Editing Orbital mechanics (section)

==History==
Until the rise of [[spaceflight|space travel]] in the twentieth century, there was little distinction between orbital and celestial mechanics. At the time of [[Sputnik]], the field was termed 'space dynamics'.<ref>{{cite book|last1=Thomson|first1=William T.|title=Introduction to Space Dynamics|date=1961|publisher=Wiley|location=New York}}</ref> The fundamental techniques, such as those used to solve the [[Keplerian problem]] (determining position as a function of time), are therefore the same in both fields. Furthermore, the history of the fields is almost entirely shared.

[[Johannes Kepler]] was the first to successfully model planetary orbits to a high degree of accuracy, publishing [[Kepler's laws of planetary motion|his laws]] in 1605. [[Isaac Newton]] published more general laws of celestial motion in the first edition of ''[[Philosophiæ Naturalis Principia Mathematica]]'' (1687), which gave a method for finding the orbit of a body following a [[parabola|parabolic]] path from three observations.<ref>{{cite book|last1=Bate|first1=R. R.|last2=Mueller|first2=D. D.|last3=White|first3=J. E.|title=Fundamentals of Astrodynamics|url=https://books.google.com/books?id=UtJK8cetqGkC&pg=PR5|year=1971|publisher=Courier Corporation|isbn=978-0-486-60061-1|page=5}}</ref> This was used by [[Edmund Halley]] to establish the orbits of various comets, including [[Halley's Comet|that which bears his name]]. Newton's method of successive approximation was formalised into an analytic method by [[Euler|Leonhard Euler]] in 1744, whose work was in turn generalised to elliptical and hyperbolic orbits by [[Johann Heinrich Lambert|Johann Lambert]] in 1761–1777.

Another milestone in orbit determination was [[Carl Friedrich Gauss]]'s assistance in the "recovery" of the dwarf planet [[Ceres (dwarf planet)|Ceres]] in 1801. [[Gauss's method]] was able to use just three observations (in the form of pairs of [[right ascension]] and [[declination]]), to find the six [[orbital elements]] that completely describe an orbit. The theory of orbit determination has subsequently been developed to the point where today it is applied in GPS receivers as well as the tracking and cataloguing of newly observed [[minor planet]]s. Modern orbit determination and prediction are used to operate all types of satellites and space probes, as it is necessary to know their future positions to a high degree of accuracy.

[[Astrodynamics]] was developed by astronomer [[Samuel Herrick (astronomer)|Samuel Herrick]] beginning in the 1930s. He consulted the rocket scientist [[Robert Goddard]] and was encouraged to continue his work on space navigation techniques, as Goddard believed they would be needed in the future. Numerical techniques of astrodynamics were coupled with new powerful computers in the 1960s, and humans were ready to travel to the Moon and return.