# How is it that all planets (and moons) in our solar system are in equilibrium orbits?

Previously, I was told that in order for any bodies to orbit each other for over a long period of time, the orbital period, distance and masses have to be precisely matched such that the bodies won't eventually collide and forming larger bodies or being swung out of orbit.

How is it then, that all 8 planets (and countless dwarf planets), and their moons, and the Sun are all in such equilibrium for over thousands of years (if not millions)? Could it be possible what we see today are what's left, i.e. countless planets or moons have been swung out of the Solar System and collided, until a stable (relatively speaking) system is reached as we observe today?

• I think the general answer to your question is yes. Any reasonably good sized objects that formed in the early solar-system which had collision-likely or gravity-assist likely orbits are likely to have already collided or been gravity assisted into a different orbit. That's why most of the reasonably large objects that remain are in highly-stable orbits, cause the stuff that wasn't stable has already been "shaken out" so to speak. Given that our solar system's been around for 4 plus billion years, this makes sense. But as this deduction and not evidence, I'm leaving it as a comment. – userLTK Oct 14 '15 at 3:00
• @userLTK Phobos is being shaken out late, crashing into Mars (after having been crushed into a temporary ring system by tidal forces) in only ~50 million years, only 1% of the age since formation. But I suppose that one should expect that 1 out of 100 moons have a property, in one respect, with 1% probability (rounding the numbers). And I wonder if Epimetheus and Janus at Saturn will dance around each other in a long term equilibrium. Looks perilous to me. Maybe future Earthlings will see a faint flash in the sky one night as the pair adds to the rings. – LocalFluff Oct 14 '15 at 10:18
• That's true, but Phobos is also a captured asteroid and I almost hate to say it about what might eventually be a very awesome crash, but it's almost too small to really fit this question. If we look at objects 20 km in diameter, there's probably dozens, perhaps hundreds in the solar system currently risk of destabilization. But a rock that size, every 50 million years hitting one of the planets - that sounds in the range of correct. – userLTK Oct 14 '15 at 10:32
• and I love the Epimetheus and Janus example. I'd forgotten about those two. But I looked and each of them is too small to really throw the other out of orbit, so I don't think anything happens to one or both of them anytime soon. They're each much larger than Phoebos, so that could be interesting if something ever happens there. – userLTK Oct 14 '15 at 10:37
• @JavaPhobic, you might find this interesting. It's a partial explanation as to why there's so much stability and so few impacts, even among smaller objects such as those in the asteroid belt. Many smaller objects tend to fall into resonance with larger ones. en.wikipedia.org/wiki/Orbital_resonance – userLTK Oct 14 '15 at 10:50

The reason why, is of course, related to gravity. Or more correctly, the gravitational potential of the system. All systems want to thermalise (in the same sense that a room of air molecules want to reach a thermal equilbirium). Although our solar system is anything but thermalised, it is constantly working to achieve this. Hence, why, at our present state of the solar system's evolution, we seem like we are in a fairly calm state. At this state, to go into more depth, we can employ Bertrand's theorem which tells us that for a central potential with an $r^{-1}$ dependance on radial distance the orbits will be stable. The stability of orbits in three spatial dimensions is due to the fact that the gravitational potential decreases with distance $r$ as $r^{-1}$.