In the solar system the dominant force is the gravitational force exerted by the sun on each planet; assuming that this is the only force, the simple elliptical orbits described by Kepler's laws are derived. However, the perturbations caused by the gravitational interaction of the planets among themselves change and complicate the curve of these orbits. The study of perturbations has led to important discoveries in astronomy. Within the solar system, the existence and position of Neptune was predicted because of the deviations of Uranus from its computed path. Likewise, Pluto was discovered by its effect on Neptune. Beyond the confines of the solar system, perturbations in the orbits of stars caused by the gravitational forces of orbiting bodies have led to the discovery of a number of extrasolar planetary systems.
In the atom the dominant force is the electrical force between the nucleus and the electrons; this force determines the characteristic structure, or energy levels, of the atom. The forces exerted by the electrons among themselves are perturbations that slightly modify this structure.