Why are the planet's orbits so stable? (or are they?)

Tomorrow will see an alignment of Mars, Earth, and the Sun. That got me wondering about why all the planets in the solar system don’t end up coalescing or having strange orbits. I can understand how everything was stable at the beginning. But after the billions and billions of revolutions, why haven’t the gravitational forces of the planets interacted with each other and nudged everyone out of place? It’s seems the constant tugging and pushing, no matter how small, would eventually cause things to get out of whack.

They do knock each other around a bit. For example, Neptune, the eighth of our nine planets (shut up) was predicted to exist precisely because perturbations in the orbit of Uranus suggested there might be something massive nearby. Sure enough, they looked, and there it was.

But the sun is quite a bit larger than all the planets, and its gravitational effects are strong enough that the planets tend to stay in relatively stable orbits around it.

The planets’ gravitational pulls DO nudge things out of place. Several of the moons of Jupiter and Saturn are thought to be captured asteroids.

The absolute biggest influence by far is the sun. There’s no real reason for the planets to have an appreciable affect on each others’ orbits unless they pass very close to each other.

Gravity doesn’t work like a big vacuum cleaner. Even over the course of billions of revolutions, the sun will have the predominant effect, overriding the nudges of the other planets over planetary distances. That’s why such big effects are only seen with asteroids - they come close enough.

The planets are very small and very far apart. Consider Mars, for example. Its closest approach to earth is 76 million kilometers, and it weighs just 6.4 X 10[sup]23[/sup] kg.

Compare that to the sun. It’s 149 million kilometers from earth, but its mass is a staggering 1.99 X 10[sup]30[/sup] kg. In other words, the gravitational force beween sun and Earth is about 2,500,000 greater than the force between Mars and Earth.

Jupiter? its pull on earth is about 18,000 times weaker than the sun.

The outer planets are spaced really far apart, and their masses are a small fraction of that of the sun; basically, compared to the sun, none of the planets pull on each other very much. It’s noticeable, as friedo points out, but not enough to radically destabilize the whole solar system.

I actually was looking this up last week for one of my students. Wikipedia:

The odds I heard quoted on another site were 100-1 against over the next 5 billion years.

See for yourself: If the Moon Were Only 1 Pixel.

Also, the effect of random perturbation on an orbit will mostly be to cause the orbit to circularize. This has, of course, already happened in our Solar System, which is why the planets’ orbits are all so circular.

There’s the Titus Bode law, which suggests there’s a regular spacing to the planets. IIRC the bigger moons of Staurn and Jupiter seen to follow this too.

the net result is that the orbital perios are relatively prime, meaning there’s as much cancelling as reincforcing when it comes to orbital parameters. IIRC gaps in the rings of Saturn are multiples of the larger moons’ orbits, and gaps in the asteriod belt are harmonics of Jupiter’s orbit, and so on.

So any situation where planets get into a harmonic, the gravitational influence will pull the planet(s) out of that situation. If it’s not stable enough, then yes the planet will go shooting off into never-never land. Smaller pieces that have this problem have probably been pulled out of their orbit and “amalgamated” with more stable planets - much as shepherd moons keep the rings in place at Saturn.

Do we know that they are? Well at least do we know that planets generally orbit in a plane?

In our own solar system our largest planet actually does not orbit our star but they co-orbit each other (the center of orbit of Jupiter and the Sun is outside the sun’s sphere), does this have any effect on why we orbit in such a manner?

Not only does the relationship *not *work for the solar system it doesn’t work for moons. [Nitpick, Titus and Bode are two people, so it’s the Titus-Bode Rule.]

That Wikipedia page suggests that some extrasolar planetary systems adhere to the Law or some variation but the original article they source that from decidedly do not say that. They make the point, in fact, that no relationship law can be applied unless all the major bodies in the system are known and that’s not the case for any extrasolar systems yet.

What you describe here is the opposite of stability. If perturbations cause things to “get out of whack”, that is the definition of an unstable system.

Imagine a pendulum. Push it a little, and it will oscillate, but eventually settle back into its original – hanging straight down – orientation. Now, turn the pendulum upside down, so that it is standing straight up like a tree. If it’s perfectly aligned, it will stay there. But any gust of air, or an insect landing on it, or any tiny perturbation will cause it to topple over, and go back to the hanging position. Therefore we say the pendulum is stable in the “down” position, but unstable in the “up” position.

Now I’m not going to get into the math, but you can imagine when the solar system was new, and basically a cloud of gas and dust with a giant fireball in the middle, most of that matter was in a highly unstable position. It coalesced into bigger and bigger rocks with various orientations and speeds and orbits – most of which were unstable. You can see evidence of this on planetary bodies without atmospheres. Those rocks are littered with craters, scarred by collisions with unstable bodies billions of years ago. But like the pendulum, things eventually settled down into a stable configuration.

Earth’s orbit is stable, since we’ve been impacted by some fairly huge asteroids over the years and we still orbit the sun the same amount of time. Halley’s comet is stable, since it returns every 75-ish years and has for recorded history. Shoemaker-Levy 9 was unstable however, as it came out of nowhere to collide with Jupiter in 1995. But Jupiter is still there, in the same orbit.

My point basically is that in a stable system, the defining characteristic is that the tugging and pushing and nudging have no effect on the overall orientation of the system.

