Monday, April 11, 2016

Low Thrust Interplanetary Orbits

If someday we here had a huge telescope and we wanted to hunt aliens, one way is to look at exo-planets and try and figure out if there is a Great Wall there or pyramids or something noticeable. Or we could look for something else. In an advanced alien civilization, there is a good chance they would be running freighters between planets, pushing back the inevitable exhaustion of resources. Could a really huge telescope see interplanetary freighters, or at least the rocket blast from one?

One little precondition for an alien civilization building cargo freighters for shipping good stuff between planets is that it make economic sense. Figuring out the economic aspects of interplanetary shipping in a civilization we don't know much about might seem challenging. At least until we remember that energy is probably the currency they use. To see if interplanetary shipping might be useful from an economic point of view, we could compare the energy it costs to get something from one planet down to the home planet where it would be used, and then compare it with the value of that 'something' in terms of energy.

One way is to look at the displacement costs. If something, say, yttrium, takes X joules/kg to get it from planet 6 in some solar system and it takes 2X joules/kg to mine the depleted resources on the home planet, it looks like interplanetary mining and shipping is a GO. It gets a little more complicated when you consider substitution. If instead of yttrium the various needs could be satisfied by a combination of erbium and thallium (these don't make sense, just think of it as names), yttrium would be used only if the costs of substitution in terms of these alternative materials was more than 2X joules/kg[yttrium], maybe 2.5X. Then the economists on the home planet of this particular solar system would know that yttrium was the best bet, home world wise, and they would also know it makes economic sense to go get it for less energy than mining it at home.

If you want to do this comparison, you need to understand how to compute X. How many joules does it take to send a ship out to planet 6, put down some mining equipment, refine the ore and get the yttrium out, launch it back and return it to the alien home planet. When it comes to doing this, there are likely a whole lot of ways to do it. Exactly one is the most economical. That's the one you need to use to figure out X.

There are some nonlinearities here. If you are going out to planet 6 and do some mining, and the home planet only needs 2000 kg of yttrium a year, it doesn't make much sense to cart mining equipment weighing 2000000 kg to planet 6, along with some lander and launcher, and also fly it back to the home planet. If the home planet needs 2000000 kg of yttrium a year, it looks like the amortization of the setup out there on planet 6 would be worth while. So does this mean mining commonly used materials is the only way to make interplanetary shipping economical? No. It does mean that every material needs a separate calculation, to make sense of what has to be plopped down on planet 6 to get the material. Or planet 4 if that's were it is located.

It also makes sense to look at multiple materials from one planet. If you are amortizing a launch pad on planet 6, it helps to have ten different things you are shipping back home. Same with everything else. And you would want to figure out the lowest cost methods for every component of this venture.

One of the components is the shipping back home of the mined materials, as well as the shipping out of whatever is needed to get the materials on the planet of origin. This brings us back to the first paragraph. We need to figure out the lowest energy using way of shipping, as that is what all the alien civilizations that can and do do interplanetary shipping would use.

Let's think about some Earth examples to settle our minds. Suppose Earth was running out of something, might as well call it yttrium, and there was a pile of it on Mars. What's the lowest energy way to get it back to Earth? The energy cost of a spaceship can mostly be in the propellant and the propulsion energy source. It takes a lot of energy to get out of a gravitational well. There is also a hotel load, but that might not be so much in comparison.

Suppose we consider low thrust trajectories. There are trajectories that loop from the vicinity of Mars, using Mars as a gravitational slingshot, to direct the spaceship back to close to Earth. There are also trajectories that loop from the vicinity of Earth, using Earth as a gravitational slingshot, to direct the spaceship back to Mars. These don't belong to the same orbit, but a small amount of transverse thrust at the most useful points, the perigee and the 'perimars', can connect them. This is the essence of a low thrust orbit. The orbit isn't an orbit, as it has some changes of parameters on each passage of a planet, but it almost is. The energy cost for getting mass from one planet's vicinity to the other's is very small.

Obviously, vicinity is not a landing. There has to be some other pieces to this space navigation. Specifically, two, one being some way to get some chunk of mass from the ground to low orbit, and two being something to bring the mass up to speed to match the spaceship's velocity as it runs past the planet. What this arrangement has done is it has reduced the energy needed to move mass from one planet to another to just about the minimium possible. Energy is necessary to get out of the gravitational well, and then to match velocity for the low thrust interplanetary almost-an-orbit. The other end of this has to be included as well, specifically something to bleed off velocity of the cargo, after it is decoupled from the interplanetary shuttle, dropping it down into low orbit. And also some energy might be needed to bring it down to the planet's surface, if aerobraking can't be used. Remember, there might not be any air on planet 6.

The same mechanism for taking cargo off the spaceship and putting it into low planetary orbit can be used to take cargo from low planetary orbit and match velocity with the spaceship. In other words, some tug-like vessel just has to do one pass per orbit of the interplanetary shuttle, where it takes cargo from low planetary orbit, boosts it to interplanetary speed and couples it with the shuttle, simultaneously extracting the reverse cargo from the shuttle and then dropping it down to planetary orbit speeds.

This three tier system may be the one that uses the least amount of energy. It also means that there is not going to be any major thrusting done in interplanetary space, where Earth's gigantic telescope was hoping to see it. The bottom line is simplicity itself. Economics on the alien solar system indicates they are not going to be giving off any signatures from interplanetary shipping that we could detect. It would have been nice, to have this isolated burn going on in the middle of barren space, where it would be easy to see. But no. We will need to find another signature to nab.

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