Tethering Titan

7 03 2018

There are two types of space elevator. This may sound a little counterfactual, given that, to our knowledge, there are currently zero types of space elevator; but I’m speaking, as you may have surmised, in a conceptual sense.

The first type of space elevator, which plays off gravity against orbital angular momentum, requires a reasonably rapidly-revolving terrestrial planet. Now, ‘reasonably rapidly revolving’ is a somewhat nebulous term, but it signifies an object with a rotation period of, say, no more than a few of your Earth days. The ‘midpoint’ for a space elevator of this type will be at the altitude of geostationary orbit, so the planet in question must have a geostationary orbit which is not prohibitively large. (Of course, ‘prohibitively large’ is also a nebulous term.) Earth, with a rotation period of almost 24 hours (note, though, that ‘rotation period’ and ‘day’ are not precisely identical concepts), has a geostationary altitude of approx. 35800 km, which ensures that objects orbiting the Earth at this altitude, and in an equatorial orbit, appear to hover over the same surface location. For Mars, with a rotation period slightly exceeding 24 hours and a weaker gravitational field than Earth, the corresponding altitude is ‘only’ around 17000 km. If a column or cable is extended from the surface to this altitude, the cable’s apex will be in balance between angular momentum and gravity. But all of the cable material beneath this will have significant weight—because it is not revolving sufficiently rapidly to attain true orbital velocity at that altitude—and this weight needs to be counterbalanced by an extension of the elevator beyond the geostationary point, either with more thousands of kilometres of cable or with a comparatively shorter cable terminating in a sufficiently large counterweight (often, a suitably-sized asteroid) to attain the balance.

Elevator type 1 trimmed

Earth and Mars aren’t the only objects in the Solar System for which such an elevator is conceptually feasible, but they’re the only significant ones. (Other objects are too slowly rotating [Mercury, Venus], too gaseous [Jupiter, Saturn etc.], too small [asteroids], or too hot [Sun] to be worth the effort.) Note, also, the requirement that the elevator must be anchored at the planet’s equator. Singapore, if it wished, could have an elevator on its doorstep. Svalbard could not.

What happens when such a space elevator fails? Kim Stanley Robinson explored this scenario in Green Mars, where the Martian elevator has its counterweight severed by, appropriately enough, Martian separatists. The cable falls, essentially wrapping itself around the equator (or as far around the equator as it can reach) with devastating impact. Woe betide anyone standing in the vicinity.

The second type of space elevator, which plays off gravity against gravity, requires a facelocked planet or moon in orbit around a more massive body. Here the ‘centre point’ of the elevator is the L1 point, where the gravitational pull of the facelocked object—say, for example, the Moon—is exactly balanced by the more massive body’s opposing pull (in this case, Earth). The location of the L1 point necessarily depends on the masses of the two opposed bodies and on the distance between them. For the Earth-Moon system, L1 is slightly more than 54000 km above the Moon’s surface. A lunar space elevator would need to be anchored to the lunar surface directly beneath L1, passing upwards through L1 and extending sufficiently far beyond this to counterbalance the weight of the elevator’s lower reaches. Note that, although this is a taller structure than the Earth elevator, it’s not necessarily more challenging from an engineering and materials perspective, since the Moon’s gravitational field is only one-sixth that of Earth.

Severing the counterweight on an elevator of this type would not (I think) turn the headless elevator into a planetary whipper-snipper, but a cascade of plummeting cable. The catastrophic impact in this scenario, therefore, would be localised around the point of surface anchorage.

Elevator type 2 trimmedClearly, our own Moon is one body that meets the criteria for a space elevator of this type. Titan, facelocked towards Saturn, is another. The separation between Titan and Saturn is much larger—approx. two million km—than that between Luna and Terra (four hundred thousand km); Titan’s mass is almost double the Moon’s; Saturn is much more massive than Earth. The takeout from all this is that Titan’s surface-to-L1 distance is only marginally shorter than the Moon’s, at just under 50000 km. Consequently, the engineering challenge involved is presumably not more significantly difficult than the requirements for constructing a lunar elevator, or a martian one, although consideration would need to be given to the particular physical conditions (principally temperature and ‘space weather’) with which the material of the elevator would need to contend, as well as the hazards of weathering and corrosion of the elevator’s lower reaches in the martian or titanian atmosphere.

Of course, there isn’t yet an elevator on Titan, neither in actuality nor in my fiction. It’s nonetheless a bit of a background presence in a few of the stories in Wide Brown Land: with only one location possible for such an elevator, at the ‘sub-Saturnian point’ defined as zero longitude and zero latitude, the construction of an elevator (or even the plans for its construction) gives one geographical region—in this case, the eastern fringe of the Quivira plateau edging into the dunefields of western Senkyo—an intrinsic industrial and commercial advantage over other regions. In my stories, I’ve posited the shift from rocketry to an elevator (as the primary means of shipping offworld) as a driver of dramatic social upheaval, with those in less-favoured settlements on Titan’s far side disgruntled and aggrieved at the loss of local opportunities while economic attention is focussed on the construction of the elevator a hundred kilometres northwest of the sprawling arcology of Sagan. I will, I suspect, actually need to build the thing at some point, though whether it features strongly in subsequent stories remains to be seen.

In any event, some of my characters will not be happy.

 

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