A Space Elevator… On Jupiter?
A 100% Original Concept.
I have to come clean. When I was first contemplating writing a post on Medium about space elevators, I was going to do it on the applications and uses of Earth-based space elevators. However, after less than an hour of research, I discovered that this topic had already been pretty well explored, and had no need for my largely speculative, opinion-based input on the subject. I still wanted to do a post about space elevators, but I wanted to do something new.
So I pondered the construction of space elevators on other planets and moons of the solar system, of which I found to my dismay, has also been very well researched and documented. Space elevators on the Moon can be constructed to Earth-Moon Lagrangian points where the Earth’s and the Moon’s gravity cancel each other out, and Mars space elevators are so practical that they could be constructed with today’s technology and materials, due to the planet’s low gravity and still relatively fast spin rate.
I felt pretty useless. I thought to myself, “What other rocky planets or moons are left in the solar system which could utilize the practical applications of a space elevator?!” And then I changed the question. “Why does it have to be a rocky planet?”
Space vessels of the future will likely have to use low mass, non volatile fuels in order to achieve maximum exhaust velocity and thrust. An example of such a spacecraft would be a ship that uses a fusion drive, combining two isotopes of hydrogen, deuterium and tritium, into helium to achieve thrust. Deuterium and tritium are fantastic fuel sources for future spacecraft, but we don’t find them often on Earth due to the fact that the Earth’s gravitational pull is not strong enough to contain these low mass atoms.
Enter Jupiter. Jupiter is literally 9/10 hydrogen, and 1/10 helium. At this point I was thinking how it may be possible to design a space elevator to “scoop” some of Jupiter’s atmosphere at one end, and transport some of that mass up through the elevator shaft to an orbital station, far above Jupiter’s atmosphere, to serve as a refueling depot for interplanetary (or maybe even interstellar) spacecraft.
This application could probably be used on any of the gas giants, but Jupiter is simply the closest and most practical selection. When you travel farther out of the solar system, you’ve already escaped most of the gravitational potential energy of the sun, at which point an interstellar traveler may ask themselves why they used so much fuel to slow themselves down to Neptune’s orbital velocity, only to have to speed back up again to continue on their voyage.
A traditional space elevator consists of four main constituents; an anchor to serve as a base, an orbital station (or massive object) to serve as a counterweight, a shaft or tether which connects the two, and a climber, or elevator car, which ascends and descends the shaft. A space elevator must be designed in such a way that the center of mass of the entire structure orbits at geostationary orbit, so that the centripetal force of the counterweight exactly equals the force of gravity on the anchor, which is fastened to a planetary surface. The tether is always in tension, so the elevator induces no weight on the Earth, and the orbit requires no extra energy (beyond maneuvering thrusters) to keep the space elevator stable.
Designing a space elevator to be operational within Jupiter’s atmosphere will be quite different. Because Jupiter has no solid surface, the “anchor” will have to be an atmospheric structure, staying aloft with the tension of the cable, and aerodynamic forces. Jupiter’s lack of a solid surface also means that it technically has no geostationary orbit. This does not prohibit the construction of a space elevator however, as long as the center of mass orbits Jupiter in a stable, circular orbit. This is the same concept as extending cables of equal mass out of either end of the ISS, one towards the Earth, and one away from the Earth. The center of mass will always be the ISS, so it’s orbit will continue to be stable. That is, until the Earth-end of the cable hits the atmosphere…
This is where my space elevator deviates the most from that of a traditional design. Because one end of a Jupiter space elevator would always be in the atmosphere by design, that end will constantly be experiencing a backwards force, and because that force is only on one end of the space elevator, a resulting torque as well. This will require thrusts from both the anchor and the orbital facility to counteract this force-torque couple to maintain a stable orbit.
