14.1: Gravitation

In the years before Newton, a general belief prevailed that different laws governed objects in the sky than objects on Earth. When Kepler wrote down the three laws of planetary motion, explaining in detail the geometrical properties of the planetary orbits around the Sun, there was no immediate idea to discern their connection with more fundamental laws. It was Isaac Newton who, in 1665–66, figured out the connection between planetary motion, the motion of the moon around the Earth, and the everyday phenomenon of objects falling onto the Earth's surface. This universal phenomenon is today known as gravitation.

Although it sounds common today, the statement that the same phenomenon governs the motion of objects on Earth and the motion of the moon around the Earth was revolutionary in Newton's times. He figured out that the acceleration of the centripetal moon around the Earth and the acceleration due to gravity have a ratio that is inversely proportional to the square of the respective object's distance from the Earth. Since the acceleration is independent of mass, according to his laws of motion, the force must be proportional to the mass. This insight led him to formulate the law of gravitation named after him.

Another piece of information required to complete Newton's law of gravitation was the gravitational constant, which was derived experimentally. The first successful experiment to measure the constant was carried out by Henry Cavendish. Once the value of this constant was known, along with Newton's laws of motion, Kepler's laws of planetary motion could be derived.

The revolution of the moon around Earth indicates the presence of a force that attracts it toward the orbit's center.

Issac Newton proposed that this attractive force is the same as that which pulls an apple toward the ground.

It was a revolutionary idea, since celestial objects and objects on Earth were believed to follow different rules.

The moon takes 27.3 days to orbit Earth. Considering the average distance to the moon, its acceleration can be estimated. 

The ratio of lunar acceleration to the acceleration of an object falling on Earth indicates that acceleration is inversely proportional to the distance squared.

Since force is mass times acceleration, the gravitational force is directly proportional to the mass and inversely proportional to the distance squared.

Observing that the acceleration of planets decreases inversely with their distance from the Sun, Newton predicted that gravitational force acts between the Sun, the planets, and their moons.

Extending this argument to all the objects in the universe, Newton formulated the law of universal gravitation.