Characteristic energy

In astrodynamics a characteristic energy ($C_3\,\!$), a form of specific energy, 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:

$C_3=v_{\infty}^2\,\!$

where

$v_{\infty} \,$ is the orbital velocity when the orbital distance tends to infinity. Note that, since the kinetic energy is one half mv², C₃ is in fact equal to twice the magnitude of the specific orbital energy ($\epsilon$) of the escaping object.

Parabolic trajectory

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

$C_3=0\,$

Hyperbolic trajectory

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

$C_3={\mu\over{a}}\,$

where:

$\mu\,$ is standard gravitational parameter,

$a\,$ is length of semi-major axis of orbit's hyperbola.

See also

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

References

• Wie, Bong (1998). "Orbital Dynamics". Space Vehicle Dynamics and Control. AIAA Education Series. Reston, Virginia: American Institute of Aeronautics and Astronautics. ISBN 1563472619.