Law of universal gravitation - Definition and Overview

The law of universal gravitation states that gravitational force between masses decreases with the distance between them, according to an inverse-square law. In addition, the theory notes that the greater an object's mass, the greater its gravitational force on another mass. Newton published his argument in Philosophiae Naturalis Principia Mathematica (1687). It is important to note that Newton was not "inventing" or "discovering" gravity; he was merely defining it mathematically. Newton would use universal gravitation, along with his laws of motion, to substantiate Kepler's laws of planetary motion. Newtonian gravitation can be derived from general relativity in the limit where the bodies are moving slowly with respect to the speed of light and the gravitational field is weak and unchanging with time. This would be a good example of the correspondence principle where the newer and more accurate or comprehensive theory breaks down to the previous theory in the domain where the previous theory is valid.

• Every object in the Universe attracts every other object with a force directed along the line of centers for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects. (See also inverse-square law.)
• Two bodies attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Strictly speaking, this law applies only to point-like objects. If the objects have spatial extent, the true force has to be found by integrating the forces between the various points.

<math>F = G \frac{m_1 m_2}{r^2} <math>

where:

• <math>F \ <math> = gravitational force between two objects
• <math>m_1 \ <math> = mass of first object
• <math>m_2 \ <math> = mass of second object
• <math>r \ <math> = distance between the objects
• <math>G \ <math> = universal constant of gravitation