The elliptical orbits of the planets

[mooeypoo]

We started some REALLY interesting stuff in our Classical Dynamics class - Keppler's laws (sp?). As an initial intro, our professor explained a bit about ellipses and the reason planets travel in an elliptical orbit around the sun.

 

This was always a sort of a conceptual problem for me, tbh; I guess because i'm used to think of things in terms of simple Newtonian physics, but I always wondered about this. It seemed to me that the "most efficient" orbit is circular, because all the forces equal one another (no change in speeds, too), and I wondered why the planets are not moving that way.

 

The professor did a good job explaining about this (let's see if I got this right) - He explained that if a planet has *exactly* the speed of that circular orbit of R radius from the sun, it would stay there, but planets usually don't have that speed - their speed is slightly higher, so they're "thrown out" to a bigger orbit (and create an ellipse) - but when they reach this orbit with a larger radius, their speed is not high enough to maintain this orbit, and they "resume" the lower orbit, and so on and so forth -- maintaining an elliptical orbit.

 

I got this part (I think), but it got me thinking. If, theoretically, a planet is FORMED *already orbitting* its star, then shouldn't it already form in the "right" orbit for it? where its speed is perfectly fitting for a circular orbit?

 

It sounds to me as if the planet was "trapped" by the sun (hence, the current orbit wasn't its original orbit) and therefore it wasn't in the 'correct' speed for that radius, and it keeps doing ellipses.

 

I can understand this happening with comits and asteroids, but the "native" planets in our solar system.. it sounds like there's something more to it.

 

The way I understand it, when a star is formed within a nebula, the gas cloud is rotating at different speeds (like rings), but at CIRCULAR 'orbits'; the star forms and the planets 'cear out' their paths from the debris and collect more matter to condense and become solid (or.. gaseus or.. whatever else). I know it's an oversimplification, but I am trying to explain my thoughts on this and why I am asking about the conclusion at the end.

 

So, technically, the planets SHOULD have all orbitted at circular orbits, because they were formed within those 'rotating' rings of gas inside the nebula. but then, they're no longer circular, they're elliptical (which says that they don't have the 'speed' for their current orbit). Is it possible they "moved" (maybe as the Sun formed and got bigger? err) to a different orbit..?

 

If I remember correctly, I've read that the planets and the Sun were formed realtively at the same time. So.. does the elliptical orbit of the planet mean that they weren't formed, initially, in their CURRENT orbit, but rather were pulled into a lower orbit after they already had an initial rotation speed (hence, after they were already blobs of matter..)

 

I'm kinda guessing here, the information is still a bit new in my mind, and I hope I understood it correctly.

 

I *think* that Neptune has a more elliptical orbit than the Earth (ours is barely 'noticeable', if i remember correctly), so is it logical to assume that Neptune was 'shifted' from its original orbit more than the Earth?

[swansont]

You may start circular, but even if you did, there will be perturbations. At the very least, from other planets.

 

This is merely a guess, but the circularity may also depend on how much matter there was in the vicinity, to collide and circularize the path.

[D H]

Some reading on this subject:

 

Lin, D.N.C. (2008), "The Chaotic Genesis of Planets", Scientific American, May 2008

http://www.sciam.com/article.cfm?id=the-genesis-of-planets

The study of planet formation lies at the intersection of astrophysics, planetary science, statistical mechanics and nonlinear dynamics. Broadly speaking, planetary scientists have developed two leading theories. ... Although researchers have not settled this controversy, most consider the sequential-accretion scenario the most plausible of the two. I will focus on it here.

 

Ford, E.B., Lystad, V., Rasio (2005), "Planet–planet scattering in the upsilon Andromedae system", Nature 434, 873-876

A major puzzle is why many of their orbits are highly eccentric; all planets in our Solar System are on nearly circular orbits, as is expected if they formed by accretion processes in a protostellar disk. Several mechanisms have been proposed to generate large eccentricities after planet formation, but so far there has been little observational evidence to support any particular model.

 

Free summary: "Mystery of extrasolar planets' eccentric orbits", Spaceflight Now, April 19, 2005

http://www.spaceflightnow.com/news/n0504/19orbits

Instead of the nice circular orbits our nine planets enjoy, most of the more than 160 extrasolar planets detected in the last decade have eccentric orbits: so elongated that many come in very close to the central star and then go out much further away.

 

Thommes, E.W., Duncan, M.J., Levison, H.F. (2002), "The formation of Uranus and Neptune among Jupiter and Saturn", The Astronomical Journal 123 2862-2883

arXiv preprint: http://arxiv.org/abs/astro-ph/0111290

The outer giant planets, Uranus and Neptune, pose a challenge to theories of planet formation. They exist in a region of the solar system where long dynamical timescales and a low primordial density of material would have conspired to make the formation of such large bodies very difficult. Previously, we proposed a model that addressed this problem: Instead of forming in the trans-Saturnian region, Uranus and Neptune underwent most of their growth among proto-Jupiter and proto-Saturn, were scattered outward when Jupiter acquired its massive gas envelope, and subsequently evolved toward their present orbits. We present the results of additional numerical simulations, which further demonstrate that the model readily produces analogs to our solar system for a wide range of initial conditions. We also find that this mechanism may partly account for the high orbital inclinations observed in the Kuiper belt.

[Mr Skeptic]

To have a circular orbit, the angular momentum has to be in the right proportion. A circular orbit has the least angular momentum for the energy of the orbit.

[D H]

To have a circular orbit, the angular momentum has to be in the right proportion. A circular orbit has the least angular momentum for the energy of the orbit.

The gas cloud should comprise a bunch of little chunks of matter all orbiting the star more-or-less circularly and in more-or-less the same plane. Any protoplanets that form should thus have nearly circular orbits. The protoplanet will orbit slightly faster than the gas around it, so the gas cloud will provide a drag force on the protoplanet. This will make protoplanet's orbit circularize even further and will make the protoplanet migrate starward.

 

This inward migration explains why we see so many star systems with hot Jupiters. It does not explain why we see so many star systems with planets in highly eccentric orbits.