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The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body. It can be used to refer to either the mean orbital speed, the average speed as it completes an orbit, or instantaneous orbital speed, the speed at a particular point in its orbit. 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:
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.
2 Transverse orbital speed
The transverse orbital speed is inversely proportional to the distance to the central body because of the law of conservation of angular momentumIn physics, angular momentum intuitively measures how much the linear momentum is directed around a certain point called the origin; the moment of momentum. Since angular momentum depends upon the origin of choice, one must be careful when discussing angu, or equivalently, Kepler's second law. This states that as a body moves around its orbit during a fixed amount of time, the line from the barycenter to the body sweeps a constant area of the orbital plane, regardless of which part of its orbit the body traces during that period of time. This means that the body moves faster near its periapsis than near its apoapsis, because at the smaller distance it needs to trace a greater arc to cover the same area. This law is usually stated as "equal areas in equal time."
