14.2:
Newton’s Law of Gravitation
Newton's law of gravitation states that "Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them."
Here, the proportionality constant G is known as the universal gravitational constant. Its value is 6.67 × 10−11 newton meter squared per kilogram squared.
Gravitational forces always act along the line joining the centers of two particles and form an action-reaction pair having equal magnitude.
For example, the force that the Earth exerts on the apple has the same magnitude as the force that the apple exerts on the Earth.
The Earth's mass is much greater than that of the apple. Therefore, its motion towards the apple is negligible compared to the apple's motion towards the Earth.
Gravitational force acts at very long distances without any direct contact between the bodies. It is this force that is responsible for holding the entire expanding universe together.
14.2:
Newton’s Law of Gravitation
Our everyday observation tells us that all objects close to the Earth naturally tend to fall to the ground. Early philosophers assumed that this downward force was unique to Earth. By the 16th century, Nicolaus Copernicus (1473-1543) put forward the heliocentric theory, which suggested that Earth and other planets orbited the sun, while the Moon orbited the Earth. However, it was Isaac Newton (1642-1727) who linked these two motions together in the 17th century. He reasoned that the force of attraction that causes the Moon to follow its path around the Earth also causes an apple to fall from a tree. He discovered the fundamental nature of gravitational attraction and published his universal law.
Newton's universal law of gravitation states that every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
A century after Newton published his law of universal gravitation, Henry Cavendish (1731-1810) determined the proportionality constant G experimentally. This constant is universal in nature, such that it applies to masses of any composition and is the same throughout the universe. The value of G is an incredibly small number (6.674 x 10-11 N·m2/kg2), showing that the force of gravity is very weak.
Although gravity is the weakest of the four fundamental forces of nature, its attractive nature binds us to Earth, causes the planets to orbit the Sun, the Sun to orbit our galaxy, and binds galaxies into clusters. Gravity is the force that forms the Universe.
This text is adapted from Openstax, College Physics, Section 6.5: Newton's Universal Law of Gravitation and Openstax, University Physics Volume 1, Section 13.1: Newton's Law of Universal Gravitation.