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Why are planetary orbits so circular?

by oldman
Tags: circular, orbits, planetary
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oldman
#1
Mar4-09, 06:18 AM
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Over in another forum I've got myself in trouble by suggesting that theoreticians haven't paid enough attention to this question. George Jones has kindly pointed out that the question seems to have been answered along the lines of "...collisions in the disk tended to make orbits more circular explains why most planets in our solar system have nearly circular orbits", which seems a very reasonable proposition.

I've also come across what looks like a quite exotic answer to this question along totally different lines by the astronomer L. Nottale in a paper entitled SCALE-RELATIVITY, FRACTAL SPACE-TIME AND GRAVITATIONAL STRUCTURES. His work has also been discussed in these forums. I find both the paper and the discussion far above me, though.

Can anyone help to straighten me out with the current consensus on this question? Has it been thoroughly worked through by theoreticians? If so, I'd appreciate a web-accessible simple-minded reference to how this was done.
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tiny-tim
#2
Mar4-09, 07:22 AM
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I think the maths is mostly to do with the stablility of solutions …

most solutions after a long time tend to an attractor, which in the case of planetary motion seem to be either circular or hyperbolic …

for the maths background, see http://en.wikipedia.org/wiki/Attractor
HallsofIvy
#3
Mar4-09, 07:43 AM
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The eccentricity of mercury's orbit is about 1/5, not all that small. The eccentricity of pluto's orbit is about 1/4 but Pluto is not a planet any more!

oldman
#4
Mar4-09, 09:20 AM
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Why are planetary orbits so circular?

Quote Quote by HallsofIvy View Post
The eccentricity of mercury's orbit is about 1/5, not all that small. The eccentricity of pluto's orbit is about 1/4 but Pluto is not a planet any more!
Yes indeed.

An eccentricity of 0.2 (Mercury) means however that the major axis differs only by 2% from the minor axis, so even its orbit can still be decribed as "nearly circular". For the other planets "nearly circular" is even more apt! Just a comment. Thanks for your reply.
oldman
#5
Mar4-09, 09:34 AM
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Quote Quote by tiny-tim View Post
I think the maths is mostly to do with the stablility of solutions …

most solutions after a long time tend to an attractor, which in the case of planetary motion seem to be either circular or hyperbolic …

for the maths background, see http://en.wikipedia.org/wiki/Attractor
Thanks. This suggestion is interesting. But why specifically would a circular orbit be an "attractor" solution for a planet? Has it been established for instance that central-force solutions, when perturbed (randomly?), are chaotic with this kind of attractor? Or is circularity established rather by computer modelling? The Wikipedia reference seems too general to make this obvious. Have you by any chance Astronomy-type references to such matters?
D H
#6
Mar4-09, 12:53 PM
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In a word, drag.

By way of analogy, the orbit of a satellite with in low Earth orbit decays due to atmospheric drag. The decay is not uniform. The satellite's orbit will first become close to circular (the perigee won't change nearly as much as the apogee). Once circularized, game over. The satellite's orbit will become smaller and smaller until it decays into to the thick atmosphere.

Planetesimals were also subject to drag with the surrounding medium. A somewhat massive planetesimal at a given orbital distance (semi-major axis) will orbit slightly faster than a piece of dust with the same semi-major axis. The acceleration of the planet and Sun toward each other is G*(Ms+Mp)/r2. For the piece of dust, the acceleration is just G*(Ms)/r2.

The planetesimals plowed through dust. The difference between the planet's and the dust's velocity (drag is proportional to vrel2) is greatest at perihelion. The impact is seen half an orbit later, so drag tends to reduce apohelion.
tiny-tim
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Mar4-09, 01:46 PM
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Quote Quote by D H View Post
In a word, drag.
…
Planetesimals were also subject to drag with the surrounding medium.
ooh, I don't think so …

the main effect on the early Earth would have been from the gravity of Jupiter …

gravitational orbits tend to be unstable, and a big bully like Jupiter can crate havoc …

any body in the wrong position either gets gently nudged into the right position, or gets turfed out into an elongated orbit …

other planets contribute to a lesser extent …

the "right" positions tend to be at "harmonic" ratios, with nothing in between

for some (but not much ) detail, see http://en.wikipedia.org/wiki/Earth%27s_orbit and http://en.wikipedia.org/wiki/Stabili...e_solar_system …
The planets' orbits are chaotic over longer timescales, such that the whole Solar System possesses a Lyapunov time in the range of 2–230 million years … in some cases the orbits themselves may change dramatically. Such chaos manifests most strongly as changes in eccentricity, with some planets' orbits becoming significantly more—or less—elliptical.
D H
#8
Mar4-09, 03:20 PM
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Quote Quote by tiny-tim View Post
ooh, I don't think so …
That remains the dominant view, so much so that the discovery that many exoplanets have highly eccentric orbits was quite the shock.

the main effect on the early Earth would have been from the gravity of Jupiter …
That Jupiter was a major player, no doubt. That it directly caused orbits to be circular, big doubt. The suspected role played by gas giants during planetary formation was the same as now: The tend to make a terrestrial planetesimals' orbits more, not less, eccentric. During planetary formation, that would have exposed a perturbed planetesimal to a thicker supply of planetary medium. Drag would have circularized the orbit.

Think about it this way: Seven of the eight planets in our solar system have orbits with extremely small eccentricities. If the solar system is as chaotic as your post suggests, that is a truly amazing coincidence. If, on the other hand, the primary effect of the chaotic nature is to merely make the planetary positions unpredictable over any extended period of time, then it is not such an amazing coincidence.

