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The orbital period is the time taken for a given object to make one complete orbit around another object.
When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.
There are several kinds of orbital periods for objects around the Sun (or other celestial objects):
Table of synodic periods in the Solar System, relative to Earth:
In the case of a planet's moon, the synodic period usually means the Sun-synodic period, namely, the time it takes the moon to complete its illumination phases, completing the solar phases for an astronomer on the planet's surface. The Earth's motion does not determine this value for other planets because an Earth observer is not orbited by the moons in question. For example, Deimos's synodic period is 1.2648 days, 0.18% longer than Deimos's sidereal period of 1.2624 d.
According to Kepler's Third Law, the orbital period T\, (in seconds) of two bodies orbiting each other in a circular or elliptic orbit is:
where:
For all ellipses with a given semi-major axis the orbital period is the same, regardless of eccentricity.
When a very small body is in a circular orbit barely above the surface of a sphere of any radius and mean density ρ (in kg/m^{3}), the above equation simplifies to (since M = \rho V = \rho {\frac {4}{3}} \pi a^3):
So, for the Earth as the central body (or any other spherically symmetric body with the same mean density, about 5515 kg/m^{3})^{[2]} we get:
and for a body made of water (ρ≈1000 kg/m^{3})^{[3]}
Thus, as an alternative for using a very small number like G, the strength of universal gravity can be described using some reference material, like water: the orbital period for an orbit just above the surface of a spherical body of water is 3 hours and 18 minutes. Conversely, this can be used as a kind of "universal" unit of time if we have a unit of mass, a unit of length and a unit of density.
In celestial mechanics, when both orbiting bodies' masses have to be taken into account, the orbital period T\, can be calculated as follows:^{[4]}
Note that the orbital period is independent of size: for a scale model it would be the same, when densities are the same (see also Orbit#Scaling in gravity).
In a parabolic or hyperbolic trajectory, the motion is not periodic, and the duration of the full trajectory is infinite.
When two bodies orbit a third body in different orbits, and thus different orbital periods, their respective, synodic period can be found. If the orbital periods of the two bodies around the third are called P_1 and P_2, so that P_1 < P_2, their synodic period is given by
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