Newton's theory of gravitation

Main article: Law of universal gravitation

In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. In his own words, “I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centers about which they revolve; and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly.”

Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted by the actions of the other planets. Calculations by John Couch Adams and Urbain Le Verrier both predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle to the discovery of Neptune.

Ironically, it was another discrepancy in a planet's orbit that helped to doom Newton's theory. By the end of the 19th century, it was known that the orbit of Mercury could not be accounted for entirely under Newton's theory, and all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) have been fruitless. This issue was resolved in 1915 by Albert Einstein's new general relativity theory. This theory accounted for the discrepancy in Mercury's orbit.

Although Newton's theory has been superseded, most modern non-relativistic gravitational calculations are based on Newton's work because it is a much easier theory to work with and sufficient for most applications.

[edit] General relativity

Main article: Introduction to general relativity

In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of to a force. The starting point for general relativity is the equivalence principle, which equates free fall with inertial motion. The issue that this creates is that free-falling objects can accelerate with respect to each other. In Newtonian physics, no such acceleration can occur unless at least one of the objects is being operated on by a force (and therefore is not moving inertially).

To deal with this difficulty, Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. (This type of path is called a geodesic). More specifically, Einstein discovered the field equations of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The Einstein field equations are a set of 10 simultaneous, non-linear, differential equations. The solutions of the field equations are the components of the metric tensor of spacetime. A metric tensor describes a geometry of spacetime. The geodesic paths for a spacetime are calculated from the metric tensor.

Gravitation is a phenomenon through which all objects attract each other. Modern physics describes gravitation using the general theory of relativity, but the much simpler Newton's law of universal gravitation provides an excellent approximation in many cases. Gravitation is the reason for the very existence of the Earth, the Sun, and most macroscopic objects in the universe; without it, matter would not have coalesced into large masses (stars and planets) and life, as we know it, would not exist. Gravitation is also responsible for keeping the Earth and the other planets in their orbits around the Sun; the Moon in its orbit around the Earth; for heating interiors of forming stars and planets to very high temperatures, for the formation of tides, for rising hot air or water (convection), and for various other natural phenomena that we observe.