Simulating Different Gravity on a Planetary Body
Intro
What is it like to be under low gravity like the Moon? Only 12 people have ever known the answer to this question, and only 4 are still alive as of the publication of this post¹. No human has yet been to Mars. It may seem like a simple novelty, but therein lies an important question about human physiology. It is well-documented that long-term exposure to null-G (like that experienced in Earth's orbit) has deleterious effects on humans, some of which may be permanent even after returning to Earth. The duration of the Moon missions (Apollo) were relatively short (measured in weeks), so we don't have any long-term data for humans under Moon gravity.
So we know that humans do well at Earth-normal gravity, and we know they do poorly in null-G, but we have no idea how humans fair anywhere in-between. This represents a huge gap in knowledge as well as a point of high risk when considering long-term missions to Mars*. Even though gravity on Mars (about 1/3 Earth gravity) is higher than that of the Moon (about 1/6 Earth gravity), we can't make any informed statements about how humans will fare.
It is primarily for this reason that the prospect of simulating lower gravity while on Earth is so enticing. If we were able to, we could conduct plenty of controlled experiments to get data on how gravity affects human physiology as well as how much gravity is really needed to maintain adequate health.
In the following sections, I will cover higher gravity simulation as well as potential options for lower gravity simulation.
Simulating Higher Gravity
The Gravitron
On a planetary body with a given surface gravity g, it is a relatively simple task to simulate higher gravity (g+). In the same way that a centrifuge spins samples to speed-up stratification/flocculation or how the Gravitron (the amusement ride) forces patrons against the wall, a large funnel can be spun such that the acceleration due to the normal surface gravity is balanced by the centrifugal acceleration of the spinning funnel to the extent that the resultant acceleration vector is perpendicular to the "plane" of the funnel and of a greater magnitude than the normal gravity. The higher gravity that needs to be simulated, the faster the spin and the steeper the angle of the funnel for a funnel of a given size. Functionally, this can work for any level of simulated gravity needed for human purposes. These simulation machines can be as small as a room or as large as a city (or larger).
Simulating Lower Gravity
Falling
Most of us have experienced the effect of lower gravitational acceleration at some point or another: when we begin to descend in an elevator, when we careen down a roller coaster, when we experience turbulence in an airplane, when we drive fast over the summit of a small hill. In each of these circumstances, the net acceleration on ourselves is lowered. The effect is however limited by time; there is only so far to fall after all. A notable example of falling used as a means of lowering gravity is the reduced-gravity aircraft or, more popularly, the Vomit Comit. These aircraft follow parabolic trajectories with the affect being the apparent reduction of gravitational acceleration in the cabin. These aircraft can simulate Null-G as well. No matter the means, falling-based methods of simulating lower gravity suffer from their inherent short timeframes. If longer-durations are desired, then other methods of gravity reduction would be required.
High Altitude
Since the effect of gravity diminishes with the square of the radius, higher altitudes experience lower gravity than lower altitudes above the surface of the planetary body. For example, at a static location (relative to the ground) 2,625 km above the surface of the Earth, the gravity experienced should be half that experienced on the surface. However, this is very high (over 41% of the radius of the Earth). If we wanted to build a structure this tall, we couldn't because a compressive structure that tall is impossible with known materials. It's also interesting to note that if this "static" location were to be connected to the surface, it would rotate at a high altitude and a 24 hour period, which would slightly reduce the effect of gravity experienced an additional amount. There are a few structures that might theoretically be able to achieve this feat: the space elevator/tether², the orbital ring³, and the space fountain⁴.
The space fountain and the orbital ring use active support (moving mass that provides energy, rigidity, and stability to the system) to keep them aloft, while the space elevator/tether uses a counterweight that goes beyond geosynchronous orbit to keep it stable via tension. I will not dive too deeply into these concepts and will instead focus on the gravitational implications. If a structure were connected to the surface of the Earth and extended to these extreme altitudes, various levels of gravity could be experienced. For structures connected to the Earth, the practical height limit for this purpose is geosynchronous orbit (35,786 km), because any Earth-tracking structure built beyond that will begin to have a centrifugal acceleration that overpowers the gravity of the planet, and objects will start to float away instead of towards the planet.
Another method for using altitude to experience lower gravity is to use constant propulsion. A vehicle at an extremely high altitude could engage its engines toward the planetary body such that the accelerations balance out and the vehicle is stationary. This approach is more fuel efficient the higher the altitude (lower the gravity). If the vehicle was lightweight enough and/or had plenty of fuel, it could remain at that altitude under the diminished gravity for quite some time before either running out of fuel or being refueled. This might represent the most straightforward and inexpensive approach to using altitude to simulate lower gravity, though the propulsion would be completely wasted when the propulsion could be used just as easily to make a real and useful journey.
The Inverted Gravitron
It may seem to some that lower gravity can be simulated by using an inverted funnel based on the design of the aforementioned Gravitron-like machine. After all, the outward spin should reduce the acceleration experienced†. Under the same conditions however, this does not work because the resultant force vector will never be perpendicular to the plane of the funnel. In fact, the faster this inverted funnel spins, the further the resultant vector will be from perpendicular, causing the occupants to be forced off the sides of the machine. There is however a solution to this problem.
So far in these Gravitron diagrams, the direction of surface gravity has always been parallel to the axis of the machine's spin. By definition, this would disallow the inverted funnel device from functioning under any spin whatsoever. However, if the machine were much, much larger, the planet's surface gravity vector would no longer be parallel with the axis of spin, and such a spin could result in a acceleration vector that is perpendicular to the plane of the funnel. What's more, the magnitude of this acceleration vector would be less than that of the surface gravity because the centrifugal acceleration would neutralize part of the acceleration due to surface gravity. In other words, lower gravity is successfully simulated.
There is a limit to this. The lowest gravity (highest reduction) that can be simulated is constrained by the size of the machine. The smaller the machine, the smaller the gravity reduction. Since these structures are truly huge the gravity reduction limitations can best be described geometrically using the following diagram.
Example of an inverted gravitron circumscribing a planetary body at the 15 degree latitude
The vertical axis represents the axis of spin for the machine, while the horizontal axis represents the plane of the centrifugal acceleration vector for the machine. The green vector in the lower left represents the direction and magnitude of the center of gravity for the planetary body (the angle A between the horizontal axis and the gravity vector is equal to the geographic latitude where the machine is located if the machine's axis and the planet's axis are parallel), while the blue vector to the right along the horizontal axis represents the centrifugal acceleration of the machine. The orange vector shown between the other two is the resultant force vector. For a given target acceleration, there is a minimum latitude that the machine must circumnavigate in order to achieve it, which is given by drawing a horizontal line from the base of the circle representing that acceleration to the edge of the circle representing the surface gravity; the angle A represents this minimum latitude required. This could be calculated in reverse too: given a certain latitude, a line could be drawn from the center to the outer circle at that latitude's angle, and a horizontal line could be drawn from that intersection to the vertical axis; the distance from the center to this intersection represents the minimum simulated gravity possible for that latitude (size of machine). For example, a machine that is capable of a maximum 25% reduction in apparent gravity would be capable of simulating a 0-25% reduction by modifying its rotation rate and platform angle relative to the local "plane" of the planetary body.
If the latitude of the machine were to equal to 0° (circumscribing the equator like a belt), then null-G would be possible. In this instance (on Earth), the machine would be travelling at orbital speed (for an altitude of zero), rotating at more than 28,000 km/h with a rotational period of 85 minutes. This represents the fastest a machine like this would spin on Earth. For comparison, a machine the size of the continental United States would only be able to simulate about 97.2% of Earth's gravity and would travel at 6,662 km/h with a rotational period of about 85 minutes‡.
Needless to say, the construction of a machine of such large size is prohibitively expensive from both a cost and politics standpoint. It is safe to say that the collective will for such a technical capability will never be worth this cost. In fact, it will in all likelihood be much cheaper to simply fund perpetual round-trip missions to the Moon and Mars and perform on-site testing of any kind.
Conclusion
Simulating appreciable lower gravity on Earth is hard, especially in comparison to simulating higher gravity. Aside from our occasional short forays with the Vomit Commit, it is unlikely that we will ever have perpetual low-gravity simulators on Earth, especially since it would likely be far easier and more versatile to use rotating habitats to simulate any gravity desired. In the far future, however, lower-gravity simulation might be gainfully accomplished with rotating rings around massive planets like gas giants or super-Earths in order to provide a comfortable level of gravity for our distant descendants.
* Launch windows for the trip to Mars open only every 26 months or so.
† Technically, the spin of the Earth reduces the weight of objects at the equator by about 0.344%.
‡ This is over five times the standard speed of sound.
