Orbital eccentricity
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In astrodynamics, under standard assumptions, any orbit must be of conic section shape. The eccentricity of this conic section, the orbit's eccentricity, is an important parameter of the orbit that defines its absolute shape. Eccentricity may be interpreted as a measure of how much this shape deviates from a circle.
Under standard assumptions eccentricity (
) is strictly defined for all circular, elliptic, parabolic and hyperbolic orbits and may take following values:
- for circular orbits:
, - for elliptic orbits:
, - for parabolic trajectories:
, - for hyperbolic trajectories:
.
For elliptical orbits, a simple proof shows that sin−1e yields the projection angle of a perfect circle to an ellipse of eccentricity e. So to view the eccentricity of, say, the planet Mercury (0.2056), simply calculate the inverse sine to find the projection angle of 11.86 degrees. Then tilt any circular object (such as a coffee mug viewed from the top) by that angle and the apparent ellipse projected to your eye will be of that same eccentricity.
