Characteristic energy

In astrodynamics the characteristic energy () 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 equal to the sum of its kinetic and potential energy:

where is the standard gravitational parameter of the massive body with mass and 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.

Characteristic energy can be computed as:

where is the asymptotic velocity at infinite distance. Note that, since the kinetic energy is , C₃ is twice the specific orbital energy () of the escaping object.

Non-escape trajectory

A spacecraft with insufficient energy to escape will remain in a closed orbit (unless it intersects the central body) with:

Parabolic trajectory

A spacecraft leaving the central body on a parabolic trajectory has exactly the energy needed to escape and no more:

Hyperbolic trajectory

A spacecraft that is leaving the central body on a hyperbolic trajectory has more than enough energy to escape:

where

is the standard gravitational parameter,

is the semi-major axis of the orbit's hyperbola.

Examples

MAVEN, a Mars-bound spacecraft, was launched into a heliocentric orbit with a characteristic energy of 12.2 km²sec⁻² with respect to the Earth.^[1]

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 1-56347-261-9.  |accessdate= requires |url= (help)

Footnotes