Editing Characteristic energy (section)

In [[astrodynamics]], the '''characteristic energy''' (<math>C_3</math>) is a measure of the excess [[specific energy]] over that required to just barely escape from a massive body. The units are [[length]]<sup>2</sup> [[time]]<sup>−2</sup>, i.e. [[velocity]] squared, or [[energy]] per [[mass]].

Every object in a [[two-body problem|2-body]] [[ballistics|ballistic]] trajectory has a constant [[specific orbital energy]] <math>\epsilon</math> equal to the sum of its specific kinetic and specific potential energy:
<math display="block">\epsilon = \frac{1}{2} v^2 - \frac{\mu}{r} = \text{constant} = \frac{1}{2} C_3,</math>
where <math>\mu = GM</math> is the [[standard gravitational parameter]] of the massive body with mass <math>M</math>, and <math>r</math> is the [[Polar coordinate system|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 ''C''<sub>3</sub> is ''twice'' the [[specific orbital energy]] <math>\epsilon</math> of the escaping object.