Newton's law of universal gravitation

Introduction

Newton's law of universal gravitation is a fundamental principle in physics that describes the gravitational interaction between two bodies with mass. It is a part of classical mechanics and was formulated in the 17th century.

Historical Background

Newton's law of universal gravitation was first published in his work, "Philosophiæ Naturalis Principia Mathematica" in 1687. This law was a significant milestone in the history of physics, as it unified the previously separate fields of terrestrial and celestial mechanics. It was a revolutionary concept that proposed a universal force acting between all matter.

A mature apple tree with ripe apples hanging from its branches.

Mathematical Formulation

The mathematical formulation of Newton's law of universal 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 their masses and inversely proportional to the square of the distance between their centers. This can be expressed as:

F = G * (m1 * m2) / r²

Where: F is the force of attraction between the two bodies, m1 and m2 are the masses of the two bodies, r is the distance between the centers of the two bodies, and G is the gravitational constant.

Gravitational Constant (G)

The gravitational constant (G) is a key part of the law of universal gravitation. It is an empirical physical constant involved in the calculation of gravitational effects. The value of G was first accurately determined from the results of the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798.

Applications and Consequences

The law of universal gravitation has wide-ranging consequences and applications. It not only explains the motion of celestial bodies but also provides the basis for understanding a variety of phenomena such as tides, gravitational lensing, and the motion of aircrafts.

Limitations and Relativity

While Newton's law of universal gravitation provides an accurate description of the effects of gravity in many contexts, it has its limitations. The theory of general relativity, proposed by Einstein in 1915, provides a more comprehensive description of gravitation at larger scales and higher masses.