Does anyone know anything about orbital mechanics?

[Arclight]

Yes, seriously. I'm currently trying to create a setting for a hard SF adventure game, and I need a bit of help. It might be a long shot, but I thought I'd ask around, anyway. I'm just going to copy and paste what I posted on rec.arts.sf.science:

Hello ladies and gents. I was wondering if you could help me figure out some issues surrounding something that I'd like to put into a SF computer adventure game that I'm working on.

Consider your run-of-the mill orbital skyhook. It extends up into space perpendicular to the surface of the planet that it orbits. Simple enough. Let's suppose that this skyhook is in orbit around Saturn. Now, if we were to lower the orbit of the skyhook so that its lower tip extends into the atmosphere of Saturn, it's going to experience quite a bit of atmospheric drag. Eventually, its orbit will decay and it will fall into the atmosphere, with the net result that we've just thrown a very large amount of money into a gas giant. Not good. The best solution is to keep the skyhook from ever entering the atmosphere.

As it turns out, though, that's exactly what we want to do in order to get at all the very useful He3 that you find in the atmosphere. So the other option is to use some sort of propulsion system to counteract the effects of the drag. Fortunately for us, Saturn has a rather powerful magnetosphere, which we can use to our advantage. Since the skyhook is nothing but a tether, it should be possible to use it as its own electrodynamic tether propulsion system: you pump electricity into it, and it raises itself out of the atmosphere. This should allow it to offset the atmospheric drag and the loss of orbital velocity caused by raising large amounts of He3 and other gases into orbit. And where does the power for the electrodynamic propulsion come from? We could burn some of that He3 in a fusion reactor, but we're looking to sell that elsewhere. Instead, why not put a number of other tethers in a higher orbit (not extending into the atmosphere) to generate electricity by passing through the magnetosphere and then beam it to our skyhook?

That's the plan, anyway. Here are the problems that I have:

First, I'm not sure that the electrodynamic propulsion system would provide thrust in the proper direction to counteract atmospheric drag and loss of momentum due to the constant pumping of gases up the skyhook. As I understand it, to raise an orbit, you want to thrust in the direction of your orbit; the tether propulsion system - again, as I understand it - will thrust in the direction that the tether is oriented. In this case, that would be perpendicular to the direction of travel. Is this correct? And, if it is, would this be sufficient to prevent orbital degradation or do I need to thrust in the direction of travel?

Second, I'm not sure just how much drag and momentum loss we're talking about, here. Would there be too much of either (or both) for the propulsion system, assuming it works, to counteract? What would the power requirements be? Would the electrodynamic power generation tethers be up to the task?

Third, if everything else can be made to work, would the fact that the drag on the skyhook is applied to one end only mean that the thing would tip over? Would it just lean and then become stable at an angle? If it would be a problem, is there anything that can be done to counteract it?

Fourth, just what is a reasonable orbital period and speed for such a setup? Ideally, the orbital period would match the rotation of Saturn at the equator (about 614 minutes), but I'm not sure that such an orbit is possible. If the orbital period is longer than the period of Saturn's rotation, would that mean that the atmosphere is blowing in the direction of the skyhook's travel? If so, how would this affect its orbit?

And if you can think of any other problems with the setup, I'd appreciate a heads-up.

Thanks a lot, guys.

[Monsieur OUXX]

Your problem is super complex, both the modelling and the gathering of the parameters for the actual calculations.

For example, you say that the hook receives a stronger drag than the satellite because it's lower in the atmosphere. Without that hypothesis, you'd just model the satellite as dot. Instead, you already need 2 dots. But then, it means you assume the pipe going from the satellite to the hook is rigid. I hope you do! Otherwise it's 2, or 3, or 10, or 100 dots you'll need in your model.

2/ Each dot is submitted to basically 3 forces: (1) the gravity, always oriented towards the center of Saturn, (2) the drag, always oriented in a direction opposed to the movement, and (3) its propelling force (additionally, the gravity will result in the so-called centrifugal force, which is only a mathematical artefact). You made the hypothesis that the altitude actually alters the drag... So you'll need a formula to calculate the drag depending on the altitude. Wow! Your problem was already a complex mechanics model, now it include thermodynamics!

