Orbital eccentricity

The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptical orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the galaxy.

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 non-negative number that defines its shape.

The eccentricity may take the following values:

circular orbit:

elliptic orbit: (see Ellipse)

parabolic trajectory: (see Parabola)

hyperbolic trajectory: (see Hyperbola)

The eccentricity is given by

where E is the total orbital energy, is the angular momentum, is the reduced mass, and the coefficient of the inverse-square law central force such as gravity or electrostatics in classical physics: