Why are solar systems (and other spinning systems) flat

The solar system is essentially flat and two dimensional, with all planets except Pluto and Mercury rotating within a few degrees of  the plane which runs through the equator of the sun – at right angles to the overall axis of rotation of the solar system. There are many other similar flat structures –spiral galaxies. the rings of Saturn, accretion discs around black holes and binary star systems. Why?

Accretion ring, white dwarf star, artist's impression. NOAO

It obviously has something to do with spinning , but there is a lot of misinformation out there, with amateur experts talking about ballet dancers and yoyos on strings and “forces” pushing objects into the ecliptic plane,  What is the real answer?

Clearly there is no simple “force” pushing spinning objects flat, otherwise the Earth’s atmosphere would look like Saturn’s rings, clustered around the Equator, and the sun would be a flat disc. The orbits of the Moon’s and Pluto’s orbit would be flat. 

In fact an object can in theory swing around the Sun in any orbit at all. Comets can and do come in from well above the solar system: Halley’s Comet is tilted at 18^o.

Dynamics was never my strong suit and it took a few days to work out the answer to why so many spinning objects in the universe are flat with a lump at the centre. Like many things in the solar system, the phenomenon is the result of system stability considerations.

Consider a car tyre out of balance. It wobbles which is inefficient and wastes energy. In much the same way, if a body orbits the sun obliquely, the system will wobble. All orbits are actually stable, at energy minima, and will last forever if not perturbed, but a round, equatorial orbit in a rapidly rotating system has lower energy than an oblique orbit – it is a better and more stable minimum. The energy difference between flat and oblique orbits depends on the moment, so large, further out objects in a rapidly spiinning system have a greater preference for the ecliptic.than closer or lighter objects.

In practice, what this means is that it is easier to knock an object out of an oblique orbit through collisions or gravitational disturbance than out of an equatorial orbit. The many random collisions in a gas cloud bump or jiggle the material into lower-energy round equatorial orbits.[1] The material jiggled to the ecliptic then further attracts the outlying material through gravity, accelerating the process.

The orbital dust cloud was already flat before the planets formed. Once the dust has cleared, the number of collisions is greatly reduced, so that oblique objects are not likely to be knocked  into an ecliptic orbit,

Pluto is a special case along with the other plutinoid bodies – it resonates with Neptune which keeps its oblique orbit stable.

So, in a universe full of chaos and entropy  – it is amazing that something as simple as spin can result in well-defined organised structures and distinctive shapes such as those of accretion discs.

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[1] This is similar to  an optimization process called simulated annealing, in which a target is knocked out of local minima by jiggling to eventually settle in a global minimum state,