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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).
Diagram illustrating Newton's derivation. The blue planet follows the dashed elliptical orbit, whereas the green planet follows the solid elliptical orbit; the two ellipses share a common focus at the point C. The angles UCP and VCQ both equal θ 1, whereas the black arc represents the angle UCQ, which equals θ 2 = k θ 1.
There are two types of orbits: closed (periodic) orbits, and open (escape) orbits. Circular and elliptical orbits are closed. Parabolic and hyperbolic orbits are open. Radial orbits can be either open or closed. Circular orbit: An orbit that has an eccentricity of 0 and whose path traces a circle.
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:
In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler in 1609 (except the third law, and was fully published in 1619), describe the orbits of planets around the Sun. These laws replaced circular orbits and epicycles in the heliocentric theory of Nicolaus Copernicus with elliptical orbits and explained how planetary ...
Epicyclical motion is used in the Antikythera mechanism, [citation requested] an ancient Greek astronomical device, for compensating for the elliptical orbit of the Moon, moving faster at perigee and slower at apogee than circular orbits would, using four gears, two of them engaged in an eccentric way that quite closely approximates Kepler's ...
Parabolic (1) and hyperbolic (3) orbits are escape orbits, whereas elliptical and circular orbits (2) are captive. The orbital plane of a revolving body is the geometric plane in which its orbit lies. Three non-collinear points in space suffice to determine an orbital plane.
For elliptical orbits, a simple proof shows that gives the projection angle of a perfect circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury (e = 0.2056), one must simply calculate the inverse sine to find the projection angle of 11.86 degrees. Then, tilting any circular object by that angle ...