the inverse-square law
Stand near a candle and it feels bright; step back and it dims quickly. Not just a little slower, but dramatically: go twice as far away and the light is not half as bright but a quarter as bright. That pattern, where a quantity falls off with the square of the distance, is called an inverse-square law, and gravity follows it exactly.
Written as a proportion, the strength is proportional to 1 / r^2, where r is the distance. So if you double r, the strength drops by a factor of 2^2 = 4; triple r and it drops by 3^2 = 9. Newton's gravity is F = G m1 m2 / r^2 and Coulomb's electric force is F = k q1 q2 / r^2; both are inverse-square. There is a beautiful geometric reason: influence spreading out from a point source is diluted over the surface of a sphere, and a sphere's area grows as 4 pi r^2, so the same influence per unit area thins out as 1 / r^2.
A useful subtlety: this clean law applies to point sources or to objects that are spherically symmetric, like a uniform planet. Newton proved (the shell theorem) that a uniform sphere pulls on things outside it exactly as if all its mass were squeezed into a point at its centre, which is why we can use r as the distance to the centre of the Earth. Inside a hollow shell, remarkably, the gravitational field is zero everywhere.
A satellite at two Earth-radii from the centre feels 1/2^2 = 1/4 of surface gravity, so instead of 9.8 m/s^2 it feels about 2.5 m/s^2. Move out to three Earth-radii and it feels only 1/9 of surface gravity.
Distance is measured from the centre of the planet, and gravity fades with the square of that distance.
The clean 1/r^2 form assumes a point source or a spherically symmetric body; for a uniform sphere, r is the distance to its centre, not its surface.