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Elliptic orbit

*** Shopping-Tip: Elliptic orbit
image:orbit5.gif thumb|400px|Two bodies with similar mass orbiting around a common [[barycenter with elliptic orbits.]] In astrodynamics or celestial mechanics a elliptic orbit is an orbit with the eccentricity (orbit) eccentricity greater than 0 and less than 1. Specific orbital energy Specific energy of an elliptical orbit is negative. An orbit with an eccentricity of 0 is a circular orbit. Examples of elliptic orbits include: Hohmann transfer orbit, Molniya orbit and tundra orbit.

Velocity
Under standard assumptions in astrodynamics standard assumptions the orbital velocity ($v\backslash ,$) of a body traveling along '''elliptic orbit''' can be computed as: :$v=\backslash sqrt\{2\backslash mu\backslash left(\{1\backslash over\{r\}\}-\{1\backslash over\{2a\}\}\backslash right)\}$ where: *$\backslash mu\backslash ,$ is standard gravitational parameter, *$r\backslash ,$ is radial distance of orbiting body from central body, *$a\backslash ,\backslash !$ is length of semi-major axis. Conclusion: *Velocity does not depend on eccentricity but is determined by length of semi-major axis ($a\backslash ,\backslash !$), *Velocity equation is similar to that for hyperbolic trajectory with the difference that for the latter, $\{1\backslash over\{2a\}\}$ is positive.

Orbital period
Under standard assumptions in astrodynamics standard assumptions the orbital period ($T\backslash ,\backslash !$) of a body traveling along elliptic orbit can be computed as: :$T=\{2\backslash pi\backslash over\{\backslash sqrt\{\backslash mu\}\}\}a^\{3\backslash over\{2\}\}$ where: *$\backslash mu\backslash ,$ is standard gravitational parameter, *$a\backslash ,\backslash !$ is length of semi-major axis. Conclusions: *The orbital period is equal to that for a circular orbit with the orbit radius equal to the semi-major axis ($a\backslash ,\backslash !$), *The orbital period does not depend on the eccentricity (See also: Kepler's laws of planetary motion#Kepler.27s third law .28harmonic law.29 Kepler's third law).

Energy
Under standard assumptions in astrodynamics standard assumptions, specific orbital energy ($\backslash epsilon\backslash ,$) of elliptic orbit is negative and the orbital energy conservation equation for this orbit takes form: : where: *$v\backslash ,$ is orbital velocity of orbiting body, *$r\backslash ,$ is radial distance of orbiting body from central body, *$a\backslash ,$ is length of semi-major axis, *$\backslash mu\backslash ,$ is standard gravitational parameter. Conclusions: *Specific orbital energy Specific energy for elliptic orbits is independent of eccentricity and is determined only by semi-major axis of the ellipse. Using the virial theorem we find: *the time-average of the specific potential energy is equal to 2ε **the time-average of ''r''^-1 is ''a''^-1 *the time-average of the specific kinetic energy is equal to -ε

Flight path angle
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Equation of motion
See orbit equation.

Orbital parameters
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Solar system
In the solar system planets, asteroids, comets and space debris have elliptical orbits around the Sun. Moons have an elliptic orbit around their planet. Many artificial satellites have various elliptic orbits around the Earth.

See also
* Characteristic energy * Circular orbit * Hyperbolic trajectory * Orbit * Orbital equation * Parabolic trajectory
- Apogee - Perigee Stunning Photographic Comparison
- Aphelion - Perihelion Stunning Photographic Comparison Category:Celestial mechanics Category:Astrodynamics es:Órbita elíptica it:Orbita ellittica ja:楕円軌� fi:Ellipsirata {{astro-stub}}

*** Shopping-Tip: Elliptic orbit