Introduction to Gravitation
The heavens have long been a subject of human fascination and study. The regular motion of the stars and planets were at once a symbol of the divine order of the universe and a profound challenge for human understanding. For the ancient Greeks the separation between the terrestrial and celestial realms was absolute--the downward motion of falling objects was thought of as a "natural tendency" towards the center of the earth. The Greeks believed explaining motion on earth was a completely different problem from explaining why the earth went around the sun.
It was Nicholas Copernicus who first proposed, in 1543, that the earth moved around the sun. His book, De Revolutionibus Orbium Caelestium (On the Revolution of the Celestial Orbs) created a revolution in science that brought scientists such as Galileo into conflict with the Catholic Church. Even Kepler believed the heavens a mystical realm that obeyed a mathematical order unlike anything on earth. His three laws of planetary motion were based on the synthesis of a huge amount of observational data, compiled over many centuries. However, although fundamentally correct, Kepler's Laws were purely empirical; they facilitated prediction of planetary motion but did not explain why the planets should move in the way they did.
It was Sir Isaac Newton who not only provided this explanation in his famous inverse square law of gravitation, but managed to "synthesize" the explanation of motion on earth and motion in the heavens. This had profound philosophical and scientific consequences. The unification into what became the laws of gravitation became a symbol of the predictive and quantitative power of science. The fact that a single law could explain the motion of a cannonball and the motion of Mars revolutionized our understanding of our place in the universe.
In the centuries after Newton, scientists and mathematicians created powerful techniques and concepts for understanding complex phenomena such as tides and perturbations. In 1915 Albert Einstein published a new theory of gravitation (The General Theory of Relativity) that conceived of gravitational effects as caused by curvature in a four-dimensional space-time surface. Although Einstein's theory explains some observations that Newton's cannot, the inverse square law has remained an important tool in modern astrophysics and cosmology. Moreover, Newton's and Kepler's laws of gravitation can explain almost all the phenomena of orbits and terrestrial motion with which we will be concerned here.