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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:^{[citation needed]}
Sidereal period (yr)  Synodic period (yr)  Synodic period (d)  
Solar surface  0.069^{[1]} (25.3 days)  0.074  27.3 
Mercury  0.240846 (87.9691 days)  0.317  115.88 
Venus  0.615 (225 days)  1.599  583.9 
Earth  1 (365.25636 solar days)  —  — 
Moon  0.0748  0.0809  29.5306 
Apophis (nearEarth asteroid)  0.886  7.769  2,837.6 
Mars  1.881  2.135  779.9 
4 Vesta  3.629  1.380  504.0 
1 Ceres  4.600  1.278  466.7 
10 Hygiea  5.557  1.219  445.4 
Jupiter  11.86  1.092  398.9 
Saturn  29.46  1.035  378.1 
Uranus  84.01  1.012  369.7 
Neptune  164.8  1.006  367.5 
134340 Pluto  248.1  1.004  366.7 
136199 Eris  557  1.002  365.9 
90377 Sedna  12050  1.00001  365.1^{[citation needed]} 
In the case of a planet's moon, the synodic period usually means the Sunsynodic period. That is to say, 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.^{[citation needed]}
According to Kepler's Third Law, the orbital period (in seconds) of two bodies orbiting each other in a circular or elliptic orbit is:
where:
For all ellipses with a given semimajor 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 radius R and mean density ρ (in kg/m^{3}), the above equation simplifies to (since a≈R and M=ρV):^{[citation needed]}
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 can be calculated as follows:^{[4]}
where:
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).^{[citation needed]}
In a parabolic or hyperbolic trajectory, the motion is not periodic, and the duration of the full trajectory is infinite.^{[citation needed]}
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 and , so that , their synodic period is given by
orbit  centertocenter distance  altitude above the Earth's surface  speed  Orbital period  specific orbital energy 

Earth's surface (for comparison)  6,400 km  0 km  7.89 km/s (17,650 mph)  85 minutes  −62.6 MJ/kg 
Low Earth orbit  6,600 to 8,400 km  200 to 2,000 km  circular orbit: 7.8 to 6.9 km/s (17,450 mph to 15,430 mph) respectively elliptic orbit: 8.2 to 6.5 km/s respectively  89 to 128 min  −29.8 MJ/kg 
Molniya orbit  6,900 to 46,300 km  500 to 39,900 km  10.0 to 1.5 km/s (22,370 mph to 3,335 mph) respectively  11 h 58 min  −4.7 MJ/kg 
Geostationary  42,000 km  35,786 km  3.1 km/s (6,935 mph)  23 h 56 min  −4.6 MJ/kg 
Orbit of the Moon  363,000 to 406,000 km  357,000 to 399,000 km  1.08 to 0.97 km/s (2,416 to 2,170 mph) respectively  27.3 days  −0.5 MJ/kg 
Binary star  Orbital period 

AM Canum Venaticorum  17.146 minutes 
Beta Lyrae AB  12.9075 days 
Alpha Centauri AB  79.91 years 
Proxima Centauri  Alpha Centauri AB  500,000 years or more 
Look up synodic in Wiktionary, the free dictionary. 
