Historically, the apparent motions of the planets were described by European and Arabic philosophers using the idea of
celestial spheres. This model posited the existence of perfect moving spheres or rings to which the stars and planets were attached. It assumed the heavens were fixed apart from the motion of the spheres, and was developed without any understanding of gravity. After the planets' motions were more accurately measured, theoretical mechanisms such as
deferent and epicycles were added. Although the model was capable of reasonably accurately predicting the planets' positions in the sky, more and more epicycles were required as the measurements became more accurate, hence the model became increasingly unwieldy. Originally
geocentric it was modified by
Copernicus to place the sun at the centre to help simplify the model. The model was further challenged during the 16th century, as comets were observed traversing the spheres.
The basis for the modern understanding of orbits was first formulated by
Johannes Kepler whose results are summarised in his three laws of planetary motion. First, he found that the orbits of the planets in our solar system are elliptical, not
epicyclic), as had previously been believed, and that the Sun is not located at the center of the orbits, but rather at one
 Second, he found that the orbital speed of each planet is not constant, as had previously been thought, but rather that the speed depends on the planet's distance from the Sun. Third, Kepler found a universal relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are respectively about 5.2 and 0.723
AU distant from the Sun, their orbital periods respectively about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter, 5.23/11.862, is practically equal to that for Venus, 0.7233/0.6152, in accord with the relationship. Idealised orbits meeting these rules are known as
This image shows the four trajectory categories with the
gravitational potential well
of the central mass's field of potential energy shown in black and the height of the kinetic energy of the moving body shown in red extending above that, correlating to changes in speed as distance changes according to Kepler's laws.
Isaac Newton demonstrated that Kepler's laws were derivable from his theory of
gravitation and that, in general, the orbits of bodies subject to gravity were
conic sections (this assumes that the force of gravity propagates instantaneously). Newton showed that, for a pair of bodies, the orbits' sizes are in inverse proportion to their
masses, and that those bodies orbit their common
center of mass. Where one body is much more massive than the other (as is the case of an artificial satellite orbiting a planet), it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body.
Advances in Newtonian mechanics were then used to explore variations from the simple assumptions behind Kepler orbits, such as the perturbations due to other bodies, or the impact of spheroidal rather than spherical bodies.
Lagrange (1736–1813) developed a
new approach to Newtonian mechanics emphasizing energy more than force, and made progress on the three body problem, discovering the
Lagrangian points. In a dramatic vindication of classical mechanics, in 1846
Urbain Le Verrier was able to predict the position of
Neptune based on unexplained perturbations in the orbit of
Albert Einstein (1879-1955) in his 1916 paper The Foundation of the General Theory of Relativity explained that gravity was due to curvature of
space-time and removed Newton's assumption that changes propagate instantaneously. This led astronomers to recognize that
Newtonian mechanics did not provide the highest accuracy in understanding orbits. In
relativity theory, orbits follow geodesic trajectories which are usually approximated very well by the Newtonian predictions (except where there are very strong gravity fields and very high speeds) but the differences are measurable. Essentially all the experimental evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy. The original vindication of general relativity is that it was able to account for the remaining unexplained amount in
precession of Mercury's perihelion first noted by Le Verrier. However, Newton's solution is still used for most short term purposes since it is significantly easier to use and sufficiently accurate.