Characteristic energy

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In astrodynamics the characteristic energy (C_3\,\!) 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 \epsilon equal to the sum of its kinetic and potential energy:

\tfrac{1}{2} v^2 - \mu/r = constant = \tfrac{1}{2} C_3

where \mu = GM is the standard gravitational parameter of the massive body with mass M and 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.

Characteristic energy can be computed as:

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

where v_{\infty} is the asymptotic velocity at infinite distance. Note that, since the kinetic energy is \tfrac{1}{2} mv^2, C3 is in fact twice the specific orbital energy (\epsilon) of the escaping object.

Non-escape trajectory[edit]

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

C_3<0\,

Parabolic trajectory[edit]

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

C_3=0\,

Hyperbolic trajectory[edit]

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

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

where

\mu\,=GM is the standard gravitational parameter,
a\, is the semi-major axis of the orbit's hyperbola.

Examples[edit]

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[edit]

References[edit]

Footnotes[edit]