In astrodynamics, the characteristic energy (${\displaystyle C_{3}}$) is a measure of the excess specific energy over that required to just barely escape from a massive body. The units are length² time⁻², i.e. velocity squared, or energy per mass.

Every object in a 2-body ballistic trajectory has a constant specific orbital energy ${\displaystyle \epsilon }$ equal to the sum of its specific kinetic and specific potential energy: $${\displaystyle \epsilon ={\frac {1}{2}}v^{2}-{\frac {\mu }{r}}={\text{constant}}={\frac {1}{2}}C_{3},}$$ where ${\displaystyle \mu =GM}$ is the standard gravitational parameter of the massive body with mass ${\displaystyle M}$, and ${\displaystyle r}$ is the radial distance from its center. As an object in an escape trajectory moves outward, its kinetic energy decreases as its potential energy (which is always negative) increases, maintaining a constant sum.

Note that C₃ is twice the specific orbital energy ${\displaystyle \epsilon }$ of the escaping object.

A spacecraft with insufficient energy to escape will remain in a closed orbit (unless it intersects the central body), with $${\displaystyle C_{3}=-{\frac {\mu }{a}}<0}$$ where

If the orbit is circular, of radius r, then $${\displaystyle C_{3}=-{\frac {\mu }{r}}}$$

A spacecraft leaving the central body on a parabolic trajectory has exactly the energy needed to escape and no more: $${\displaystyle C_{3}=0}$$

A spacecraft that is leaving the central body on a hyperbolic trajectory has more than enough energy to escape: $${\displaystyle C_{3}={\frac {\mu }{|a|}}>0}$$ where

Also, $${\displaystyle C_{3}=v_{\infty }^{2}}$$ where ${\displaystyle v_{\infty }}$ is the asymptotic velocity at infinite distance. Spacecraft's velocity approaches ${\displaystyle v_{\infty }}$ as it is further away from the central object's gravity.