Concept

Gravitational field — where it appears

The acceleration a test body experiences at a point, being the gradient of the gravitational potential. Outside all the mass it is a sum of spherical harmonics whose coefficients fall as Kaula's rule, and how many of them a spacecraft can feel is set by its altitude.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Why a shell pulls a point inside it not at all. A double cone from a point inside a uniform shell. In the narrow-cone limit the far patch is 2.80 times further away and 2.80 times wider — the same number, checked to a part in a thousand before this figure is drawn. Its mass is greater by the square of that ratio and its pull weaker by the same square, so the two cancel in every direction.

A sphere pulls exactly like a point, and the proof is a pair of cones

Every orbit ever computed treats the Sun as a dot. That is not an approximation — for a spherical body it is exact, and the reason is a cancellation between two patches of a shell.

gravitation · Shell theorem

The tidal field is a difference. The pull of a distant body at each point of a sphere, minus its pull at the sphere's centre. What remains stretches along the line to the source and squeezes across it — two bulges, not one.

The tide is a difference, which is why there are two of them

The Moon pulls the ocean toward it. That explains one bulge. The second one, on the far side, is the whole of the physics — and it comes from subtracting.

gravitation · Tides

Named alongside it

The objects these essays reach for when they reach for this one.

Angular momentum Black hole Eccentricity Free-fall Gauss's law Gravity gradient Inverse square law Oblateness Roche limit Shell theorem Tidal force Tidal locking

All concepts