Law of Universal Gravitation

The Law of Universal Gravitation explains that gravitational force decreases with distance. In addition, the theory notes that the greater an object's mass, the greater its gravitational force. 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 graviation, along with his laws of motion, to substantiate Kepler's laws of planetary motion.

• 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.
• 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.

where:

• F = gravitational force between two objects
• m₁ = mass of first object
• m₂ = mass of second object
• r = distance between the objects
• G = universal constant of gravitation