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# Orbital speed

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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 can be described by Kepler's second law, which 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."

The mean orbital speed can be derived either from observations of the orbital period and the semimajor axis of its orbit, or from knowledge of the masses of the two bodies and the semimajor axis.

$v_o = {2 \pi r \over T}$

$v_o = \sqrt{m G \over r}$

where $v_o$ is the orbital velocity, r is the length of the semimajor axis, T is the orbital period, m is the mass of the other body, and G is the gravitational constant. Note that this is only an approximation that holds true when the orbiting body is of considerably lesser mass than the central one.

More precisely,

$v_o = \sqrt{m_2^2 G \over (m_1 + m_2) r}$

where $m_1$ is now the mass of the body under consideration, $m_2$ is the mass of the body being orbited, and r is specifically the radius between the two bodies, ignoring the barycenter. This is still a simplified version; it doesn't allow for elliptical orbits, but it does at least allow for bodies of similar masses.

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