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The orbital speed at any position in the orbit can be computed from the distance to the central body at that position, and the specific orbital energy, which is independent of position: the kinetic energy is the total energy minus the potential energy.

Thus, under standard assumptions the orbital speed () is:

• in general:
  • elliptic orbit:
  • parabolic trajectory:
  • hyperbolic trajectory:

where:

• is the standard gravitational parameter
• is the distance between the orbiting bodyIn astrodynamics, an orbiting body is a body that orbits central body . Under standard assumptions in astrodynamics: it is orders of magnitude lighter than central body (i. See also Central body Standard assumptions in astrodynamics Astrodynamics Celestia and the central bodyIn astrodynamics a central body is a body that is being orbited by orbiting body . Under standard assumptions in astrodynamics: it is orders of magnitude heavier than orbiting body (i. it is a center of an inertial frame of reference for orbiting body, it
• is the specific orbital energy
• is the semi-major axisIn geometry, the semi-major axis (also semimajor axis a applies to ellipses and hyperbolas. Ellipse The semi-major axis of an ellipse is one half of the major axis running from the center, through a focus, and to the edge of the ellipse. The major axis is

Note:

• Velocity does not explicitly depend on eccentricityMathematics In mathematics, eccentricity is a parameter associated with every conic section, see Conic section#Eccentricity. It can be thought of as a measure of how much the conic section deviates from being circular. In particular, The eccentricity of a but is determined by length of semi-major axisIn geometry, the semi-major axis (also semimajor axis a applies to ellipses and hyperbolas. Ellipse The semi-major axis of an ellipse is one half of the major axis running from the center, through a focus, and to the edge of the ellipse. The major axis is (),

1 Radial trajectories

In the case of radial motion:

• if the energy is non-negative: the motion is either for the whole trajectory away from the central body, or for the whole trajectory towards it. For the zero-energy case, see escape orbitAn escape orbit (also known as C''3 0 orbit) is the high-energy parabolic orbit around the central body. A body in this orbit has at each position the escape velocity with respect to this central body, for this position. If this energy were further increa and capture orbitA capture orbit is the high-energy parabolic orbit that allows the capture other than crashing directly to the central body's surface (or atmospheric re-entry). Capture orbit is identical to escape orbit just the direction is reverse. Both are also known.
• if the energy is negative: the motion can be first away from the central body, up to r=μ/|ε|, then falling back. This is the limit case of an orbit which is part of an ellipse with eccentricity tending to 1, and the other end of the ellipse tending to the center of the central body.