Gravity's First PunchNewton’s Law of Universal Gravitation (1687)

Gravity's First Punch lands on everything, and it lands the same way every time.

The rule on this page is from Newton's Principia of 1687: every mass attracts every other with a force proportional to the product of the masses and falling off with the square of the distance between them. The famous check is the Moon. It orbits about 60 Earth radii from Earth's centre, so the inverse square predicts that it falls toward Earth 60 × 60 = 3,600 times more gently than an apple at the surface. Work out how far the Moon drops from a straight line each second, and that is what you find.

Newton never knew G. His law fixes ratios: Moon against apple. To get the force in newtons you have to measure the pull between two objects in a laboratory, and that pull is absurdly weak. In 1798 Henry Cavendish did it with a torsion balance, lead spheres and a fine wire, reading the deflection through a telescope from outside the room so his body heat would not stir the air. He reported his result as the density of the Earth. G can be extracted from his numbers; the symbol came later.

G remains the hardest fundamental constant to pin down. The value on this page, 6.674 30 × 10⁻¹¹, carries an uncertainty of about 22 parts per million, while the speed of light and the electron's charge are now exact by definition.

The punch is not undefeated. Mercury's orbit swings round slightly faster than Newton allows, and Einstein's general relativity accounts for the difference. Newton's law is what Einstein's theory becomes when gravity is weak and motion is slow, which covers almost everywhere you will ever stand.

The punch does not bend spacetime. It is right anyway, nearly always.