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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:
|Object||Sidereal period (yr)||Synodic period (yr)||Synodic period (d)|
|Solar surface||0.069 (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 (27.32 days)||0.0809||29.5306|
|Apophis (near-Earth asteroid)||0.886||7.769||2,837.6|
|90377 Sedna||12050||1.00001||365.1|
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.
You can also use a more simple method, knowing the semi major axis, to calculate the period:
where is the period in Earth years and is the semi major axis, in Astronomical Units.
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/m3), the above equation simplifies to (since ):
So, for the Earth as the central body (or any other spherically symmetric body with the same mean density, about 5515 kg/m3) we get:
and for a body made of water (ρ≈1000 kg/m3)
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 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 and , so that , their synodic period is given by
the Earth's surface
|speed(relative to Earth's surface)||Orbital period||specific orbital energy|
|Standing on Earth's surface at the equator (for comparison -- not an orbit)||6,378 km||0 km||465.1 m/s (1,040 mph)||1 day (24h)||−62.6 MJ/kg|
|Orbiting at Earth's surface (equator)||6,378 km||0 km||7.9 km/s (17,672 mph)||1 h 24 min 18 sec||−31.2 MJ/kg|
|Low Earth orbit||6,600 to 8,400 km||200 to 2,000 km||circular orbit: 6.9 to 7.8 km/s (15,430 mph to 17,450 mph) respectively|
elliptic orbit: 6.5 to 8.2 km/s respectively
|1 h 29 min to 2 h 8 min||−29.8 MJ/kg|
|Molniya orbit||6,900 to 46,300 km||500 to 39,900 km||1.5 to 10.0 km/s (3,335 mph to 22,370 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||0.97 to 1.08 km/s (2,170 to 2,416 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|
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