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A Keplerian orbit (or Kepler orbit) is an orbit (path of an astronomical object gravitationally bound to another, particularly, a repeating pattern) that forms a perfect ellipse, parabola, or hyperbola (i.e., conic section), and a specific orbital speed (Keplerian speed), adhering to a generalization of Kepler's laws. This is the case for a point mass orbiting another point mass with no other mass near enough to affect them, i.e., an orbit maintained purely by the gravitation between two points (or spherically-symmetric objects). Planets and stars often approximate the behavior of point masses, for approximating spheres whose shells each have its mass distributed homogeneously (spherically symmetric): such spheres act like point masses. The dynamics of Newton's laws explain Keplerian orbits but general relativity (GR) only approximates them and differences can be found given strong gravity and/or precise measurement. In addition to the effects of GR, orbits generally diverge from perfect Keplerian due to additional nearby mass, such as another planet near enough to affect the orbit, and/or a host planet's divergence from the symmetric distribution of mass described above, such as having a region near the surface that is especially massive, and from affects of surrounding material, such as orbital decay from drag.
An orbit may be described as faster or slower than Keplerian if factors other than gravity are contributing, though it still may be in the shape of a Keplerian orbit.
The term osculating orbit is essentially a synonym for Keplerian orbit, most commonly used to describe the theoretical orbit a particular object would have if it were not for sources of perturbation such as other bodies, tidal forces, radiation pressure, etc.