Math · chapter 1 of 13
Everything pulls on everything
Two things pull on each other. The pull goes up with the weight and down with the square of the distance. That one line is the whole engine.
Put two rocks in empty space and let go. They drift toward each other. Newton wrote down how hard, and the sentence has held for three hundred years.
Weight helps the pull. Distance hurts it, and it hurts it twice over: move the rocks twice as far apart and the pull drops to a quarter. Ten times as far, a hundredth. That is what inverse square means, and it is the reason a tractor a mile off does nothing to your coffee while the Earth under the porch holds you in the chair.
The second line matters as much as the first. The pull is a force, and a force divided by weight is how fast something picks up speed. Divide, and your own weight cancels out. A feather and an anvil dropped on the Moon land together — the Moon pulls the anvil harder, and the anvil is harder to move, by the same factor.
So each rock's speeding-up depends on the other rock's weight, not its own. Hold that and the rest of this site follows.
Reading it: The pull between two things equals a fixed number G, times the first weight, times the second weight, divided by the distance between them multiplied by itself.
Reading it: How fast the first one picks up speed does not depend on its own weight at all. Only on the other one's weight and the distance.
This cancellation is why the Sun's grip on the Earth can be worked out without knowing what the Earth weighs.
Reading it: G is a tiny number, which is why you never feel your neighbour's gravity.
Measured, not derived. The 2022 value carries an uncertainty of 22 parts in a million — the worst-known of the fundamental constants.
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