People will live in Space. But our bodies need Gravity. How we can do it? Several concepts of artificial gravity were defined. I think that I might have just invented a new one. I called it the Konecny Space Station after myself. Just in case somebody once built it. It is quite simple. ;-)
The solution is not based on some “Startrek” weird technology or continuous acceleration by Epstein's drive of The Expanse TV Series. It is all based on the known high school physics. And it only works close to planets or moons, while people still being in orbit.
Why not use a wheel space station
A rotating wheel space station, also known as a von Braun wheel, is a concept for a wheel-shaped space station. It creates artificial gravity by its spin. The principle was well visualized in the Martian movie. However, a much larger and faster rotation would be required than how it is captured in the movie.
The centrifugal acceleration required for artificial gravity is derived as follows: a = Ω² * r. They are many limiting factors to the size and rotation rate. For example, if you start running in the opposite direction to the spin. You might lose the sense of weight, the floor would just rotate below you. The rotation would jeopardize our senses and we could quickly lose our balance.
David Kipping, principal Investigator of Cool Worlds lab from Columbia University, made an excellent Youtube video on this topic. Practically speaking, the minimum dimensions are a few hundred meters in diameter. The comfort zone is quite restricted.
So the spinning compartments in the Martian movies were not realistic. Stanley Kubric made a better job in the film 2001: A Space Odyssey. The space station in the film has 300m in diameter. However, it takes several thousands of tons of material to build a station of such size. For example, International Space Station (ISS) weighs about 420t and has 70m in size.
In film 2001, the space station spins once per minute, which would generate about 1.655 m/s2 ~ 16% of the 1G we do experience on earth. That is about the same as Moon gravity and it seems reasonable for the comfort of living in Space. We could build even larger cylindric space stations with kilometers in size, which would allow simulating 1G gravity. However, that could not be built without the capability of mining asteroids. What are the alternatives?
Tethered Space Stations
As the station rotation rate has to be slow, the radius needs to be large. That can be achieved by connected two parts of the stations or spaceships with a tether. They would act as a counterweight and spin around their combined center of mass. The tether can be a few hundred meters long. For example, two Starships in 1500m tether formation with 1 rpm could provide artificial gravity 1G.
It is a very simple solution for interplanetary travel, however not really feasible for space stations near a planet. It would be very difficult to embark on such a station and keep it stable. Could we use a tether a different way removing that limitation?
Planet Orbiting Konecny Space Station
Konecny Space Station is a type of non-rotating tethered space station. The orbital system is a coupled two-mass system. The upper part of the station (High station) is placed in an orbit around a celestial body such as Earth. The suspended station (Down station) at a specific height above the surface of the celestial body.
The joined bodies would revolve around the Earth with the same angular speed. The Down Station would be dragged by the gravity towards the Earth and the High station would be pushed outwards by the centrifugal force.
These two forces need to be balanced [a = (G* MassOfPlanet /r² ) — (Ω² * r) ]to keep the space stations connected via the tether stable. As a result, both stations would experience a constant acceleration (artificial gravity).
The acceleration direction would be towards Planet for the Down station and outwards for the High station. Hence people living in the High station will have a unique experience. They will look up standing on their feet to see Earth. It will be like looking through the roof window, but instead of just stars, you will see the mother Earth.
Earth-orbiting Konecny Space Station
They are many configurations, how this system could be implemented. Further from Earth, the High station is, higher G can be achieved. Less revolution per day means a higher pull towards the planet. Hence a higher acceleration can be achieved in the Down Station. See an example of acceleration [m/s²] depending on its distance for 10x revolution around Earth per day:
We can see that at 430km above Earth (~ISS high) we can achieve 4.81m/s2 (about 0.5G) for Down Station. To enjoy 1G, the High station would need to be about 13700 km above Earth's surface.
The angular speed is one of the key parameters to adjust. The following diagram provides an overview of three different speeds: 5x, 10x, and 13x revolution per day. Too small speed would require very long tethers. Higher speeds would reduce the pull to Earth. So the Down Station will need to be heavier than the High station. However, it would allow shortening the length of the tether for achieving 1G.
I made a few variants to find a solution optimizing the length of the tether to make the system technically feasible. The sweet spot seems to be 12.5 revolations per day with Down Station 522 km above Earth and High station to 2700 km. Both stations would be the same mass and experience about 0.27G. It is a bit less than on Mars, but about twice as much as on the Moon. It would mitigate most of the issues coming from the microgravity environment.
