Characteristic energy

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:

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.