The time scale over which the orbits in our solar remain predictable in terms of state is relative short -- a few millions of years. The time scale over which orbital shape (semi-major axis, eccentricity, inclination) remains stable is very long -- much longer than the life span of the solar system for most planets. Mercury is the big exception. The time scale over which Mercury's orbit maintains its basic shape is a few billion years.

In short, the solar system started out with planets in nearly circular orbits. Their orbits remain nearly circular because, except for Mercury (and maybe Mars), the time scale to complete chaos is much greater than the total lifespan of the Sun.
tiny-tim
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Mar4-09, 03:33 PM
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Quote Quote by D H View Post
That Jupiter was a major player, no doubt. That it directly caused orbits to be circular, big doubt. The suspected role played by gas giants during planetary formation was the same as now: The tend to make a terrestrial planetesimals' orbits more, not less, eccentric.
I agree Jupiter generally tends to make orbits more eccentric …

but this gets rid of anything that's in the wrong position, or in the right position but with the wrong behaviour …

leaving only well-brought up planets like Earth …

so perhaps I should have said: what causes the present planets to have nearly circular orbits? the effect of (mostly) Jupiter turfing out anything that didn't
Nabeshin
#10
Mar4-09, 03:41 PM
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Quote Quote by tiny-tim View Post
I agree Jupiter generally tends to make orbits more eccentric …

but this gets rid of anything that's in the wrong position, or in the right position but with the wrong behaviour …

leaving only well-brought up planets like Earth …

so perhaps I should have said: what causes the present planets to have nearly circular orbits? the effect of (mostly) Jupiter turfing out anything that didn't
In this model would the gravitational ejection from the solar system happen pre or post planetesimals?
Phrak
#11
Mar4-09, 04:12 PM
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So far we have: inelastic collisions with dust, 'evaporative cooling'--interactions with smaller bodies, and planetary interactions.

Planetary interactions alone have time reverse symmetry don't they?, unless there's some stochastic thing among many planets I don't see. If so, as Jupiter would tend to stabilize the Earth from an excentric orbit to a circular orbit, it would also destabilize an Earth in a circular orbit to an excentric orbit.
oldman
#12
Mar5-09, 12:10 AM
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Quote Quote by D H View Post
In a word, drag....The planetesimals plowed through dust. The difference between the planet's and the dust's velocity .... is greatest at perihelion. The impact is seen half an orbit later, so drag tends to reduce apohelion.
Thanks for this clear answer to what turned out to be a naive question. The further discussion by yourself, Phrak, Tiny Tim and Nabeshin is illuminating too.
vtorcelli
#13
Oct25-11, 04:22 PM
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Two explanations have been suggested on this forum: (i) drag, and (ii) the influence of other planets, especially Jupiter. The influence of Jupiter does not explain why Jupiter itself has a near circular orbit, and, more importantly, why its Galilean satellites have very nearly circular orbits, or why the rings of Saturn are nearly circular, or why even the Moon's orbit has low eccentricity. It seems that almost everything in a planet-forming nebula, or a satellite-forming one, tends to move together in a circle, despite some persistent small-scale chaos. What goes (locally) too fast is slowed down, and what goes too slow is pushed along. Of course, it is a complicated process, and it is not due entirely to two-body collisions with dust grains or boulders. But in one word that's mostly what it is: drag.
twofish-quant
#14
Oct26-11, 01:11 AM
P: 6,863
The explanation that the planetary scientists I know seem to like is the anthropic one. If the planets didn't have circular orbits, we wouldn't been here to see them.

One reason this this turning into a very popular explanation is that so far in our studies of exoplanets, it appears that a solar system with nice round orbits seems to be uncommon.

Also the paper that you reference is pure-crankdom. The trouble with any sort of fractal theory is that if you have some gravity/fractal/QM effect that explains the motion of planets, then you should be able to create some easy-to-do experiment to show that this happens in the lab. For example, if there is some fractal/QM/gravity effect then surely GPS satellites ought to behave differently in some orbits and not others.
twofish-quant
#15
Oct26-11, 01:21 AM
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Quote Quote by oldman View Post
Thanks for this clear answer to what turned out to be a naive question.
It's not a naive question. It's is very deep and complex one. And as far as I can tell, the answer right now is "we don't really know."

There is an old scientist joke. Observer goes up to a theorist, and says "I've discovered something wonderful." Theorist responds "Great!!! I've got a theory for that." Next day, observer looks disappointed. "It looks like I pointed my telescope backwards, and everything I told you was wrong, and the facts are actually the complete opposite." Theorist says "No problem. I've got a theory for that too!!!!"
D H
#16
Oct26-11, 03:08 AM
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Quote Quote by twofish-quant View Post
Also the paper that you reference is pure-crankdom.
Nice catch! This is an old thread, but ... cranky link deleted.
twofish-quant
#17
Oct26-11, 10:57 PM
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Quote Quote by D H View Post
Nice catch! This is an old thread, but ... cranky link deleted.
One problem with cranky papers is that the truth may be much weirder than the cranks. It's not out of the question at this point that we may be one of the few solar systems that have regular stable circular orbits.

The other thing is that for things like the Galliean satellites. The orbits are synchronized so there is a physical reason for their orbits being where they are. The other solar system objects are not "locked" but one wonders if they once where.

Also, the dividing line between productive theorist and total crank is less clear than it seems. Frank Tipler who popularized the anthropic principle is both totally brilliant and totally nuts. (If he turns out to be right about the omega point, I'll have drinks with him at the Restaurant at the End of the Universe and apologize for that statement.)

The same could be said for Roger Penrose.
narrator
#18
Oct27-11, 12:33 AM
P: 219
Are planetary orbits analogous to the orbits of electrons? And if so, do their orbits infer anything towards answering this question?


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