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| {{about||the music album|Orbital Period (album)}}
| | My name is Hortense Nicolai but everybody calls me Hortense. I'm from Denmark. I'm studying at the college (1st year) and I play the Viola for 6 years. Usually I choose music from my famous films ;). <br>I have two sister. I love Metal detecting, watching movies and Geocaching.<br><br>Have a look at my site [http://www.metalmusicarchives.com/artist/arthur-falcone arthur falcone] |
| {{Refimprove|date=January 2013}}
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| The '''orbital period''' is the time taken for a given object to make one complete [[orbit]] around another object.
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| When mentioned without further qualification in astronomy this refers to the '''sidereal period''' of an astronomical object, which is calculated with respect to the [[star]]s.
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| There are several kinds of orbital periods for objects around the [[Sun]] (or other celestial objects):
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| * The '''sidereal period''' is the temporal cycle that it takes an object to make a full orbit, relative to the [[star]]s. This is the orbital period in an inertial (non-rotating) [[frame of reference]].
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| * The '''synodic period''' is the temporal interval that it takes for an object to reappear at the same point in relation to two or more other objects, e.g. when the [[Moon]] relative to the [[Sun]] as observed from [[Earth]] returns to the same illumination phase. The synodic period is the time that elapses between two successive [[Conjunction (astronomy)|conjunctions]] with the Sun–Earth line in the same linear order. The synodic period differs from the sidereal period due to the Earth's orbiting around the Sun.
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| * The '''draconitic period''', or '''draconic period''', is the time that elapses between two passages of the object through its [[orbital node|ascending node]], the point of its orbit where it crosses the [[ecliptic]] from the southern to the northern hemisphere. This period differs from the sidereal period because both the orbital plane of the object and the plane of the ecliptic precess with respect to the fixed stars, so their intersection, the [[line of nodes]], also precesses with respect to the fixed stars. Although the plane of the ecliptic is often held fixed at the position it occupied at a specific [[epoch (astronomy)|epoch]], the orbital plane of the object still precesses causing the draconitic period to differ from the sidereal period.
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| * The '''anomalistic period''' is the time that elapses between two passages of an object at its [[periapsis]] (in the case of the planets in the [[solar system]], called the [[perihelion]]), the point of its closest approach to the attracting body. It differs from the sidereal period because the object's [[semimajor axis]] typically advances slowly.
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| * Also, the Earth's '''tropical period''' (or simply its "year") is the time that elapses between two alignments of its axis of rotation with the Sun, also viewed as two passages of the object at [[right ascension]] zero. One Earth year has a slightly shorter interval than the solar orbit (sidereal period) because the inclined axis and equatorial plane slowly precesses (rotates in sidereal terms), realigning before orbit completes with an interval equal to the inverse of the precession cycle (about 25,770 years).
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| ==Relation between the sidereal and synodic periods==
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| Table of synodic periods in the Solar System, relative to Earth:{{citation needed|date=January 2011}}
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| {| class="wikitable sortable"
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| | '''Sidereal period''' ([[julian year (astronomy)|yr]])
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| | '''Synodic period''' (yr)
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| | '''Synodic period''' ([[day|d]])
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| |-
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| | [[Solar rotation|Solar surface]]
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| | 0.069<ref>The motion of the solar surface is not purely gravitational and therefore does not follow Kepler's laws of motion</ref> (25.3 days)
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| | 0.074
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| | 27.3
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| |-
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| | [[Mercury (planet)|Mercury]]
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| | 0.240846 (87.9691 days)
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| | 0.317
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| | 115.88
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| |-
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| | [[Venus]]
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| | 0.615 (225 days)
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| | 1.599
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| | 583.9
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| |-
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| | [[Earth]]
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| | '''1''' (365.25636 [[solar day]]s)
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| | —
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| | —
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| |-
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| | [[Moon]]
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| | 0.0748
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| | 0.0809
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| | 29.5306
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| |-
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| | [[99942 Apophis|Apophis]] (near-Earth asteroid)
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| | 0.886
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| | 7.769
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| | 2,837.6
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| |-
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| | [[Mars]]
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| | 1.881
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| | 2.135
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| | 779.9
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| |-
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| | [[4 Vesta]]
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| | 3.629
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| | 1.380
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| | 504.0
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| |-
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| | [[Ceres (dwarf planet)|1 Ceres]]
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| | 4.600
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| | 1.278
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| | 466.7
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| |-
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| | [[10 Hygiea]]
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| | 5.557
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| | 1.219
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| | 445.4
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| |-
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| | [[Jupiter]]
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| | 11.86
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| | 1.092
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| | 398.9
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| |-
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| | [[Saturn]]
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| | 29.46
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| | 1.035
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| | 378.1
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| |-
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| | [[Uranus]]
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| | 84.01
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| | 1.012
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| | 369.7
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| |-
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| | [[Neptune]]
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| | 164.8
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| | 1.006
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| | 367.5
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| |-
