LearnMechanics & orbitsSome maths
Tides
The stretching a body feels because gravity pulls harder on its near side than its far side.
Why it matters
Tidal forces raise oceans, heat moons from the inside, lock rotations to orbits, and eventually tear bodies apart inside the Roche limit.
The maths, in layers
1 · Intuition
What matters is not the strength of gravity but its *difference* across the body — the gradient. That falls off as the cube of distance, not the square.
2 · The equation
F_tidal ≈ 2·G·M·m·R / d³
- R
- radius of the body being stretched
- d
- distance to the body doing the stretching
What people usually get wrong
There is one tidal bulge, on the side facing the Moon.
There are two. The near side is pulled toward the Moon more than the Earth's centre is; the far side is pulled less, so it is left behind. In the Earth's frame both look like bulges — which is why there are two high tides a day, not one.
Leads to
- Orbital resonanceTwo orbiting bodies exerting regular, repeating gravitational tugs on one another because their periods form a ratio of small whole numbers.
- Precession of the equinoxesThe slow conical wobble of Earth's rotation axis, one turn every 25,772 years, driven by the Sun and Moon pulling on our equatorial bulge.