Orbital eccentricity

Orbital Eccentricity

Orbital eccentricity

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The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit.


In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit. The eccentricity of this Kepler orbit is a positive number that defines its shape.

The eccentricity may take the following values:

The eccentricity <math>e</math> is given by

e = sqrt</math>

where E is the total orbital energy, <math>L</math> is the angular momentum, <math>m_text</math> is the reduced mass. and <math>alpha</math> the coefficient of the inverse-square law central force such as gravity or electrostatics in classical physics:

F = frac</math>

(<math>alpha</math> is negative for an attractive force, positive for a repulsive one) (see also Kepler problem).

or in the case of a gravitational force:
e = sqrt</math>

where <math>epsilon</math> is the specific orbital energy (total energy divided by the reduced mass), <math>mu</math> the standard gravitational parameter...
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