# Space elevator off Europa without running into a nearby moon?

Would it be possible to build a space elevator off Europa?

(The space elevator would only be for the purpose of getting items out of Europa's gravity well relative to Jupiter. At that point, the items would still be in Jupiter's gravity well.)

Length of the elevator:

My first concern was with how long the elevator would need to be. My understanding is that a space elevator on Earth would need to go past the geostationary orbit of Earth. I take it that the same would hold true of building a space elevator on any body...perhaps on Europa we could call this distance the "Europastationary orbit."

It looks like the nearest that any other moon would pass to Europa is Io at 150,000 km. So the "Europastationary orbit" would have to be considerably less than that in order to not be majorly perturbed when Io passes Europa.

To calculate the "Europastationary orbit":

Europa's orbital period around Jupiter is 3.5512 days, and it's tidally locked, so I suppose "Europastationary" orbit would have to be whatever orbit allows a body to orbit Europa every 3.5512 days as well.

The orbital period in seconds is: 3.5512 days x 24 x 3600 = 306,823.68 sec.

The mass of Europa is 4.8 x 1022 kg.

So, I think that using Kepler's Third Law, I can calculate the orbital distance needed: $$a = \sqrt[3]{GMT^2 \over 4\pi^2}$$

(where $$a$$ is the orbit's semimajor axis, $$G$$ is the gravitational constant, $$M$$ is the mass of the more massive body and $$T$$ is the orbital period)

Which reduces to the cube root of: (6.67 x 10-11) x (4.8 x 1022) x (9.4141 x 1010) / 39.47835 = 19,700 km.

Earth's geostationary orbit is 42,000 km and Europa, having less mass, should yield a smaller number, so maybe I calculated that correctly.

42,000 km is a lot less than 150,000km so maybe we're safe from Io.

Are there any other physical constraints what would be problematic? Or is anything about my understanding/calculations wrong?

I'm not overly concerned with how much it would cost.

• I'm inclined to believe this won't be stable, whether point in, toward Jupiter, out (toward Callisto's orbit), or forward or backward along Europa's path. Too many big moons, too close together, too nearly resonant. Forward or aft might be maintainable, with a big enough station-keeping budget. – Zeiss Ikon Jan 2 at 18:30
• I think tidal effects from a Jupiter will be a big problem. The top of the elevator will feel a significantly stronger pull from Jupiter when it’s on that side of Europa than when it’s on the far side. – Mike Scott Jan 2 at 18:31
• @MikeScott you're forgetting Europa is tidally locked. Jupiter will always be stationary relative to the tether, so the tidal forces from Jupiter will always be static. – Morris The Cat Jan 2 at 18:40
• @MorrisTheCat You’re quite right, and I am quite wrong. – Mike Scott Jan 2 at 19:24
• Why would you want a space elevator on Europa? It is an airless world, so constructing a mass-driver is trivial. Considering the much simpler construction, the total circumvention of tidal issues and the vastly superior scalability and throughput, makes justifing the construction of a space elevator hard. – TheDyingOfLight Jan 2 at 21:28

As far as I can tell, your math is correct. One item of significance is that the counterweight at the end of your tether is generally going to be quite a bit further out than Europastationary orbit, probably by at least a third. This is because you want your transfer station to be right at the stationary point, but you want the center of mass of the entire system to be further out than that, which means your counterweight+cable extending outward from the transfer station needs to be more massive than the transfer station and the cable leading down to Europa's surface.

All of that having been said, it's not orbital collision that you need to worry about at all, it's tidal forces of the other bodies in the system. Io's orbit doesn't need to intersect with your elevator at all to cause problems, it just needs to cause enough tidal force to disrupt the orbital equilibrium of your elevator.

Now, I don't have the L337 Math Skillz to prove it, but I THINK the solution lies in placement of the elevator to leverage Jupiter's gravity as a stabilizing influence. Since Europa is tidally locked, that means Jupiter will likewise be stationary relative to both the transfer station and the counterweight. Intuitively you would think that you would want the tether to hang directly towards Jupiter, but I think the ideal configuration would be to have it hand directly towards one of the Jupiter/Europa Lagrange points. This would effectively leverage Jupiter's gravity to keep the tether taut.

