Gravitation

Before Newton, scholars believed different laws governed objects in the sky versus on Earth. Newton unified these by proposing that the force pulling the moon toward Earth's center matched the force pulling an apple to the ground. This revolutionary insight connected planetary motion, lunar orbits, and everyday gravity under one universal phenomenon.

By analyzing the moon's 27.3-day orbit and comparing lunar acceleration to Earth's surface gravity, Newton found acceleration decreases inversely with distance squared. Since force equals mass times acceleration, gravitational force is directly proportional to mass but inversely proportional to distance squared, establishing the inverse square law.

Newton observed that planetary acceleration decreases inversely with distance from the Sun, mirroring the moon-Earth relationship. He predicted gravitational force acts between the Sun, planets, and their moons. Extending this pattern to all objects in the universe, he formulated the law of universal gravitation governing celestial and terrestrial bodies alike.

The inverse square law states gravitational acceleration is inversely proportional to distance squared. Objects closer to a massive body experience stronger acceleration; doubling distance reduces acceleration to one-quarter. This relationship explains why the moon's acceleration differs from objects falling on Earth and why acceleration due gravity on other planets varies with their size and distance from the Sun.

Newton's law of gravitation required the gravitational constant to quantify the strength of gravitational attraction between masses. This constant was derived experimentally, with Henry Cavendish conducting the first successful measurement. Once known, the gravitational constant allowed Newton's laws of motion and gravitation to predict and derive Kepler's laws of planetary motion.

Gravitational acceleration is independent of an object's mass, meaning all objects fall at the same rate regardless of mass. According to Newton's laws of motion, if acceleration is constant, force must be proportional to mass. This insight led Newton to conclude gravitational force depends directly on mass, forming a cornerstone of his universal gravitation law.

Kepler's laws described planetary orbits geometrically but lacked fundamental explanation. Newton showed that gravitational force, following the inverse square law, produces the orbital patterns Kepler observed. With the gravitational constant determined experimentally, Newton's laws of motion and gravitation could mathematically derive all three of Kepler's laws, unifying celestial mechanics.