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Classical Mechanics

Gravity

Gravity was Newton's most sweeping idea. Before him, the fall of an apple and the wheeling of the Moon seemed unrelated. He proposed they are the same force, obeying one law that reaches across all of space.

Universal gravitation

Every mass attracts every other mass. The strength of the pull grows with the masses and weakens rapidly with distance, as the square of the separation:

A diagram of Newton's universal gravitation: two masses separated by a distance r, with equal and opposite force arrows pulling them together, and the Earth-and-Moon shown as the same idea at large scale.
A diagram of Newton's universal gravitation: two masses separated by a distance r, with equal and opposite force arrows pulling them together, and the Earth-and-Moon shown as the same idea at large scale.
F=Gm1m2r2.

Here m1 and m2 are the two masses, r the distance between them, and G a tiny universal constant that sets the overall strength. The inverse-square falloff is crucial: double the distance and the force drops to a quarter.

The apple and the Moon

Newton's leap was to realise that the force pulling the apple to the ground is the very same force that holds the Moon. The Moon is falling too (constantly falling toward the Earth) but it also moves sideways fast enough that it keeps missing, curving around instead of hitting. One law, tested on the apple, could be stretched to the heavens and made to predict the Moon's motion. It worked, and the division between earthly and celestial physics dissolved.

Weight and g

Near the Earth's surface this law gives every object the same downward acceleration, about 9.8m/s2, usually written g. That is why, ignoring air resistance, a hammer and a feather fall side by side: gravity supplies more force to the heavier hammer, but the hammer's greater mass resists acceleration by exactly the same factor, and the two effects cancel. Your weight is simply this gravitational force on your mass; step onto another planet with different mass and radius, and your weight changes while your mass does not.

The reach of the law

Universal gravitation explained the tides, the paths of comets, and the orbits of the planets, all from a single formula. It was the first great demonstration that the universe runs on discoverable law, and it sets up the final lesson, where gravity and inertia together produce the orbits that circle the Sun.