3/ The satellite is propelled not by an engine, but... by a magnet! WTF? And the force it generates depends on the altitude! --> Do you have the forumla and the values to feed it?

4/ So the drag depends on the altitude... And you say that the more powerful the magnet is, the more it changes the drag! And this magnet is not only the satellite, but actually the whole pipe! (which could be made of several points, as described in 1/) I hope for you there is a linear relation between all those functions, otherwise you'll need a supercomputer to solve the equations!

5/ "would this be sufficient to prevent orbital degradation?" Well, once again, do you have the formula for your tether's magnetic force? And the ones for Saturne? And do assume that the magnetic force generated by Saturne is constant around its surface? (especially towards the magnetic poles?)

6/ "I'm not sure just how much drag and momentum loss we're talking about" Same thing. It all depends on the hypothesis you take (all of the above) and values you choose to feed the formulas. What is the mass of each item, etc? If you change any of those parameters, then the drag could become too high, or the skyhook could tip (as you mentionned) or go away in space, etc. Anything is possible! Finding the bounds of each equation required you to write them down, and to calculate it all.


IF I'm writing all that, it's not to discourage you.. It's actually a very interesting idea. It's just that, at the same time you throw many ideas, with plenty of details, but without choosing your basic start hypothesis. You need a clear (and simple) model, and you'll definitely need actual values for all the parameters before you'll be able to answer any of those questions.

[Anian]

Why don't you write a space opera like a normal person? Make it so technology is from a mystical alien civilization or some biotech... 

I'm sorrry, that was a joke. Seriously though, I suggest more searching on Google for stuff like "orbital mechanic calculations) etc.
Very interesting technology, but how hardcore is this game where you need such calculations? Sounds like something 10 people in the world can play.

[RickJ]

What will the tether be attached to?  The density of Saturn is 0.687 grams per cubic centimeter which is less than water so there would be nothing solid to which a tether could be attached.     

http://www.universetoday.com/guide-to-space/saturn/does-saturn-have-a-solid-core/
http://www.universetoday.com/guide-to-space/saturn/density-of-saturn/

[Monsieur OUXX]

What will the tether be attached to?

HE made it quite clear: The tether must be considered as a cable, which very nature makes it an electromagnet that interacts with Saturn's atmosphere; the Force created makes it float.

[Arclight]

Your problem is super complex, both the modelling and the gathering of the parameters for the actual calculations.

For example, you say that the hook receives a stronger drag than the satellite because it's lower in the atmosphere. Without that hypothesis, you'd just model the satellite as dot. Instead, you already need 2 dots. But then, it means you assume the pipe going from the satellite to the hook is rigid. I hope you do! Otherwise it's 2, or 3, or 10, or 100 dots you'll need in your model.

2/ Each dot is submitted to basically 3 forces: (1) the gravity, always oriented towards the center of Saturn, (2) the drag, always oriented in a direction opposed to the movement, and (3) its propelling force (additionally, the gravity will result in the so-called centrifugal force, which is only a mathematical artefact). You made the hypothesis that the altitude actually alters the drag... So you'll need a formula to calculate the drag depending on the altitude. Wow! Your problem was already a complex mechanics model, now it include thermodynamics!

Not too complex. The skyhook is in orbit, so there is no downward gravitational force - the only gravity that I need to worry about is what's keeping the thing in orbit. The only things that I need to worry about are atmospheric drag (reduces orbital velocity and causes the whole apparatus to tip as the drag is applied only to one end of the skyhook), the propulsive force of the electrodynamic propulsion system (this is in the same direction as the skyhook orbits, so can, presumably, counteract the drag), and the loss of momentum due to raising mass up the skyhook from the atmosphere of Saturn to the high tip of the apparatus. Basically, the drag and the momentum loss reduce orbital velocity and the propulsion increases it.

