The orbital speed of a body, generally a planet a natural satellite an satellite or a multiple star is the speed at which it orbit around the barycenter of a system, usually around a more mass ve 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

Radial trajectories

In the case of radial motion: * If the energy is non-negative: The orbit is open. The motion is either directly towards or away from the other body, the motion never stops or reverses direction. See radial hyperbolic trajectory * For the zero-energy case, see radial parabolic trajectory * If the energy is negative: The orbit is closed. The motion can be first away from the central body, up to rμ/|ε| (apoapsis), 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. See radial elliptic trajectory radial trajectories free-fall time

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 momentum or equivalently, Johannes Kepler s Kepler's laws of planetary motion 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."

Mean orbital speed

For orbits with small [[eccentricity (orbit)|eccentricity]] the length of the orbit is close to that of a circular one, and the mean orbital speed can be approximated either from observations of the orbital period and the semimajor axis of its orbit, or from knowledge of the mass s of the two bodies and the semimajor axis. :$v\_o\; \backslash approx\; 2\; \backslash pi\; a\; \backslash over\; T\}$ :$v\_o\; \backslash approx\; \backslash sqrt\backslash mu\; \backslash over\; a\}$ where $v\_o\backslash ,\backslash !$ is the orbital velocity, $a\backslash ,\backslash !$ is the length of the semimajor axis $T\backslash ,\backslash !$ is the orbital period, and $\backslash mu\backslash ,\backslash !$ is the standard gravitational parameter Note that this is only an approximation that holds true when the orbiting body is of considerably lesser mass than the central one, and eccentricity is close to zero. Taking into account the mass of the orbiting body :$v\_o\; \backslash approx\; \backslash sqrtm\_2^2\; G\; \backslash over\; (m\_1\; +\; m\_2)\; r\}$ where $m\_1\backslash ,\backslash !$ is now the mass of the body under consideration, $m\_2\backslash ,\backslash !$ is the mass of the body being orbited, $r\backslash ,\backslash !$ is specifically the distance between the two bodies (which is the sum of the distances from each to the center of mass), and $G\backslash ,\backslash !$ is the gravitational constant This is still a simplified version; it doesnt allow for ellipse orbits, but it does at least allow for bodies of similar masses. When one of the masses is almost negligible compared to the other mass as the case for Earth and Sun one can approximate the previous formula to get: :$v\_o\; \backslash approx\; \backslash sqrt\backslash fracGM\}r\}\}$ or :$v\_o\; \backslash approx\; \backslash fracv\_e\}\backslash sqrt2\}\}$ Where Mis the (greater) mass around which this negligible mass or body is orbiting, and v_eis the escape velocity For an object in an eccentric orbit orbiting a much larger body, the length of the orbit decreases with eccentricity $e\backslash ,\backslash !$, and is given at ellipse#Circumference This can be used to obtain a more accurate estimate of the average orbital speed: :$v\_o\; \backslash frac2\backslash pi\; a\}T\}\backslash left1-\backslash frac1\}4\}e^2-\backslash frac3\}64\}e^4\; -\backslash frac5\}256\}e^6\; -\backslash frac175\}16384\}e^8\; -\; \backslash dots\; \backslash right]$lt;/ref> The mean orbital speed decreases with eccentricity.

See also

*Escape velocity *Delta-v budget *Hohmann transfer orbit *Bi-elliptic transfer

References

Category:Celestial mechanics bg:Орбитална скорост ca:Velocitat orbital cs:Kruhová rychlost es:Velocidad orbital eo:Orbita rapido fr:Vitesse orbitale ko:공전 속도 hr:Orbitalna brzina id:Kecepatan orbit it:Velocità orbitale ka:პირველი კოსმოსური სიჩქარე mr:कक्षीय वेग nl:Omloopsnelheid (astronomie) ja:軌道速度 nn:Banefart pl:Prędkość orbitalna pt:Velocidade orbital ru:Орбитальная скорость sk:Kruhová rýchlosť sl:Tirna hitrost sr:Прва космичка брзина fi:Ratanopeus sv:Omloppshastighet ta:சுற்றுப்பாதை வேகம் th:อัตราเร็วในวงโคจร uk:Перша космічна швидкість vi:Tốc độ vũ trụ cấp 1 zh:轨道速度