Editing Celestial mechanics (section)

==History==
{{For|early theories of the causes of planetary motion|Dynamics of the celestial spheres}}

Modern analytic celestial mechanics started with [[Isaac Newton]]'s [[Philosophiæ Naturalis Principia Mathematica|''Principia'' (1687)]]. The name '''celestial mechanics''' is more recent than that. Newton wrote that the field should be called "rational mechanics". The term "dynamics" came in a little later with [[Gottfried Leibniz]], and over a century after Newton, [[Pierre-Simon Laplace]] introduced the term ''celestial mechanics''. Prior to [[Johannes Kepler|Kepler]], there was little connection between exact, quantitative prediction of planetary positions, using [[Greek astronomy#Eudoxan astronomy|geometrical]] or [[Babylonian astronomy#Neo-Babylonian astronomy|numerical]] techniques, and contemporary discussions of the physical causes of the planets' motion.

===Laws of planetary motion===
{{For|detailed treatments of how his laws of planetary motion can be used|Kepler's laws of planetary motion|Kepler problem}}

[[Johannes Kepler]] was the first to closely integrate the predictive geometrical astronomy, which had been dominant from [[Ptolemy]] in the 2nd&nbsp;century to [[Copernicus]], with physical concepts to produce a [[Astronomia nova|''New Astronomy, Based upon Causes, or Celestial Physics'']] in 1609. His work led to the [[Kepler's laws of planetary motion|laws of planetary orbits]], which he developed using his physical principles and the [[planet]]ary observations made by [[Tycho Brahe]]. Kepler's elliptical model greatly improved the accuracy of predictions of planetary motion, years before Newton developed his [[Newton's law of universal gravitation|law of gravitation]] in 1686.

===Newtonian mechanics and universal gravitation===
[[Isaac Newton]] is credited with introducing the idea that the motion of objects in the heavens, such as [[planet]]s, the [[Sun]], and the [[Moon]], and the motion of objects on the ground, like [[cannon]] balls and falling apples, could be described by the same set of [[physical law]]s. In this sense he unified ''celestial'' and ''terrestrial'' dynamics. Using [[Newton's law of universal gravitation|his law of gravity]], Newton confirmed [[Kepler's laws of planetary motion|Kepler's laws]] for elliptical orbits by deriving them from the gravitational [[two-body problem]], which Newton included in his epochal ''[[Philosophiæ Naturalis Principia Mathematica]]'' in 1687.

===Three-body problem===
{{main article | Three-body problem}}
After Newton, [[Joseph-Louis Lagrange]] attempted to solve the three-body problem in 1772, analyzed the stability of planetary orbits, and discovered the existence of the [[Lagrange point]]s. Lagrange also reformulated the principles of [[classical mechanics]], emphasizing energy more than force, and developing a [[Lagrangian mechanics|method]] to use a single polar coordinate equation to describe any orbit, even those that are parabolic and hyperbolic. This is useful for calculating the behaviour of planets and [[comet]]s and such (parabolic and hyperbolic orbits are [[conic section]] extensions of Kepler's [[elliptical orbit]]s). More recently, it has also become useful to calculate [[spacecraft]] [[trajectory|trajectories]].

[[Henri Poincaré]] published two now classical monographs, "New Methods of Celestial Mechanics" (1892–1899) and "Lectures on Celestial Mechanics" (1905–1910). In them, he successfully applied the results of their research to the problem of the motion of three bodies and studied in detail the behavior of solutions (frequency, stability, asymptotic, and so on). Poincaré showed that the three-body problem is not integrable. In other words, the general solution of the three-body problem can not be expressed in terms of [[algebra]]ic and [[transcendental functions]] through unambiguous coordinates and velocities of the bodies. His work in this area was the first major achievement in celestial mechanics since Isaac Newton.<ref>J. Stillwell, Mathematics and its history, [https://books.google.com/books?id=V7mxZqjs5yUC&pg=PA254 page 254]</ref>

These monographs include an idea of Poincaré, which later became the basis for mathematical "[[chaos theory]]" (see, in particular, the [[Poincaré recurrence theorem]]) and the general theory of [[dynamical system]]s. He introduced the important concept of [[Bifurcation theory|bifurcation points]] and proved the existence of equilibrium figures such as the non-ellipsoids, including ring-shaped and pear-shaped figures, and their stability. For this discovery, Poincaré received the Gold Medal of the Royal Astronomical Society (1900).<ref name="Gold Medal to Poincaré">{{cite journal |date=1900 |title=Address Delivered by the President, Professor G. H. Darwin, on presenting the Gold Medal of the Society to M. H. Poincaré |journal=Monthly Notices of the Royal Astronomical Society |volume=60 |issue=5 |pages=406–416 |doi=10.1093/mnras/60.5.406 |issn=0035-8711 |doi-access=free |author-last=Darwin |author-first=G.H.}}</ref>

===Standardisation of astronomical tables===
[[Simon Newcomb]] was a Canadian-American astronomer who revised [[Peter Andreas Hansen]]'s table of lunar positions. In 1877, assisted by [[George William Hill]], he recalculated all the major astronomical constants. After 1884 he conceived, with A.M.W. Downing, a plan to resolve much international confusion on the subject. By the time he attended a standardisation conference in [[Paris]], France, in May&nbsp;1886, the international consensus was that all ephemerides should be based on Newcomb's calculations. A further conference as late as 1950 confirmed Newcomb's constants as the international standard.
===Anomalous precession of Mercury===
[[Albert Einstein]] explained the anomalous [[Tests of general relativity#Perihelion precession of Mercury|precession of Mercury's perihelion]] in his 1916 paper ''The Foundation of the General Theory of Relativity''. [[General relativity]] led astronomers to recognize that [[Newtonian mechanics]] did not provide the highest accuracy.