Orbital Eccentricity

# Orbital eccentricity

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Description:
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.

## Definition

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 [itex]e[/itex] is given by

[itex]
e = sqrt[/itex]

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

[itex]
F = frac[/itex]

([itex]alpha[/itex] is negative for an attractive force, positive for a repulsive one) (see also Kepler problem).

or in the case of a gravitational force:
[itex]
e = sqrt[/itex]

where [itex]epsilon[/itex] is the specific orbital energy (total energy divided by the reduced mass), [itex]mu[/itex] the standard gravitational parameter...

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