Newton was born on December 25th, 1642 (Julian calendar then in use; January 4th, 1643 Gregorian) and died on March 20th, 1727. His achievements across the fields of mathematics and physics were revolutionary. Perhaps the best known contributor to Classical Mechanics, he formulated the Three Laws of Motion, and the Law of Gravity in 1687.
Newton's Three Laws of Motion
A body at rest stays at rest, and a body in motion stays in motion, unless it is acted on by an external force
Force equals mass times acceleration: F = ma (or, force is the time rate of change of momentum).
To every action there is an equal and opposite reaction.
This was an incredible intellectual achievement, and these Laws served us well for over 200 years. Newton's laws of motion continue to work just fine for the majority of the time. When you and I move about, or when NASA sends a mission to the Moon or to Mars, Newton's equations are sufficient; one does not have to resort to Einstein and Relativity! However, once velocities start to approach the speed of light, or you are very close to very large masses, like a black hole, where the curvature of space becomes large, Newton breaks down. Thus, Newton’s laws are really a sub-set of, or an approximation to, Relativity at relatively low velocities in flat space.
A fundamental issue with Newtonian mechanics is the fact that space and time are defined as absolute; that is, all observers would report seeing any event identically. As we will see in the discussion of Relativity, this is not the case. Observers in relative motion do not see the event unfolding in the same way; at least when their relative speeds approach the speed of light.
Newton's Theory assumes and, in fact, requires, that gravity propagates instantaneously. In Newtonian terms, any significant delay in the propagation of gravity would lead, for example, to instability in planetary orbits. It was not until the middle of the 19th century that observations identified anomalies in Newton's predictions for planetary orbits. To give Newton credit, he considered this instantaneous "action at a distance" unsatisfactory. He wrote in 1692: "That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."
Another issue was that, while Newton's theory predicts the "bending" of light by gravity, his prediction proved to be only half what was observed.
Newton’s Law of Gravity
Objects are attracted by a force acting along the line between them. The force, "F", is proportional to the product of their masses, and is inversely proportional to the square of the distance between them:
F = G x (m1 x m2) / r2
is the Gravitational Constant
|is the value of the force between the two objects
||are the masses of the two objects
||is the distance between the two objects