The Ergosphere
Wednesday, March 03, 2004

Wanted: Orbital mechanic. Must have own tools.

Stephen Den Beste writes about the issues of getting something from Luna to a LaGrange point.

In particular, he states:

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. [1]

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. [2]

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. [3]

Then he reconsidered, and stated:
There are actually two ways to change momentum. The other is to use gravity.
Unfortunately, I believe he missed a number of salient points:
  1. You don't have to fling mass off the station unless the incoming mass has some difference in angular momentum.  If the velocity difference is in the inward or outward direction the push will tend to change the orbital period, but there is an easy remedy for this:  balance the incoming payloads so that their radial momentum is distributed more or less evenly over each full orbit, and the effect is to change the orbital period slightly.  You can balance this with small amounts of delta-V if and when you have to vary the pace of mass delivery.
  2. Even if you do pick up some angular momentum, you can use magsails or the like to offset the change with minimal expenditure of mass.
  3. Why would you need a high-thrust engine?  The whole point of going into space to do your manufacturing is that it is an energy-rich environment.  This is the perfect place for low-thrust, high-impulse engines.  The momentum delivered by the steady arrival of high-mass, low-velocity lumps of regolith that cannot be dissipated against gravity could be thrown away on a much smaller stream of high-velocity material, and the copious solar energy flows could supply the required power.
The sad part about this is that most of the ground work for the transfer of lunar mass (for ore or shielding) had been done in the 1970's and early 1980's, and ought to be well-known by now.  The relative difficulty of transfer to the Lagrange points was the reason for adopting the 2:1 resonant orbit as the preferred orbit for a space construction facility using lunar materials; if I recall correctly a freighter capturing material at L2 (which is not stable, but metastable) would fall naturally into the 2:1 resonant orbit if allowed to fall away from L2.

There are further possibilities if you assume that skyhooks are practical; if my old calculations were correct the distance from the Moon to the Earth-Moon L1 point is only about 2000 miles, and the gravitational loads are small enough to allow such a skyhook to be built with graphite (not nanotube) fiber or even sapphire whiskers.  To get mass off Luna using one of those all you would need to do is haul it out some distance beyond L1 and let it go; since the net attraction past L1 is Earthward it might even be feasible to power the entire lift process with gravity, allowing each payload falling toward the construction facility to pull the next one up from the lunar surface.  (Tide gets the regolith out!)

I don't mean to put Stephen down, but he hasn't put as much study into the issue as the extremely acute minds of the Space Studies Institute era.  I stand in awe at some of their work, such as the papers presented at the AAS conference on orbital tethers (volume 61, if you can find it).  When that kind of brainpower has gone before, it behooves one to be careful before pronouncing something impossible.  

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