This, by the way, is the proposed layout for putting a Space Elevator on Earth's moon, which is a similar orbital configuration. Doing this on Europa would be a lot more complicated because of the other Gallilean moons, but Jupiter might be throwing enough mass around to stabilize things.

You would just need to build in some additional strength to allow the tether to absorb the tidal forces of Io's passage without breaking.

• Thanks so much for your answer; makes a lot of sense. I was picturing the elevator going through the L1 LaGrange point, but now you have me thinking that L4 or L5 would be better, as that would minimize the amount of tidal forces that Io and Ganymede have on the tether, as well as make those tidal forces be roughly the same on different parts of the tether, instead of them being vastly different stronger at one end. – levininja Jan 2 at 19:02
• @levininja As long as you make sure that the (stable) tidal effects of Jupiter's gravity are greater than the (transient) effects from Io and Callisto, you should be ok, I think. – Morris The Cat Jan 2 at 19:09
• @levininja you can't use the L4 or L5 points as you won't be able to tension the cable. Europa's own gravity will just pull it back down onto the surface. – Starfish Prime Jan 2 at 19:36

My main concern is that the synchronous point and counterweight (which you haven't considered, but will be even further out) of your elevator cable is not going to be within Europa's Hill sphere or its gravitational Sphere of Influence. That means it will be orbiting Jupiter, and anything that orbits Jupiter further away than Europa does (or closer, for that matter) will be travelling at a different speed to Europa. That means your tether will bend and flex and then Interesting Things will happen... perhaps it falls into a messy (and probably decaying) partial ring around Europa, or maybe it sort of whips back and forth. Neither is a desirable state for an elevator.

You might think that you can run your elevator out to a Lagrangian point... after all, speculative Lunar space elevator designs do just that, running out to the L1 and L2 points. Unfortunately the Jovian system is busy enough that the Jupiter-Europa Lagrangian points end up being too close other moons at very regular intervals... Io, Europa and Ganymede are in a 1:2:4 orbital resonance, so there's a close encounter every orbit or two. Not enough to destablise things immediately, but enough to cause problems, especially over time. You may be able to fix this with the application of a generous amount of station-keeping thrust, but this is likely to be expensive in terms of getting power and reaction mass up to the counterweight.

Similar issues apply to the L4 and L5 points which will also be regularly tweaked by both Io and Ganymede, but with the additional issue that keeping the cable under tension will be challenging (as there's probably no stable point to place a counterweight) and you'll find that Europa's own gravity will tend to slowly haul the cable in until the endpoint falls into a death-spiral orbit.

You might consider other means of acheiving orbit, such as a skyhook, space fountain or even a launch loop and its larger cousins, orbital rings which will be much easier to build in a vacuum and around a body with gravity as low as Europa than they are around Earth. Even simple laser-driven steam rockets and electromagnetic catapults would do the job.

For a non orbit-mechanical issue, remember that the radiation environment around Europa is punishing. The Europa Clipper mission involves a probe with a hefty aluminium and titanium radiation vault to keep the radiation-hardened electronics in reasonable working order, and an orbit that takes it out of Jupiter's radiation belts and then back in for a close encounter with Europa so as to minimise time in the "death zone". This will be a serious risk for your elevator climbers and station-keeping hardware, let alone any fragile meaty cargo your elevator might have to carry. The same issue will apply to other launch mechanisms than elevators, with the possible exception of a buried electromagnetic catapult (but that only handles launching, not landing).

• This might be a feature, rather than a bug. If you position the elevator such that Jupiter is trying to pull the tether directly AWAY from Europa, that actually fulfills the function of the counterweight in terms of keeping the tether taut. Consider a configuration where the tether extends outwards from Europa at an angle so that the transfer station trails behind Europa. The counterweight will WANT to orbit Jupiter more slowly than Europa does, but is being pulled along by the attachment. This keeps the tether taut, which is the whole point. – Morris The Cat Jan 2 at 19:15
• @MorrisTheCat the problem is that there's a fairly tricky balancing act in keeping the tether taut without altering the orbital speed of the counterweight. The fact that counterweighted elevators are simply not proposed for tidally locked bodies, or those with small SOI (like moons) should be a big red flag here. – Starfish Prime Jan 2 at 19:26