The unlikely marriage of orbiting bodies O.k. so we have an orbiting body such as the Earth around the sun or the moon around the Earth. The fact that they are orbiting does not fascinate me, it is my intuitive sense that there is a much greater chance of bodies not finding a stable orbit. Therefore falling out of kilter and either crashing into one another or wandering off into space. It is the equilibrium that I find difficult. That all the forces involved have balanced so that two or more objects can orbit each other for very long periods. Why does everything around us seem to have fallen into this complicit and unlikely marriage of mutual harmony? What am I missing?
 A: There is no real need of general or special relativity in your question.
Newtonian physics is pretty much enough.
What you miss is that:

*

*There is a lot of dissipative mechanisms involved in arranging the stable orbits

*A lot of material with unfavorable kinetic energy or angular momentum is either thrown away or falls over some celestial body. Or, if said in reverse: some of the available material is used to carry away the excess angular momentum or energy.

Imagine the primpordial cloud of gas and dust with the proto-Sun in the centre.
Particles in the cloud have random speeds and directions. The whole cloud has some average rotation.
Particles constantly scatter into each other and exchange momentum. The scattering gradually averages their rotation and now you have a disk instead of a cloud.
The cloud is shaped into disk by something quite resembling friction.
Those particles that don't settle in the disk are either thrown away on escape trajectories or fall into the Sun.
Now, any concentric layer on the disk has almost perfect circular orbit. When particles clump into planets, they are already near their final orbit.
The final orbit is averaged over the particles that coalesced into the big clump.
Quite simplified, but you may get the idea.
There are also orbits that are not shaped by friction, but by a single event (collision, near encounter, etc...). They manifest their origin by their high eccentricity (e.g. comets).
In some cases, eccentric orbits circularize with time. This is also done by friction (in this case, tides).
A: One way of thinking about this is to use a tool called the effective potential; orbiting bodies fall in a minimum of the effective potential, so the equilibrium is stable to perturbations around the equilibrium. You may contrast this with unstable equilibriums, which can happen at maxima of potentials (such as balancing a pencil on its tip).
