Stardate 20040302.0959

(Captain's log): A few days ago, Tom sent me the following email:

While discussing the enormity of the problems involved in creating a self-sustaining off-world human habitation, you dismissed the idea of moon mining and catapulting the ore into space. I first heard about the idea some 30-35 years ago. The objection you raised that caught my attention was that there was enormous energy (maybe this isn't the right word) attached to the ore "projectile" and that a lot of energy would be needed to stop the projectile. I'm going to reveal the shallowness of my understanding here, but couldn't a trajectory be worked out under which the ore matched the velocity of the L5 (or some other) orbit and the ore would more or less "stop"? Or, in the alternative, is it conceivable that a device could be made to receive by transfer ("catching" the projectile) and "use" the energy brought it by the ore, in the nature of an earthbound waterwheel? How much variation would there be in the "ending" location of each projectile?

To which I responded:

I'm afraid not. Until such time as someone changes the laws of physics, what you're describing is impossible. (And I'm using that word rigorously: I don't mean "very difficult", I mean it cannot be done in this universe by anyone.)

The problem isn't kinetic energy, it's momentum. No matter how you work it out, momentum is always conserved. If rocks flung off the moon approach the L5 point, and are caught by a station there, the total momentum of the station will change. And the only known way to deal with that is to fling mass back off the station in the opposite direction.

It doesn't have to be the same amount of mass, but the momentum (mass times velocity) has to be the same. If it isn't, you get an orbital change.

One way or another, rocks flung off the moon have to be decelerated somehow at the L5 point, and the only way we know of to do that is with rocket engines or some equivalent. The theoretical best case for such a system in terms of propellant efficiency is a particle accelerator which fires mass at nearly the speed of light, but such a system will have a very low thrust. All known high-thrust engines are extremely inefficient in terms of propellant.

But after I mailed that, I kept thinking about it and realized I had been wrong.

There are actually two ways to change momentum. The other is to use gravity. But it isn't usually possible to arrange for the use of planetary-sized masses for that purposes, though the so-called "orbital slingshot" is one way in which it can be done.

And it may well be possible in the case of the L4 and L5 Lagrange points.

The five Lagrange points are locations in a star/planet system where small bodies can hold stable orbits. In the case of L1, L2, and L3, the orbital velocity is unnatural, being too slow for L1 and too fast for L2 and L3. Objects in those positions which are perturbed slightly off of them will tend to drift away.

NASA's SOHO is in the Earth's L1 point, but they constantly have to monitor its position and correct it. But L4 and L5 are different.

Objects in the L4 and L5 points have the correct orbital velocity, and for complicated reasons, if they're perturbed out of the point then they enter an overall orbit around the star which seems to "orbit" the point. That's why the L4 and L5 points for major planets tend to accumulate garbage, most famously the Trojan asteroids in Jupiter's L4 and L5 points. (Which is why L4 and L5 are also known as the "Trojan points".)

And that was what occurred to me. There may actually be a way to use gravity instead of a reaction drive. I don't know if the math works out; I can't calculate it. Both kinetic energy and momentum have to be taken into consideration, but of those the energy is easier to manage, since excess energy can be converted to heat and radiated away. (It's still a tough problem, but "tough" is a lot easier than "impossible".)

The idea would be to put the colony off-center from either L4 or L5, so that from the point of view of the Earth it seemed to "orbit" the Lagrange point. Mass from Luna would be fired towards the colony but scheduled to arrive when it was at a point in its "orbit" when it was moving towards the Earth. Capture of the incoming mass would change the momentum of the station, but since the motions were in opposite direction the effect would not be additive.

Or perhaps mass arrives on both sides of the station's "orbit"; some new mass adding momentum (increasing the "orbital" radius) and some decreasing it (canceling the effect of the previous mass).

The perceived "orbit" is an illusion caused by looking at the system from an accelerating frame of reference. In reality, the station would be in orbit around the Sun. But the effect of this would be to bleed away the excess momentum using Earth's gravitational influence.

That leaves the problem of orbital energy, which is where Tom began. But it isn't necessarily th