By Newton's time, work by Galileo, Kepler, Descartes, Hooke, and others had led to an understanding of inertial motion and the need for a central force to account for the curved paths of the planets around the Sun.
Newton's law of inertia says that the momentum of an object remains constant unless it is acted on by an unbalanced force. The momentum of an object is the product of its mass and velocity.
Newton's law of force says that when a force acts on a body, it causes a change in its momentum in the direction in which the force is applied. Usually, the law of force is expressed as F = ma.
Newton's law of action and reaction says that when one body exerts a force on a second body, the second body exerts a force on the first equal in magnitude but opposite in direction.
Newton's law of universal gravitation states that every two particles of matter attract each other with a force that depends on the product of their masses and varies inversely with the square of the distance between them. The law of gravitation is expressed as FG = GMm/d2.
Angular momentum is the momentum associated with rotation or revolution. Angular momentum can be transferred from one object to another or redistributed. However, it is always conserved.
Newton found that orbiting objects attracted to the Sun by the force of gravity obey Kepler's laws. He discovered a general form of Kepler's third law relating the separation, orbital period, and masses of any two orbiting bodies. This relationship is the basis of most astronomical mass determinations.
Circular speed is the orbital speed of a body that moves in a circular orbit. The circular speed at a given orbital distance has approximately the same value as the average orbital speed for an elliptical orbit having a semimajor axis equal to the circular distance.
A body moving at escape velocity leaves the solar system on a parabolic path and never returns. At any distance from the Sun, escape velocity is the square root of 2 times the circular speed at that distance.
Tidal forces are differences in gravitational force. They occur because the various parts of a body are in different directions and at different distances from the object attracting them. Tidal forces stretch the body in the direction toward and away from the attracting object. The strongest tidal forces are felt by large bodies near massive attractors.
