Orbital eccentricity
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- This page refers to eccentricity in astrodynamics. For other uses, see the disambiguation page eccentricity.
Under standard assumptions eccentricity ([e\,\!]) is strictly defined for all circular, elliptic, parabolic and hyperbolic orbits and may take following values:
- for circular orbits: [e=0\,\!],
- for elliptic orbits: [0
- for parabolic trajectories: [e=1\,\!],
- for hyperbolic trajectories: [e>1\,\!].
Calculation
Eccentricity of an orbit can be calculated from orbital state vectors as a magnitude of eccentricity vector:- [e= \left | \mathbf \right |]
- [\mathbf\,\!] is eccentricity vector.
For elliptic orbits it can also be calculated from distance at periapsis and apoapsis:
- [e==1-\frac+1}=\frac+1}-1]
Examples
For example, the eccentricity of the Earth's orbit today is 0.0167. Through time, the eccentricity of the Earth's orbit slowly changes from nearly 0 to almost 0.05 as a result of gravitational attractions between the planets (see graph [link]).Other values: Pluto 0.2488 (largest value among the planets of the Solar System), Mercury 0.2056, Moon 0.0554. For the values for all planets in one table, see [de].
See also
External links
- [World of Physics: Eccentricity]
- [The NOAA page on Climate Forcing Data] includes (calculated) data from [Berger (1978), Berger and Loutre (1991)] and [Laskar et al. (2004)] on Earth orbital variations, including eccentricity, over the last 50 million years and for the coming 20 million years
- [The orbital simulations by Varadi, Ghil and Runnegar (2003)] provide another, slightly different series for Earth orbital eccentricity, and also a series for orbital inclination
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