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| | [[Pluto|134340 Pluto]]
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| | 248.1
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| | 1.004
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| | 366.7
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| |-
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| | [[Eris (dwarf planet)|136199 Eris]]
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| | 557
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| | 1.002
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| | 365.9
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| |-
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| | [[90377 Sedna]]
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| | 12050
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| | 1.00001
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| | 365.1 {{citation needed|date=December 2013}}
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| |-
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| |}
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| In the case of a planet's [[natural satellite|moon]], the synodic period usually means the Sun-synodic 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 (moon)|Deimos]]'s synodic period is 1.2648 days, 0.18% longer than Deimos's sidereal period of 1.2624 d.{{citation needed|date=November 2011}}<!--- The Earth-synodic period can also be calculated, but it varies with the planet's position with respect to the Earth; in the Deimos example, at Mars opposition the Earth-synodic period would be about 1.2604 d because Earth's motion overtakes Mars. At Mars conjunction, Deimos's Earth-synodic period would be 1.2692 d because Earth's motion now accentuates Mars's apparent motion. Since the Earth--extra-planetary moon synodic period reflects Earth-planet-moon alignments, it is fairly meaningless. --->
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| ==Calculation==
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| ===Small body orbiting a central body===
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| According to [[Kepler's laws of planetary motion|Kepler's Third Law]], the '''orbital period''' <math>T\,</math> (in seconds) of two bodies orbiting each other in a circular or [[elliptic orbit]] is:
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| :<math>T = 2\pi\sqrt{a^3/\mu}</math>
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| where:
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| * <math>a\,</math> is the orbit's [[semi-major axis]], in meters
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| * <math> \mu = GM \,</math> is the [[standard gravitational parameter]], typically in <math>m^3/s^2</math>
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| * <math> G \,</math> is the [[gravitational constant]],
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| * <math> M \,</math> is the mass of the more massive body.
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| For all ellipses with a given semi-major axis the orbital period is the same, regardless of eccentricity.
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| ===Orbital period as a function of central body's density===
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| 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<sup>3</sup>), the above equation simplifies to (since a≈R and M=ρV):{{citation needed|date=July 2012}}
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| :<math>T = \sqrt{ \frac {3\pi}{G \rho} }</math>
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| So, for the Earth as the central body (or any other spherically symmetric body with the same mean density, about 5515 kg/m<sup>3</sup>)<ref>{{citation |url=http://www.wolframalpha.com/input/?i=density+of+the+earth |title=Density of the Earth |publisher=wolframalpha.com}}</ref> we get:
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| :<math>T = 1.41 </math> hours
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| and for a body made of water (ρ≈1000 kg/m<sup>3</sup>)<ref>{{citation |url=http://www.wolframalpha.com/input/?i=density+of+water |title=Density of water |publisher=wolframalpha.com}}</ref>
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| :<math>T = 3.30 </math> hours
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| 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" [[time standard|unit of time]] if we have a unit of mass, a unit of length and a unit of density.
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| ===Two bodies orbiting each other===<!-- This section is linked from [[Binary star]] -->
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| In [[celestial mechanics]], when both orbiting bodies' masses have to be taken into account, the '''orbital period''' <math>T\,</math> can be calculated as follows:<ref>Bradley W. Carroll, Dale A. Ostlie. An introduction to modern astrophysics. 2nd edition. Pearson 2007.</ref>
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| :<math>T= 2\pi\sqrt{\frac{a^3}{G \left(M_1 + M_2\right)}}</math>
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| where:
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| * <math>a\,</math> is the sum of the [[semi-major axis|semi-major axes]] of the ellipses in which the centers of the bodies move, or equivalently, the semi-major axis of the ellipse in which one body moves, in the frame of reference with the other body at the origin (which is equal to their constant separation for circular orbits),
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| * <math>M_1+M_2\,</math> is the sum of the masses of the two bodies,
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| * <math>G\,</math> is the [[gravitational constant]].
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| 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|date=November 2011}}
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| In a parabolic or hyperbolic trajectory, the motion is not periodic, and the duration of the full trajectory is infinite.{{citation needed|date=November 2011}}
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| ===Synodic period===
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| 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 <math>P_1</math> and <math>P_2</math>, so that <math>P_1 < P_2</math>, their synodic period is given by
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| :<math>\frac{1}{P_{syn}}=\frac{1}{P_1}-\frac{1}{P_2}</math>
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| {{Earth orbits}}
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| ==Binary stars==
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| {| class="wikitable"
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| ![[Binary star]]!!Orbital period
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| |-
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| | [[AM Canum Venaticorum]]
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| | style="text-align: right" | 17.146 minutes
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| |-
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| | [[Beta Lyrae]] AB
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| | style="text-align: right" | 12.9075 days
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| |-
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| | [[Alpha Centauri]] AB
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| | style="text-align: right" | 79.91 years
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| |-
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| | [[Proxima Centauri]] - [[Alpha Centauri]] AB
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| | style="text-align: right" | 500,000 years or more
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| |}
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| ==See also==
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| * [[Geosynchronous orbit derivation]]
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| * [[Sidereal time]]
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| * [[Sidereal year]]
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| * [[Opposition (astronomy)]]
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| * [[List of periodic comets]]
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| ==Notes==
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| {{Reflist}}
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| == External links ==
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| {{Wiktionary|synodic}}
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| {{Orbits}}
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| {{DEFAULTSORT:Orbital Period}}
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| [[Category:Time in astronomy]]
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| [[Category:Orbits]]
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