Sunday, April 17, 2016

Billiard Balls and Transfer Shuttles

Interplanetary orbits are nice in that there aren't any meaningful energy losses. The spaceship just travels around some orbit, an ellipse approximately, until some close encounter with a planet happens, when there might be a bit of an energy change. Some energy changes add energy to the spaceship and others subtract it. That means there is a whole lot of orbits in which the change is zero, and the lack of any sudden effects means that orbits near a zero change orbit have small energy changes. If you were a mathematician, you would express this by saying there is a N-dimensional manifold of zero-energy-change orbits to choose from, but since I am too lazy to figure out N, this comment wouldn't add much.

So, in the previous post on interplanetary mining, it was pointed out that there are low-thrust orbits that go from one planet to another and back again, or more specifically, to the vicinity of one planet from the vicinity of another planet. Works for the Earth-moon system too, but that's another question. The implication of this is that the majority of the distance to be traveled in interplanetary mining doesn't cost any energy. Pretty nice to hear for all those who would be thrilled to be involved in such an adventure, or even to learn about it. Pretty nice to hear for all those who desperately want to know if an alien civilization would find interplanetary mining cost-effective. Since resources dictates the life-span of an alien civilization, this is an important question.

All that energy saving is fine, but there is still the question of how much energy is used in taking the cargo and matching it to this particular orbit that is traveling by the vicinity of your origin-of-materials planet. Could be lots and a spoiler for the idea.

Unless you shoot pool, or by its more elite name, billiards. If you've played a bit, you know how to shoot one ball with the right spin and velocity directly into another, and have the one you hit stop dead after transferring its momentum to the second ball. This works because the balls all have the exact same mass, and they are so hard they lose almost no energy through inelastic processes at the impact. Let your mind race freely and go to a frame of reference moving at some speed, I mean, the whole table is moving. The same thing happens, meaning that the balls exchange their velocities.

Now expand your horizons, and suppose you were watching the spaceship coming toward the vicinity of your planet. It is traveling cargo-container first, and some elastic transfer takes place when they separate. The spaceship slows down and the freed cargo-container speeds up and deviates a little toward the planet. This freed cargo container just happens to be heading smack-dab toward another cargo container, which just happens to be loaded with exactly the same mass, and they both have a magnetic coupling device which allows them to impact without contact. In other words, they exchange velocities, but not exactly. Back in the world of billiard balls, if you ever so slightly miss a dead on impact, you still wind up transferring almost all the velocity to the second ball. If you are actually trying to miss by a teensy bit, you wind up steering the second ball to some interesting place, like a corner pocket. If you are actually trying to miss the second cargo container by a small amount, and you know what you are doing, you send the second cargo container to a rendezvous point where the spaceship has gone, where it winds up close to matching the spaceship's velocity. This makes it easy to grab, with only a little thrust needed. Lots of velocity change between the two cargo containers, but nobody had to pay for the thrust to slow one down and speed up the other one. The first one is left in the old transfer orbit.

This means getting a cargo container onto the spaceship can be done with little thrust, meaning little fuel dragged up to orbit and little propulsive energy consumed. Provided you are willing to move the same mass every time you go from planet A to planet B or in the opposite direction. Could be some trips have some dead mass, and sometimes some cargo has to wait for the next spaceship. But you have gotten energy costs really down now. Not much energy for the whole orbit and not much energy to deliver the cargo to a transfer orbit somewhere around planet A or B.

There is still the energy necessary to get the cargo off the surface of the planet up to the transfer orbit. The same billiard ball trick can save some energy getting the cargo container down from a high transfer orbit to a low planetary orbit, if the same mass can be moved up as is moved down. You have to get the mass up there for the next spaceship anyway. So we are left with getting the mass from the surface up to some orbit, maybe still pretty deep into the exosphere.

So, in figuring out if interplanetary mining and resource extraction would be useful in prolonging the life-span of an alien civilization, some optimization simulations would be in order to figure out just how little thrust would be necessary, and some more details about how to account for propulsive fuel transfer to the spaceship, and some more details; then do some details on transfer orbit transfers as well. The disadvantages are that these orbits are not prompt, nor are they timely. Delays occur, and if you are trying to run a parcel post service from Planet A to Planet B, you are going to have to use a different thrust strategy and use a lot more energy.

Another problem might be the g-loading on the cargo container. This depends on the type of elastic momentum transfer mechanism you can invent. The longer the distance the transfer can be stretched over, the lower the g-loading. However, minerals and elements and such are pretty resistant to g-loading, and the shuttle itself can be built strongly. After all, you will be using it over and over again, so the costs can be amortized over a lot of resources.

Some other details might seem to be necessary, but they are not. How do you get the crew onto the shuttle? Well, what do you need a crew for? If this operation can't be automated, what can be? It is straightforward. Maybe you think an alien crew-member is necessary to cover unforeseen circumstances, but that's what AI is for.

So, an interesting question arises. What materials would be shipped? How long could mining planets extend the life-span of an alien civilization? What is the factor involved? Is it two or ten or a hundred?

If it is a hundred, that means something in terms of the age of the universe. A population running at maximum population, measured by waste heat released into the home planet's environment, might last ten thousand years, if they did everything right with recycling. Drop the population by a thousand, and the lifespan is now poking up toward ten million years. Add a factor of a hundred, and we are at a billion years, which is a very long time, compared to anything, because nothing can be older than the universe, which is a bit over ten billion years. That means it is quite important to try and guess if that number, the ratio of the no-interplanetary shipping to yes-interplanetary shipping, is two or a hundred. It makes all the difference to calculations of populating the galaxy.

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