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 length²time⁻², i.e. 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 kinetic and 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.

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