orbital angular momentum

A figure skater pulling in her arms spins faster; a planet swinging close to the Sun races faster. Both obey the same hidden bookkeeping: angular momentum, a measure of 'spinning motion' that, left alone, stays exactly constant. For an orbit it is the quantity that nature keeps locked while the body weaves in and out.

Orbital angular momentum is, roughly, mass times speed times the distance from the center, but only the part of the speed that goes sideways (around the center) counts, not the part going inward or outward. Because gravity always pulls straight toward the central body, it can never twist the orbit, so this quantity is conserved. That single fact is Kepler's second law in disguise: equal areas in equal times is exactly the statement that orbital angular momentum does not change. When the planet is near and moving fast, or far and moving slow, the product balances out to the same value.

Conservation of angular momentum is one of the deepest organizing principles in astrophysics. It explains why collapsing gas clouds spin up into flat spinning disks (and so why solar systems and galaxies are disk-shaped), why an orbit cannot simply fall straight into the Sun unless something carries its angular momentum away, and why accretion onto stars and black holes is governed by the slow outward transport of angular momentum through a disk.