In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless 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 elliptic orbit, 1 is a parabolic (escape orbit or capture 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:

The eccentricity e is given by

$${\displaystyle e={\sqrt {1+{\frac {\ 2\ E\ L^{2}\ }{\ m_{\text{rdc}}\ \alpha ^{2}\ }}}}}$$

where E is the total orbital energy, L is the angular momentum, m_rdc is the reduced mass, and ${\displaystyle \alpha }$ the coefficient of the inverse-square law central force such as in the theory of gravity or electrostatics in classical physics:$${\displaystyle F={\frac {\alpha }{r^{2}}}}$$(${\displaystyle \alpha }$ is negative for an attractive force, positive for a repulsive one; related to the Kepler problem)

or in the case of a gravitational force:$${\displaystyle e={\sqrt {1+{\frac {2\varepsilon h^{2}}{\mu ^{2}}}}}}$$

where ε is the specific orbital energy (total energy divided by the reduced mass), μ the standard gravitational parameter based on the total mass, and h the specific relative angular momentum (angular momentum divided by the reduced mass).