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 ϵ equal to the sum of its kinetic and potential energy:
ϵ = 1 2 v 2 − μ / r = c o n s t a n t = 1 2 C 3 where μ = G M 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.
Note that C3 is twice the specific orbital energy ϵ of the escaping object.
A spacecraft with insufficient energy to escape will remain in a closed orbit (unless it intersects the central body) with:
C 3 < 0 A spacecraft leaving the central body on a parabolic trajectory has exactly the energy needed to escape and no more:
C 3 = 0 A spacecraft that is leaving the central body on a hyperbolic trajectory has more than enough energy to escape:
C 3 = − μ a where
μ = G M is the
standard gravitational parameter,
a is the semi-major axis of the orbit's
hyperbola (which is negative by convention).
Also:
C 3 = v ∞ 2 where v ∞ is the asymptotic velocity at infinite distance. Spacecraft's velocity approaches v ∞ as it is further away from the central object's gravity.
MAVEN, a Mars-bound spacecraft, was launched into a trajectory with a characteristic energy of 12.2 km2sec−2 with respect to the Earth. When simplified to a two-body problem, this would mean the MAVEN escaped Earth on a hyperbolic trajectory slowly decreasing its speed towards 1 2.2 k m / s = 3.5 k m / s But since the Sun's gravitational field is much stronger than Earth's, the two-body solution is insufficient. The characteristic energy with respect to Sun was negative, and MAVEN – instead of heading to infinity – entered an elliptical orbit around the Sun. But the maximum velocity on the new orbit could be approximated to 33.5 km/s by assuming that it reached practical "infinity" at 3.5 km/s and that such Earth-bound "infinity" also moves with Earth's orbital velocity of about 30 km/s.