This is technically true of every orbiting body. The Earth doesn’t orbit around the center of the Sun. The Earth and the Sun orbit around a common point which just happens to be below the surface of the Sun. The fact that the Jupiter-Sun system orbits around a point outside of the Sun is just a difference of degree.

This isn’t just the Sun and Jupiter; all bodies orbit in a non-rotating frame at the common center of mass which astronomers call the barycenter. When one mass is much, much larger than another, such as M[SUB]Sun[/SUB]>>M[SUB]Earth[/SUB] the difference from a Sun-centered rotational system is almost immeasurably tiny, so it can be ignored for its influence on other bodies (like satellites) for even relatively long intervals of time. This is basic celestial mechanics, albeit more complex than that predicted to only a first degree of accuracy by Kepler’s laws of planetary motion. (Despite being referred to as “laws” the assumptoin of elliptical orbits is only a rough approximation of Newtonian mechanics.)

To the question of the o.p., this can occur and is referred to as planetary migration. It will happen when two bodies with masses which are within a few orders of magnitude of each other perturb (transitorially influence) one anothers orbits. Such systems are never truly stable, but they can often exist in a range of quasi-chaotic perturbations from which the perturbence energy never exceeds the gravitational potential energy required to permanently separate the objects (referred to as characteristic or “C3” energy where the orbit transitions from a really eccentric ellipse to a parabola). They don’t happen in our system with the major planets because they are so widely separated that they don’t dramatically perturb one another, but they can happen to smaller bodies, of which the early solar system was probably crowded with.

However (goes the conventional theory, backed up by stochastic simulation) the large influence of Jupiter and Saturn tended to fling these objects up and out, clearing out most of interplanetary space of debris except for the mostly stable band between Mars and Jupiter where the asteroid belt lies. The asteroid belt, despite what you may have heard, was not a planet shattered by impact or torn asunder by competing gravitational influences, but instead happens to be an area of relative gravitational invariance where the Sun’s gravity dominates all other influences. These areas are known as “KAM tori” after the Kolmogorav-Arnold-Moser which predicts regions of stability in dynamical, perturbative systems.

The orbits of the planets (save, perhaps, for Pluto and other minor planets) is very stable and will remain so long past the point that the Sun expands and engulfs the inner system. The attitude of the planets may change to some greater or lesser degree dependant upon other influences; Jacques Laskar, for one, predicts that planets without large moons will experience dramatic changes in attitude or tilt due to even minor perturbations, though the evidence and validity of this claim is still somewhat contentous. (Laskar’s work is largely by simulation and mostly references his past work.) The gyroscopic dynamics of planets, especially those with viscous cores like the Earth, are still not well understood or precisely characterized for intervals of astronomical length.

Stranger

My understanding is that the orbit of sun-Jupiter is different in that the orbit baricenter is outside the radius of the sun. So they are co-orbiting:

Jupiter is the only planet that has a center of mass with the Sun that lies outside the volume of the Sun,

I would also like to note (sorry if this has been mentioned before) that “at the beginning” things were far more unstable than they are now and we’re looking at the stable state of a once chaotic system.

Yes, the orbit of each major planet is on a plane, the angles between the planes of the planets and both the ecliptic (Earth’s plane) and the sun’s equator are known, and the orbital planes are close to being in the same plane (all within 8 degrees). Minor planets are more erratic.

I hadn’t heard about Jupiter and the sun co-orbiting. That’s kind of cool. I think what Stranger is saying is that whether they’re co-orbiting slightly or not does not affect how stable their orbit is, and the current configuration is pretty stable for the major planets. I’d agree with JohnT’s summary.

That’s . . . . comforting . . . sort of.

On the point about how weak the pull of other planets is, I remember a story about Patrick Moore, who used to enjoy debunking astrologers.

A ‘famous’ astrologer claimed that the planets influenced new born babies at the time of their birth (apparently a basic tenet of astrology) by their gravitational pull. Moore pointed out that a fat midwife would have a greater gravitational effect than all the planets combined.

It turns out things weren’t stable in the beginning. Current thinking is that in the first 5 million years, the planets did some migrating. This theory is known as the Grand Tack. According to this model, Jupiter formed about where the inner asteroid belt is now, migrated inward to about Mars’ current distance. At that point, it falls into a resonance with Saturn (which has also migrated inward), and then the two migrate outward. All this to explain why Mars’ mass is so low.

Later on (about half a billion years or so), the outer planets migrate further out as described in what is known as the Nice model. It’s only after all this movement (and possible expulsion of a fifth gas giant) that things settled down to the way they are today.

Somewhere in there is the Big Splash theory, where a small planet, named Theia and thought to be about 10% of Earth’s current mass, collides with the proto-Earth. Most of it gets incorporated into the Earth, but some ends up in orbit along with some of Earth. That debris in orbit coalesces into the Moon.

Note that these are are all just models and are subject to change and modification. Or even outright replacement with a better model.

You may want to read this article from American Scientist - Are Planetary Systems Filled to Capacity?

Note the article is from 2007 so maybe check and see if they’ve published any newer ones. I’m off to check.

I’m very concerned that no one in this thread is taking seriously the threat to the stability of planetary orbits posed by Nibiru.

Here’s a nice little browser game, the goal of which is to create a stable configuration of planets: