# Orbital Eccentricity

## Description

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.

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: e=0

-elliptic orbit: 0<e<1 (see Ellipse)

-parabolic trajectory: e=1 (see Parabola)

-hyperbolic trajectory: e>1 (see Hyperbola)

The eccentricity e is given by the formula shown here.

Related formulas## Variables

e | orbital eccentricity (dimensionless) |

E | total orbital energy (joule) |

L | angular momentum (joule*s) |

m_{red} | reduced mass (kg) |

a | coefficient of the inverse-square law centrl force (N*m^{2}) |