The tether would have 2178 km long. Do we have some material, which could keep a couple of stations together? Or is this concept doomed like Space Elevator?
Material for the tether
Luckily, it seems that we don’t need to wait for some magical materials like a carbon nanotube. Let’s have a look at Zylon the second-best material, which is actually generally available. It is a synthetic polymer material invented and developed in the 1980s. It has 5.8 GPa of tensile strength, which is 1.6 times that of Kevlar. Like Kevlar, Zylon is used in a number of applications that require very high strength with excellent thermal stability like tennis racquets, SpaceX Crew Dragon parachutes.
The breaking length of zylon is 379 km. This is calculated with 1G force pulling on the cable. So with lower pull, we could stretch the tether longer. That is our case. The tether will always pass through the point of zero-G, where Earth gravity and Centrifugal force equalize. We could have a Middle space station here. It would have microgravity and docking will be similar as nowadays docking to ISS. Equal mass will need to be send up and down. The position of the Middle would serve as stabilization element. By adjusting the length of the tether between stations & effective ion drives, we could keep the stations ligned and forces balanced.
The Middle station would be about 1470 km above the Earth's surface. So we have two parts of the tether, 1230 km to High Station and 948 km to Down Station. The maximum acceleration would be 0.27G at the end of the cables, where the stations are. The average is around 0.15G. That is about 6.5x less than 1G. So we could have cables up to 2500km long, which is about twice more than needed. So zylon material seems sufficient for the tether.
We would need to get it into the orbit of the Middle Station. So how much would 1230 km of zylon ribbon weigh? With a typical density of 1.55 t/m3 and s tether dimension of 30mm x 1.5mm, we would get to 85tons. That is well in the reach of the SpaceX Starship SuperHeavy Rocket. And with the cost of 20 USD/m (list price starts at £17.36/m), we would need 24.6 million USD for the bottom part and 19 million for the upper part of the tether. That is less than 50 million USD, which is very affordable. Each tether should withhold space stations of several hundred tons. It would be wise to use multiple ribbons.
The Down and High stations would be built using the Middle Station. The equal mass components of Down and High would be moved up and down respectively at the same time. So the centrum of gravity remains at the same spot, where the Middle station is located. People could work in the Middle station and live in either the Down or the High station. The climber would be able to reach the distance in a few hours.
Konecny Space Station at Mars
The same principle could be used on Moon, but Mars is much more interesting. The planet Mars has one big advantage: Phobos. It is a small moon with an irregular shape and means a radius of 11 km. It is just about 6000 km above the surface and one revolution around Mars takes 7hours and 39 minutes.
Phobos could serve as the High Station, more specifically as an anchor for the Down Station. The tether will hang down towards the planet. The change of the Phobos trajectory caused by Down Station will be negligible. The Down Station could be also very low — just above the surface due to the limited Mars atmosphere. For example 54km would provide 3.41m/s² (0.34 G) and people living there would experience almost the same gravity as being on the Mars surface.
What will be a benefit of such a low-hanging station? I can image also one additional huge benefit placing the Down station just above the surface. It would be moving only about ~550 m/s relatives to the planet's surface. This speed is comfortably achievable by a jet-plane/small rocket. So that kind of vehicle could hook to an extra tether below the Down station and being pulled in. So it would be very cheap to transport the material and staff from the Down station to the ground. Rocket engine will propel the plane up and it would glide down & land using its boosters.
Hence Phobos could serve as a space dock for interplanetary ships, which would not need to be designed for an atmospheric entry. The material will be transported down/up to the Down station using a tether climber. The climber could be electrically propelled. Hence it would reduce the cost of transportation dramatically, almost to zero. The climber would use its potential energy to charge batteries on the Phobos during its descent. And later use that energy & extra power from a solar array on Phobos to climb up.
Material going down might not be the same mass as the one going up. However, given the mass of Phobos (1.0659×10^16 kg), this system could serve for several centuries without changing the Phobos orbit trajectory much. The Mars colonization and terraforming could be very efficient. And the rocket fuel for intra-planetary ships could be made on Mars and with a little loss very effectively transported to Phobos for the ships refueling. We could explore the outer solar system with ease.