Characteristic energy

In astrodynamics, the characteristic energy ( C 3 {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 twice the energy per mass. In astrodynamics, the characteristic energy ( C 3 {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 twice the energy per mass. Every object in a 2-body ballistic trajectory has a constant specific orbital energy ϵ {displaystyle epsilon } equal to the sum of its specific kinetic and specific potential energy: where μ = G M {displaystyle mu =GM} is the standard gravitational parameter of the massive body with mass M {displaystyle M} , and r {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 ϵ {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