The design of the anchor could be similar to that of a ramjet thruster here on Earth, where supersonic hydrogen enters one end, is heated up using an array of microwaves or lasers, and then expelled at even faster velocities to produce the required thrust to counteract the drag from the atmosphere. Along the way, a percentage of this mass would be collected and sent up the elevator shaft to be stored in the orbital facility for the refueling station, and to be used for the station’s counteracting thruster. At first, I envisioned the anchor to dip down into Jupiter’s atmosphere where the pressure is the same as that on Earth: 1 bar.
The center of mass of the elevator would likely be orbiting relatively close to Jupiter’s “surface” (where it’s pressure is the same as that on Earth, 1 bar), potentially only a thousand kilometers or so above it. This means that the atmospheric velocity of the anchor will be enormous. To account for this, the anchor and elevator shaft must be designed with diamond supersonic airfoil cross sections. The entire length of the shaft will be comprised of several jointed sections, maybe a hundred meters in length or so each, to allow for flexibility in the design.
Finally, the orbital station simply needs docking ports to allow for refueling, and it’s own thruster to provide a counteracting torque to the atmospheric torque from before. The overall design concept can be seen below.
Crunching the Numbers
I knew right away that there were way too many variables to try and calculate all of this by hand, so I created a MATLAB program to help me iteratively solve for an optimum design. The first step was to set some defining characteristics of my elevator so that there weren’t so many variables. I used my vast array of engineering intuition to choose some initial parameters. These parameters with justification are included below:
- Orbital facility at 2000 km, where Jupiter’s atmospheric pressure is the same as Earth LEO (where the ISS orbits). This is a high enough altitude to allow spacecraft to refuel from, but also minimizes elevator length, saving cost on materials and construction.
- Supersonic drag coefficients of the shaft and anchor of 0.2 and 0.5 respectively, as supersonic drag coefficients are usually relatively low.
- Elevator shaft cross section is a diamond shape with a length of 10 meters and a width of 3.5 meters. This is large enough to allow for large payloads to be shipped up and down, as well as the masses of hydrogen.
- Anchor dimensions are 35*35 meter intake with a 100 meter length.
- 12 kg/s of hydrogen is collected to fill the refueling tank. This is enough to fill the Saturn V in ~46 hours, which seems fair.
The next step was to determine the drag force on the elevator shaft. The formula for drag force is as follows:
- rho = air density
- A = surface area in air stream
- C_D = Drag coefficient
- v = air stream velocity
Determining the drag force on the anchor is easy, because all of those parameters remain constant at a constant altitude, like an airplane. However, the elevator shaft less like an airplane, and more like swinging a bucket on a rope around you really fast. The bucket (orbital station) has the fastest velocity, while the rope’s velocity (the shaft) is dependent on distance from you, and has a slower velocity closer to your body. This is why solving for the drag force on the elevator shaft was so difficult. Literally every variable is changing. Jupiter’s atmospheric density gets more tenuous at higher altitudes, and the velocity gets faster closer to the orbital station.
Solving for Jupiter’s air density was, within itself, a problem because I couldn’t find any sort of model online that represents Jupiter’s atmospheric conditions. I had to actually invent my own formulas to model pressure and temperature based on data from Wikipedia, and then use the ideal gas law to solve for air density. Once I had all of these variables crunched, I could form an integral to solve for the drag on the cable.
Once I had the overall force of drag as an integral over height, I could determine the force and the torque that Jupiter’s atmosphere would induce on the elevator… Like swinging that same bucket from before through the path of a leaf blower that pushes it backwards. This would allow me to determine the force of the engines which would provide the counteracting thrusts to this atmospheric drag. This was a simple statics equation:
At first, I contemplated using an entirely separate engine to provide the thrust, like a fusion drive or a souped-up chemical rocket using some of the hydrogen that is collected. But then I realized that this anchor is already designed like a gigantic intake sucking in air like a ramjet, and all it would need to do is collect the hydrogen it needs for the orbital facility, and then heat up the rest of it like hell to increase its velocity out the reverse end to create a thrust. To determine this temperature, I would need to know the required exhaust velocity, and to determine that I would need to solve for the mass flow rate. Easy peasy.
