Newtonian Celestial Mechanics

Abstract

Newton’s theory of gravity is based upon absolute time and space (the Newtonian space-time). According to Newton’s Philosophiae Naturalis Principia Mathematica (originally published in 1687 in Latin), absolute time and space respectively are independent aspects of objective reality:

Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external measure of duration by the means of motion, which is commonly used instead of true time …

According to Newton, absolute time exists independently of any perceiver and progresses at a consistent pace throughout the universe. Also, space in the Newtonian framework has absolute character, in the sense that it regulates the inertial forces that appear if some observer is accelerated (or rotates) with respect to Newton’s absolute space, and that cannot be understood as arising from some kind of interaction with the direct physical neighbourhood (in this sense Newton’s theory is ‘non-relativistic’ but nevertheless can be formulated in a covariant manner). The absolute aspects of the Newtonian space-time lead to the globally determined bundle of inertial frames, where inertial forces are absent, and to the symmetries defined by the Galilean group.