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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).
An elliptic Kepler orbit with an eccentricity of 0.7, a parabolic Kepler orbit and a hyperbolic Kepler orbit with an eccentricity of 1.3. The distance to the focal point is a function of the polar angle relative to the horizontal line as given by the equation ()
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.
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:
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.
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 ...
The following diagram illustrates the positions and relationship between the lines of solstices, equinoxes, and apsides of Earth's elliptical orbit. The six Earth images are positions along the orbital ellipse, which are sequentially the perihelion (periapsis—nearest point to the Sun) on anywhere from January 2 to January 5, the point of ...
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 ...