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An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
Although the eccentricity is 1, this is not a parabolic orbit. Most properties and formulas of elliptic orbits apply. However, the orbit cannot be closed. It is an open orbit corresponding to the part of the degenerate ellipse from the moment the bodies touch each other and move away from each other until they touch each other again.
A highly elliptical orbit (HEO) is an elliptic orbit with high eccentricity, usually referring to one around Earth.Examples of inclined HEO orbits include Molniya orbits, named after the Molniya Soviet communication satellites which used them, and Tundra orbits.
For values of e from 0 to just under 1 the orbit's shape is an increasingly elongated (or flatter) ellipse; for values of e just over 1 to infinity the orbit is a hyperbola branch making a total turn of 2 arccsc(e), decreasing from 180 to 0 degrees.
The orbit of every planet is an ellipse with the sun at one of the two foci. Kepler's first law placing the Sun at one of the foci of an elliptical orbit Heliocentric coordinate system (r, θ) for ellipse. Also shown are: semi-major axis a, semi-minor axis b and semi-latus rectum p; center of ellipse and its two foci marked by
Elliptical orbits take the shape of an ellipse, and are very common in two-body astronomical systems. A relatively small body (such as a planet) orbiting a larger one (such as a star) in an elliptical orbit, with the larger body located at one of the focal points of the ellipse elongation
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution respectively. Other terms used are ellipticity , or oblateness . The usual notation for flattening is f {\displaystyle f} and its definition in terms of the semi-axes a {\displaystyle a} and b {\displaystyle b} of ...
If the ellipse is rotated about its major axis, the result is a prolate spheroid, elongated like a rugby ball. The American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an oblate spheroid, flattened like a lentil or a plain M&M.