Editing Perturbation theory (section)

===Beginnings in the study of planetary motion===
Since the planets are very remote from each other, and since their mass is small as compared to the mass of the Sun, the gravitational forces between the planets can be neglected, and the planetary motion is considered, to a first approximation, as taking place along Kepler's orbits, which are defined by the equations of the [[two-body problem]], the two bodies being the planet and the Sun.<ref name=EoM>{{cite web |title = Perturbation theory |website = Encyclopedia of Mathematics (encyclopediaofmath.org) |url = http://www.encyclopediaofmath.org/index.php?title=Perturbation_theory&oldid=11676 }}</ref>

Since astronomic data came to be known with much greater accuracy, it became necessary to consider how the motion of a planet around the Sun is affected by other planets. This was the origin of the [[three-body problem]]; thus, in studying the system Moon-Earth-Sun, the mass ratio between the Moon and the Earth was chosen as the "small parameter". Lagrange and Laplace were the first to advance the view that the so-called "constants" which describe the motion of a planet around the Sun gradually change: They are  "perturbed", as it were, by the motion of other planets and vary as a function of time; hence the name "perturbation theory".<ref name=EoM/>

Perturbation theory was investigated by the classical scholars – Laplace, [[Siméon Denis Poisson]], [[Carl Friedrich Gauss]] – as a result of which the computations could be performed with a very high accuracy. The [[Discovery of Neptune|discovery of the planet Neptune]] in 1848 by [[Urbain Le Verrier]], based on the deviations in motion of the planet [[Uranus]]. He sent the coordinates to [[Johann Gottfried Galle|J.G. Galle]] who successfully observed Neptune through his telescope – a triumph of perturbation theory.<ref name=EoM/>