor during vertical motion. A strong enough tip could cause you to stumble over while standing up or climbing ladders. A simple way to deal with this is to have a single deck with no ladders or staircases. Of course efficient use of space might demand the inclusion of multiple decks, here then elevators or carefully designed ladders for ascent and descent could be designed for this environment. Even so astronauts would likely need to be trained to stand up slowly when getting up. Perceived inclines of an 8% grade or higher would exceed the maximum slope of most ramps here on Earth. If astronauts stand up no faster than 1 foot per second this would place the following limit in our design specifications of a habitat which further constrains our allowed comfort zone. Coriolis isn’t just a problem for climbing ladders or standing up, it affects your balance even by turning your head from side to side. When you do this the inertia of the vestibular fluid inside your inner ear causes a slight delay between the motion of your head and the fluid within it. The fluid is then pushed back into place by pressure causing movement of sensory hair cells within the ear. Now if we do this on board a rotating spacecraft moving your head in one direction would lead to an increased downward force versus the other. That would slightly change the distribution of fluid inside the semicircular canals. This differential gravity may confuse our vestibular system and create a sense of nausea and sickness. The fluid itself also undergoes a small amount of vertical motion and thus would be pushed to one side by the tipping Coriolis effect. This raises the question as to how fast a rotation can we cope with before this becomes a problem and occupants experience nausea. In most proposals of rotating habitats, it is these effects of the Coriolis on the vestibular system – sometimes called canal sickness – which most strongly constrain the engineering design. These studies usually cite experiments on human subjects conducted here on Earth using slowly rotating rooms. A variety of studies come to agreement that at rotation rates below one or two revolutions per minute, subjects are able to complete complex tasks over prolonged periods. But above this spin rate, it takes humans days to adapt and beyond six rpm, people struggle to ever adapt. These experiments guided the design of the Stanford torus which aims to rotate at one revolution per minute in order to avoid canal sickness. But to recreate 1G of centrifugal force at just one rpm demands a very large radius almost a kilometer. Using this one rpm or slower constraint we can see that the comfort zone is greatly diminished and now it becomes clear why previously proposed rotational habitats need to be so vast and thus expensive. But it’s important to remember that these experiments do not recreate the environment of a space station because they cannot remove the Earth’s gravity. Typically the rotation chamber is oriented such that the spin axis is aligned with the Earth’s gravitational field lines the rotation rates are slow enough that the centripetal force is small and your sense of down comes from the Earth’s gravity – not the centrifuge itself. This change in orientation, chosen in order to accommodate the Earth’s gravity, means that the Coriolis acceleration act in perpendicular directions to that experienced by the crew of a rotating spacecraft. So imagine walking around the floor or moving your head from side to side both of which are lateral motions. In an O’Neill cylinder, the Coriolis accelerations act up and down during these activities, slightly affecting the apparent strength of gravity. In contrast for the rotation chambers used on Earth those same movements lead to a tipping Coriolis acceleration, trying to knock you over to one side. A study by Graybiel et al. using this exact set up finds that at 10 rpm even experienced test pilots are not able to adapt. At this rotation rate, walking across the room causes a tipping Coriolis acceleration of 0.3 G, making you feel like you’re walking a 30 percent grade slope. What’s more if the rotation chamber subjects jump up and down or stand up sharply, they would feel no Coriolis effect at all because that is oriented with the centrifuges rotation axis. This is again in stark contrast to the case of a rotational habitat in space. In conclusion the Earth-based rotation chamber experiments may be simulating a harsher environment than that experienced by our prospective astronauts, or indeed at the very least a very different environment. Simple lateral motions of the head and body should not result in tipping forces but this is generally what is happening in these types of experiments. This is important because in comparing lateral and vertical accelerations Nestia et al. found that humans have a higher sensitivity to horizontal accelerations than vertical ones. So these slow rotation room experiments are certainly worthwhile, but an upper safety limit of 6 rpm may be overly conservative this is very important because if humans can tolerate Coriolis accelerations at rotation rates of 10 rpm or higher then Coriolis forces no longer become a design limiting factor and much smaller feasible artificial gravity systems could be conceived. For these reasons let’s be optimistic and assume that humans can plausibly cope with 6 rpm environments which gives us our final comfort zone as depicted here. Let us finally turn to the question of shape and ask whether aside from the cylinder or torus could there be opportunities to further optimize our astronaut comfort levels at small rotational radii. Recall that when astronauts move along the rotational axis they experience no Coriolis effect accordingly one might be tempted to design a train like carriage hanging off a tether connected to a counterweight. As the carriage spins the occupants are pushed to the floor in their quasi 1-dimensional habitat simulating gravity. Such a design aims to provide the least exposure to Coriolis accelerations. But Coriolis is not the only thing we need to worry about in designing a safe environment. If this train were too long and thus massive the rotation axis is no longer the primary axis of rotation but instead becomes the intermediate axis. Rotation about such an axis is unstable and subject of violent tumbling as demonstrated on board the ISS with this T-handle experiment. During this tumbling motion the occupants would be thrown about the habitat in a clearly unacceptable manner. Tumbling can also occur for O’Neill cylinders. A cylinder has two principal axes of rotation – one along the length of the cylinder shown here in blue and another perpendicular to the ends shown here in red. O’Neill rotates his cylinder about the blue axis but that’s actually the smaller principal axis of rotation. Any slight disturbance to the distribution of mass inside the cylinder such as people moving around inside could lead to tumbling due to the rotational instability imposed. One could imagine pumping water around the cylinder to redistribute mass accordingly using thrusters or reaction wheels to correct for any perturbations or even using a second cylinder next door which counter rotates and that’s actually the idea that O’Neill originally envisaged. Finally, it’s worth noting that for the Stanford torus, things are much simpler this rotation actually occurs now around the primary axis and thus the structure should be far more stable. Could we see a demonstration of centrifugal artificial gravity in the near term? The ISS offers perhaps our best hope being a permanent station for space experiments. In 2011, Mark Holdeman and Edward Henderson proposed an ISS demonstration of a centrifuge as part of their grander plan for a space station called Nautilus X. A small rotating torus would be attached to the ISS recreating partial gravity at an estimated cost of 100 million dollars. Sadly this concept went no further than the initial drawings though. A few years prior in 2005 Kirk Sorensen argued that the simplest path would be a habitat attached to a more massive counterweight via a tether spinning sufficiently fast to recreate artificial gravity in the lower mass object. Sorensen pointed out that by making the tether retractable the gravity on board could be controlled at will much like how an ice skater can extend his or her legs to control their rate of spin. The habitat itself could perhaps be something like the NASA trans hab concept with several decks and a higher decks featuring weaker artificial gravity. This is about where things stand with no concrete plans for a space-based artificial gravity experiment on the horizon. Long term human presence in space environments will at some point need to solve this problem either through engineering or biological solutions or perhaps a combination of the two. Let me know down below what kind of design you are most excited about to simulate gravity and whether you think this should be a priority for NASA and other space agencies in the near future. Thank you for taking the time to watch this slightly different video from us here at the Cool Worlds Channel. Let me know if you like these styles of videos and as always thank you for watching, stay thoughtful and stay curious.