1. First off, I will state that this topic has absolutely nothing to do with the real world. However, I think it does still have to do with physics. Though, if the mods think this should be moved elsewhere, feel free.

The details of where this question comes from aren't particularly important, but the question has been bugging me for a while. I'm trying to figure out how to make a consistent set of astrophysical rules for how a set of spheres can move around each other when none of them are in the center of motion. Obviously, this isn't constrained by real world considerations, such as gravity, or at least, not exactly.

The main constraints I'm working with are that none of the spheres should crash into one another, but things should still move around (it's no fun if things just spin in place). While real gravity certainly covers this, it's much too chaotic for what I had in mind.

Another thing to point out is that there are three types of spheres. I'm calling them stars, planets and black holes, but they're all about the same size. The stars aren't hot, just bright, and the black holes don't necessarily have more pull than any other sphere. They may or may not behave differently; I haven't really decided.

So far, the best I've come up with is to have each sphere moving around in a circle, but without some logical center for the circle, that doesn't really make much sense.

(And William, before you say anything, just because it's fantasy doesn't mean logic and reason have no place. It's called verisimilitude, and in my opinion it's an important part of any work of fiction.)

2.

3. An equilateral triangle?

4. ???

I forgot to mention that there could be any number of each type of sphere in a system, though there's almost always at least one of each. (If you want something more concrete, the count of each type would follow an exponential distribution, more or less.)

5. I know I didn't make any sense. The last time I opened a physics book was two years ago.

I imagined a star, a planet and a black hole in every corner of an equilateral triangle. The triangle can rotate with its center as the gravitation point.

6. How about you just have them all moving randomly, and then when two spheres get close to eachother the potential energy between the two planets rises to infinity so they can't actually collide.

7. Then they'd all just drift apart. There's still a lot of empty space between systems.

As for the triangle, that'd work if there was only one of each, but I don't really want to limit systems to just that. Past three things, just putting them into a ring shape doesn't really work very well.

Any idea what would happen if three things were trying to circle each other (a star tries to circle a planet, a planet tries to circle a black hole and a black hole tries to circle a star)?

8. I guess the simplest - and least bonky - solution has pairs, which are pairs themselves, and so on to the point where you stop multiplying ghosts, and set them down. You may have three types and if you want equal proportions make it fractal.

9. I'm not sure I understand what you mean. Something like A and B are circling together, C and D are too, and the two pairs are circling together too?

10. Originally Posted by MagiMaster
First off, I will state that this topic has absolutely nothing to do with the real world. However, I think it does still have to do with physics. Though, if the mods think this should be moved elsewhere, feel free.

The details of where this question comes from aren't particularly important, but the question has been bugging me for a while. I'm trying to figure out how to make a consistent set of astrophysical rules for how a set of spheres can move around each other when none of them are in the center of motion. Obviously, this isn't constrained by real world considerations, such as gravity, or at least, not exactly.

The main constraints I'm working with are that none of the spheres should crash into one another, but things should still move around (it's no fun if things just spin in place). While real gravity certainly covers this, it's much too chaotic for what I had in mind.

Another thing to point out is that there are three types of spheres. I'm calling them stars, planets and black holes, but they're all about the same size. The stars aren't hot, just bright, and the black holes don't necessarily have more pull than any other sphere. They may or may not behave differently; I haven't really decided.

So far, the best I've come up with is to have each sphere moving around in a circle, but without some logical center for the circle, that doesn't really make much sense.

(And William, before you say anything, just because it's fantasy doesn't mean logic and reason have no place. It's called verisimilitude, and in my opinion it's an important part of any work of fiction.)
I don't think you need any more than one type of object, spheres will do it. And the only force that you need is gravity.

If you have two of these spheres then you can solve the equations that describe the system and what you have is the two bodies moving around the center of mass of the two-body system. You can find this in any physics text on classical mechanics. It is worked out in what are called center-of-mass coordinates.

Now suppose that you have three bodies. The obvious thing is to look at coordinates relative to the center of mass of the three bodies. You would then expect things to go in about the same way as for the two-body case. The only problem is that it doesn't work. So how do you fix it and solve the problem? The answer is that this problem has been around for a couple of hundred years, has been attacked by some of the best minds in science and mathematics, and nobody has cracked it. There is no known closed form solution to describe the orbits of more than two bodies. One can do computer simulations, which are subject to all of the usual errors, round-off and propagating errors, that go along with simulations.

If you have a LOT of bodies, then you can attack the problem statistically, and get some feel for the behavior of the overall population. That is what is done to derive thermodynamics from fundamental principles. But the price that is paid is that one has no idea of the detailed motion of any specific particle.

11. Originally Posted by MagiMaster
I'm not sure I understand what you mean. Something like A and B are circling together, C and D are too, and the two pairs are circling together too?
Yeah.

Development: Take one body. Split it into two orbiting bodies. Now take one of those, split it again. And so forth. You could split some or all as you progress, for asymmetry, and stop when you grow bored.

12. @DrRocket: In the setting I'm working on, there are three types of objects, but they may or may not behave the same. As for gravity, it's too unstable for this. (For one thing, this universe is infinitely old.) I'd be all for equations describing something gravity-like (and I've already toyed with a simulation one one form of such equations), but gravity as we understand it won't really work in this case.

@Pong: That could work. I'll have to think about it a bit and see if it fits.

Edit: I think I might have thought of something. If there's a scalar field full of (what's the right term for that?) something like smooth noise, and the objects give off the same type of energy, then if the objects try to move towards a low point in the field, they'll all sort of clump together without colliding or sitting still, right?

Edit again: Hmm... I may need to take this next question to the math forum, but any idea how to find the gradient of such a thing? It'd be nice to have an analytic solution, but since the field is noise, I don't know how possible that is.

 Bookmarks
Bookmarks
 Posting Permissions
 You may not post new threads You may not post replies You may not post attachments You may not edit your posts   BB code is On Smilies are On [IMG] code is On [VIDEO] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are On Terms of Use Agreement