“A” here is our intake area. Okay, so there is this small problem of not expanding my nozzle to the ambient pressure (Pe-Po in the equation), which will detract a bit from my overall thrust, but I ran a quick number crunch and found that it doesn’t affect it much when you’re talking about thrusts on the order of 10⁸ N (Yes, this is how much we may need). So for my intents and purposes, the thrust is really only the mass flow rate multiplied by the exhaust velocity. This would allow me to solve for an exhaust velocity and, in turn, the temperature of the “combustion” chamber assuming a standard ramjet configuration.
The chamber temperatures required for this “ramjet” are far above traditional ramjet engines here on Earth, so a different method other than combustion is required to heat the incoming air to suitable temperatures. At this point, there was only one solution; microwaves. But microwaves take power. To solve for power, you literally have to find out how to heat incoming gas traveling at ~40,000 m/s from about 200 K to >8000 K in the distance of the inside length of the anchor (maybe a hundred meters?). Yeah, we’re gonna need a powerful nuclear reactor.
Now we have a bucket spinning around Jupiter at hypersonic velocities screaming through the atmosphere and counteracting all forces with its own set of engines, transporting mass up a 2000 kilometer shaft to an orbital station to serve as a refueling post. This raises one more problem… Isaac Newton at his finest (or worst).
When you transport mass continuously up an elevator shaft, you induce a resulting force downward on the elevator structure. It’s not much (compared to the mass of the whole elevator), but it would be enough to destabilize its orbit over a few days or weeks. This could simply be counteracted by designing the anchor as an airfoil of sorts, at a small angle of attack to create an upward lifting force on the elevator to keep it stable.
Everything else was left to science. Then I ran the program several times with several different anchor altitudes to find which one yielded the most appealing results. Here are some examples:
First I tried with the anchor at 1 bar of atmospheric pressure, or 0 km. First note that the thrust is gargantuan, something on the order of 10¹³ N, or almost a million Saturn V rockets. Secondly, the mass flow rate is atrocious and would probably be enough to tear any sort of anchor structure to pieces. The exhaust velocity is a sizable fraction of the speed of light, and the combustion chamber temperature is hotter than the surfaces of blue giant stars. Finally, the required power to heat that chamber with microwaves and/or lasers is something like the output of 25,000 modern nuclear fission reactors. This is just silly. Obviously, the anchor needs to be higher up in the atmosphere where the drag will be lower.
After several iterations, I was most satisfied with my elevator’s parameters when the anchor was at an altitude of 237 km:
The thrust here is a bit high, ~5*10⁸ N (15 Saturn V’s), and the chamber temperature exceeds 8000 K by a fair amount (hotter than the surface of the sun), but many of the other properties are quite fair. The mass flow rate is below 2000 kg/s, which is not an unbelievable amount of stress on the anchor, and the exhaust velocity is within the range of theorized fission and fusion rockets of the near(ish) future. The power required to heat the incoming gas to the proper velocity is comparable to that of modern mid-sized fission reactors which power cities on Earth, and the atmosphere is still thick enough to collect enough fuel for our refueling post.
Is it feasible? Not with today’s technology, no. We’ll need to make a few jumps in propulsion, nuclear power, thermal control, and material science for this idea to become practical.
But is it practical? Quite possibly. If ships only had to carry enough fuel to get to Jupiter, instead of ferrying all of the fuel to get back as well, ships could be built larger and faster, in turn increasing their carrying capacity and range.
Finally, would it be cool? Hell yes it would! Just think of how awesome it would be to have a fuel-collecting mega-structure orbiting Jupiter at that low of an orbit! It would be a massive science and engineering feat. Furthermore, it would look awesome to approaching ships, like one of those weird floating cities from Star Wars on Bespin (only upside-down?)
Did I spend too much time on this project? Probably, yes. Thanks for the read!