text: or the same as for an ellipse, depending on the convention for the sign of a.
  In this case the specific orbital energy is also referred to as characteristic energy (or ) and is equal to the excess specific energy compared to that for a parabolic orbit.
  It is related to the hyperbolic excess velocity  (the orbital velocity at infinity) by
  It is relevant for interplanetary missions.
  Thus, if orbital position vector () and orbital velocity vector   () are known at one position, and  is known, then the energy can be computed and from that, for any other position, the orbital speed.
  Rate of change
  For an elliptic orbit the rate of change of the specific orbital energy with respect to a change in the semi-major axis is
  where
  is the standard gravitational parameter;
  is semi-major axis of the orbit.
  In the case of circular orbits, this rate is one half of the gravitation at the orbit. This corresponds to the fact that for such orbits the total energy is one half of the potential energy, because the kinetic energy is minus one half of the potential energy.
  Additional energy
  If the central body has radius R, then the additional specific energy of an elliptic orbit compared to being stationary at the surface is