The tipping problem, apparently, can also be counteracted by bending the skyhook in the middle. If the upper portion is bent backward with respect to the direction of travel, the thrust for that section of the tether will be up and forward. The thrust for the portion below the bend will be forward only. This means that the forward thrust (the only part that we care about for increasing orbital velocity) is stronger in the lower portion - handy, since this extra thrust on the lower portion can be made to exactly counteract the force of drag on that portion, halting the tipping effect.

3/ The satellite is propelled not by an engine, but... by a magnet! WTF? And the force it generates depends on the altitude! --> Do you have the forumla and the values to feed it?

No, but I don't need to be that exact. All that I need to know is that the more power you pump into the system, the more thrust comes out. The propulsion system does work so long as there is a planetary magnetosphere for it to act against.[/quote]

4/ So the drag depends on the altitude... And you say that the more powerful the magnet is, the more it changes the drag! And this magnet is not only the satellite, but actually the whole pipe! (which could be made of several points, as described in 1/) I hope for you there is a linear relation between all those functions, otherwise you'll need a supercomputer to solve the equations!

Again, I don't really need to know exactly. A plausible approximation should do.

5/ "would this be sufficient to prevent orbital degradation?" Well, once again, do you have the formula for your tether's magnetic force? And the ones for Saturne? And do assume that the magnetic force generated by Saturne is constant around its surface? (especially towards the magnetic poles?)

6/ "I'm not sure just how much drag and momentum loss we're talking about" Same thing. It all depends on the hypothesis you take (all of the above) and values you choose to feed the formulas. What is the mass of each item, etc? If you change any of those parameters, then the drag could become too high, or the skyhook could tip (as you mentionned) or go away in space, etc. Anything is possible! Finding the bounds of each equation required you to write them down, and to calculate it all.

I don't have the formulae - I was hoping someone here might know how to run the numbers. I can find the data itself, but I need to know what numbers I need before I can do that.

IF I'm writing all that, it's not to discourage you.. It's actually a very interesting idea. It's just that, at the same time you throw many ideas, with plenty of details, but without choosing your basic start hypothesis. You need a clear (and simple) model, and you'll definitely need actual values for all the parameters before you'll be able to answer any of those questions.

Why don't you write a space opera like a normal person? Make it so technology is from a mystical alien civilization or some biotech... 

Pah! This is my hard SF game universe - the transhuman, post-singularity "new space opera" game universe is a future project.

Very interesting technology, but how hardcore is this game where you need such calculations? Sounds like something 10 people in the world can play.

Oh, it won't come up at all. The game may not even be set around Saturn (though a future one might). This is how I write any type of fiction - I worldbuild the heck out of the setting so that everything is consistent and makes sense. Not only do I want the science to be plausible, the economy of the solar system needs to make sense for the setting and plot to work.

What will the tether be attached to?  The density of Saturn is 0.687 grams per cubic centimeter which is less than water so there would be nothing solid to which a tether could be attached.     

http://www.universetoday.com/guide-to-space/saturn/does-saturn-have-a-solid-core/
http://www.universetoday.com/guide-to-space/saturn/density-of-saturn/

What will the tether be attached to?

HE made it quite clear: The tether must be considered as a cable, which very nature makes it an electromagnet that interacts with Saturn's atmosphere; the Force created makes it float.

The tether is not attached to anything. Think of a very long cable (thousands of kilometres) that is about ten metres in diameter. Stand it straight up and down with respect to the planetary surface. Not put it in orbit such that it remains in that orientation. The tether is not attached to anything at the top or bottom - it hangs there, orbiting the planet. And it is the fact that it is in orbit, not that is possesses electrodynamic propulsion that keeps it aloft - the propulsion system is necessary only to counteract the degradation of the orbit that results from drag and loss of kinetic energy.  Complicated, I know, but the basic concept is sound. I'm just trying to work out the specifics.

Thanks to everyone so far, by the way. You're all helping me think this through.