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In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1 (thus excluding the circular orbit).
The elliptical orbits of planets were indicated by calculations of the orbit of Mars. From this, Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits. The second law establishes that when a planet is closer to the Sun, it travels faster.
Maneuvering into a large circular orbit, e.g. a geostationary orbit, requires a larger delta-v than an escape orbit, although the latter implies getting arbitrarily far away and having more energy than needed for the orbital speed of the circular orbit. It is also a matter of maneuvering into the orbit.
Johannes Kepler formulated his three laws of planetary motion, which describe the orbits of the planets in the Solar System to a remarkable degree of accuracy utilizing a system that employs elliptical rather than circular orbits. Kepler's three laws are still taught today in university physics and astronomy classes, and the wording of these ...
All bounded orbits where the gravity of a central body dominates are elliptical in nature. A special case of this is the circular orbit, which is an ellipse of zero eccentricity. The formula for the velocity of a body in a circular orbit at distance r from the center of gravity of mass M can be derived as follows:
The view rotates with the mean anomaly, so the object appears to oscillate back and forth across this mean position with the equation of the center. The object also appears to become smaller and larger as it moves farther away and nearer because of the eccentricity of the orbit. A marker (red) shows the position of the periapsis.
Figure 2: Varying speeds of elliptical orbits. Now imagine two stars orbiting each other in elliptical orbits with the special case where both are tidally locked such that over the course of an orbit the same sides face each other (ω=Ω on average). Although Ω is constant for one orbit, ω varies throughout the orbit.
The eccentricity of an orbit is a measure of how elliptical (elongated) it is. All the planets of the Solar System except for Mercury have near-circular orbits (e<0.1). [8] Most exoplanets with orbital periods of 20 days or less have near-circular orbits, i.e. very low eccentricity.