(or 'A little learning is a dangerous thing')

I read an

article recently describing the amount of hydrocarbons on Saturn's moon, Titan.

I wanted to kick around the numbers for a

space elevator on

Titan, one that would allow the oil to be lifted from the surface, and then thrown out of Saturn's orbit to enter the inner solar system.

So far, I've only managed to characterize the length of the elevator ribbon, not the cross section, or mass of the completed ribbon. These could be computed using a similar method as in shown in

The Space Elevator book, but with the additional influence of Saturn's gravity is included in computing each ribbon segment.

All of my numbers are approximations.

Imagine a planet with Saturn's mass, with a day that is 15.94 Earth days long. An object in a synchronous orbit would have an orbital period of 15.94 days. The theoretical elevator for this planet needs to extend past synchronous orbit, out into space, to hold the elevator up, with the appropriate counterweight at the end. A space elevator for Titan is similar to the portion of this imaginary elevator that extends past the planetary synchronous orbit.

Titan is tidally locked with Saturn, with an period of 15.94 days. A space elevator could be built extending directly towards or directly away from Saturn from Titan's surface, providing that that length of the elevator passes through the Saturn/Titan

L1 or L2 point respectively, and is capped with the appropriate counterweight. The elevator must pass through the Lagrangian point in order to be long enough to exert a force away from Titan that will hold the ribbon up.

The distance of L1 and L2 from the center of Titan is approximated by computing the radius of the

Hill Sphere, which is approximately fifty-two thousand kilometers, so an elevator that passes a distance greater than this from the center of the moon, with the appropriate counterweight (if needed) should be stable.

If the elevator ribbon is longer than three hundred thousand kilometers, it should be able to toss a payload with sufficient speed to escape Saturn's orbit.

Escape velocity is a function of the mass of the planet and the distance from the planet, so as a payload moves outward along the ribbon, the escape velocity decreases. Traveling outward from the orbit of Titan, this would cross the orbit of the next moon out,

Hyperion. Approximately every twenty-one days, Hyperion would pass in the vicinity of the ribbon. Since the orbits of Titan and Hyperion are not exactly co-planer, Hyperion would not necessarily intersect the elevator ribbon on every orbit. Provisions would still need to be made for deflecting the ribbon if necessary.

A pilot ribbon for Titan would be deployed from a satellite placed in L2. With all of the hydrocarbons available on Titan, it would make sense to lower a package to the surface to manufacture additional ribbon material. An exponentially tapered ribbon could then be built deployed from the surface, built from local materials, and hoisted by the pilot ribbon.

I realize that I haven't calculated what happens to the payload once release from the ribbon, or characterized the orbit required to reach the inner solar system, or how to get the payload to the Earth's surface. All I've done is characterize the length of ribbon required for a payload to escape Saturn's orbit, but this is an interesting start.