Characteristic energy - Definition and Overview

In astrodynamics a characteristic energy (<math>C_3\,\!<math>) is a measure of the energy required for an interplanetary mission that requires attaining an excess orbital velocity over an escape velocity required for additional orbital maneuvers. The unit of the characteristic energy is km²s^-2.

Characteristic energy can be computed as:

<math>C_3=v_{\infty}^2\,\!<math>

where

<math>v_{\infty} \,\!<math> is the orbital velocity when the orbital distance tends to infinity.

Parabolic trajectory

For a spacecraft that is leaving the central body (e.g. earth) on a parabolic trajectory:

<math>C_3=0\,\!<math>

Hyperbolic trajectory

For a spacecraft that is leaving the central body on a hyperbolic trajectory:

<math>C_3={\mu\over{a}}\,\!<math>

where:

<math>\mu\,\!<math> is standard gravitational parameter,

<math>a\,\!<math> is length of semi-major axis of orbit's hyperbola.

See also

• Specific orbital energy
• Orbit
• Parabolic trajectory
• Hyperbolic trajectory