Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: range41 on 05/06/2011 16:44:58
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It seems that engineers need to spend a great deal of time calculating trajectories to land satellites and probes into stable orbits, yet across the universe stable orbits seem to "just happen". What is going on that makes stable orbits so prominent in the universe?
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Systems that involve three or more bodies of roughly equal mass (give or take one or two orders of magnitude), tend to be chaotic. They're always swapping orbits; occasionally there are collisions or planets get thrown out of the system. Consequently, the system keeps changing until it becomes stable. Stable systems last; unstable systems don't. That's why there are so many stable systems and so few unstable ones.
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The basic physics of gravity (inverse square law, in Newtonian approximation) just happens to be what is required, when combined with the laws of motion, to produce stable orbits of two bodies around each other, or of several small bodies around a much larger body. It is in the math.
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Depends on what you mean by stable I guess? All orbits are to some degree chaotic as I understands it. It's called 'resonance' and was first defined by Jules Henri Poincaré as he tried to solve the 'three-body problem' (http://en.wikipedia.org/wiki/Henri_Poincar%C3%A9#The_three-body_problem). Doing so he found that there was no general solution to it. Karl Frithiof Sundman solved it finally by using a 'infinite series solution to the three-body problem in 1906 and 1909.'
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The reason we see stable orbits everywhere is because they exist for a long time not because they happen easily. In fact if two bodies approach and interact under gravity it is not possible for them to form a stable orbit unless something else intervenes to change things. They will just perform hyperbolic paths past each other and go on their way. Things that can cause this to change are; the presence of a third body, a collision, the presence of gas or dust to create "friction" or possibly the presence of electric or more likely magnetic fields to affect the motion (this last one is not usually considered).
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By the way, all orbits are non-linear. Not even NASA will be able to calculate the exact position of Jupiter if trying for the next thousand years, or maybe even hundred? Even though I'm not sure where that non-linearity will become great enough to make a calculation questionable I can guarantee that it is so. And if orbits were stable this wouldn't be a fact.
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Is it that orbits by their nature are non-linear - or that orbits in a multiplanet system are inherently non-linear?
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I guess I should clarify that I meant "relatively stable" orbits, like planets and moons. I understand that planets and moons drift etc. So, for example, in the collision that caused the moon to form from the earth, is there some mechanism that caused the two bodies to form a relatively stable orbit - or as some of the answers suggest - was it just luck?
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I guess I should clarify that I meant "relatively stable" orbits, like planets and moons. I understand that planets and moons drift etc. So, for example, in the collision that caused the moon to form from the earth, is there some mechanism that caused the two bodies to form a relatively stable orbit - or as some of the answers suggest - was it just luck?
You can look at the Earth-moon system as a two-body system because the moon's orbit is always far closer to Earth than to any other large body, like Mars. Two-body systems are inherently stable.
The collision that formed the Earth-moon system probably left a ring of debris circling Earth; it may have contained many small moons. That would have been a very unstable system, and many collisions would have occurred; some moons might have been ejected from Earth orbit. Each collision would have reduced the total energy of the system. Once the dust settled after each collision, there would have been fewer moons. Finally, all the moons were consolidated into one, and the remaining debris showered the moon, covering it with craters.
It all comes down to the fact that unstable systems experience collisions and ejections until they become stable. Consequently, stable systems last much longer, which is why there are more of them.
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A two-body orbit can be stable, assuming 'perfect gravitational spheres' (Newton), but for anything above that, or not perfectly symmetric, you will get a chaotic, non-linear solution as I understands it. The resonance I was talking about is simply the time it takes for an orbit around some center, so the Jovian satellite Io that makes a orbit in half the time of its brother Europa (roughly) has a resonance of 2 to 1 (expressed 2:1). For each orbit of Europe, Io makes two.
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You can find a three body simulation and the free simulator here http://www.askoh.com/assemblies/index.html (3body.zip)
While mucking around with it I increased the mass of one of the bodies. Consequently, one of the other two took off, never to be seen again!