The orbital period is the time taken for a given object to make one complete orbit about another object. Periodicity is the quality of occurring at regular intervals or periods (in Time or Space) and can occur in different contexts A Clock marks In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star

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. A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth

There are several kinds of orbital periods for objects around the Sun:

• The sidereal period is the time that it takes the object to make one full orbit around the Sun, relative to the stars. The Sun (Sol is the Star at the center of the Solar System. A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth This is considered to be an object's true orbital period.
• The synodic period is the time that it takes for the object to reappear at the same point in the sky, relative to the Sun, as observed from Earth; i. The Sun (Sol is the Star at the center of the Solar System. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 e. returns to the same elongation (and planetary phase). (For other uses of elongation see Elongation) Elongation is an Astronomical term that refers to the angle between the Sun and a planet Planetary phase is the term used to describe the appearance of the illuminated section of a Planet. This is the time that elapses between two successive conjunctions with the Sun and is the object's Earth-apparent orbital period. Conjunction is a term used in Positional astronomy and Astrology. The synodic period differs from the sidereal period since Earth itself revolves around the Sun.
• The draconitic period is the time that elapses between two passages of the object at its ascending node, the point of its orbit where it crosses the ecliptic from the southern to the northern hemisphere. An orbital node is one of the two points where an Orbit crosses a Plane of reference which it is inclined to The ecliptic is the apparent path that the Sun traces out in the sky during the year It differs from the sidereal period because the object's line of nodes typically precesses or recesses slowly. An orbital node is one of the two points where an Orbit crosses a Plane of reference which it is inclined to
• The anomalistic period is the time that elapses between two passages of the object at its perihelion, the point of its closest approach to the Sun. In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from The Sun (Sol is the Star at the center of the Solar System. It differs from the sidereal period because the object's semimajor axis typically precesses or recesses slowly. In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae
• The tropical period, finally, is the time that elapses between two passages of the object at right ascension zero. Right ascension (abbrev RA; symbol α) is the Astronomical term for one of the two Coordinates of a point on the Celestial sphere It is slightly shorter than the sidereal period because the vernal point precesses. An equinox is the event of the Sun passing over the Earth's equator in its annual cycle

Relation between sidereal and synodic period

Copernicus devised a mathematical formula to calculate a planet's sidereal period from its synodic period. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In Mathematics and in the Sciences a formula (plural formulae, formulæ or formulas) is a concise way of expressing information

Using the abbreviations

E = the sidereal period of Earth (a sidereal year, not the same as a tropical year)

P = the sidereal period of the other planet

S = the synodic period of the other planet (as seen from Earth)

During the time S, the Earth moves over an angle of (360°/E)S (assuming a circular orbit) and the planet moves (360°/P)S. The sidereal year is the time taken for the Sun to return to the same position with respect to the Stars of the Celestial sphere. A tropical year (also known as a solar year) is the length of time that the Sun takes to return to the same position in the cycle of seasons as seen from Earth This article describes the unit of angle For other meanings see Degree.

Let us consider the case of an inferior planet, i. The terms " inferior planet " and " superior planet " were originally used in the Ptolemaic Cosmology to differentiate those planets e. a planet that will complete one orbit more than Earth before the two return to the same position relative to the Sun.

and using algebra we obtain

For a superior planet one derives likewise:

Generally, knowing the sidereal period of the other planet and the Earth, P and E, the synodic period can easily be derived:

,

which stands for both an inferior planet or superior planet. Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. The terms " inferior planet " and " superior planet " were originally used in the Ptolemaic Cosmology to differentiate those planets The terms " inferior planet " and " superior planet " were originally used in the Ptolemaic Cosmology to differentiate those planets

The above formulae are easily understood by considering the angular velocities of the Earth and the object: the object's apparent angular velocity is its true (sidereal) angular velocity minus the Earth's, and the synodic period is then simply a full circle divided by that apparent angular velocity.

Table of synodic periods in the Solar System, relative to Earth:

	Sid. P. (a)	Syn. In Astronomy, a Julian year (symbol a) is a unit of measurement of Time defined P. (a)	Syn. P. (d)
Mercury	0. A day (symbol d is a unit of Time equivalent to 24 Hours and the duration of a single Rotation of planet Earth with respect to the 241	0. 317	115. 9
Venus	0. The VENUS ( V ictoria E xperimental N etwork U nder the S ea project is a cabled sea floor observatory operated by the University 615	1. 599	583. 9
Earth	1	—	—
Moon	0. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 0748	0. 0809	29. 5306
Mars	1. 881	2. 135	780. 0
4 Vesta	3. TemplateInfobox Planet. --> 4 Vesta (ˈvɛstə Vesta is the second most massive object in the Asteroid belt 629	1. 380	504. 0
1 Ceres	4. Ceres (ˈsɪəriːz 600	1. 278	466. 7
10 Hygiea	5. 557	1. 219	445. 4
Jupiter	11. 87	1. 092	398. 9
Saturn	29. 45	1. 035	378. 1
Uranus	84. 07	1. 012	369. 7
Neptune	164. Neptune ( English|AmE] ] is the eighth and farthest Planet from the Sun in the Solar System. 9	1. 006	367. 5
134340 Pluto	248. 1	1. 004	366. 7
136199 Eris	557	1. 002	365. 9
90377 Sedna	12050	1. TemplateInfobox Planet.--> 90377 Sedna (ˈsɛdnə) is a Trans-Neptunian 00001	365. 1

In the case of a planet's moon, the synodic period usually means the Sun-synodic period. A natural satellite or moon is a Celestial body that Orbits a Planet or smaller body which is called the primary. That is to say, the time it takes the moon to run its phases, coming back to the same solar aspect angle for an observer on the planet's surface —the Earth's motion does not affect this value, because an Earth observer is not involved. For example, Deimos' synodic period is 1. TemplateInfobox Planet.--> Deimos (ˈdaɪməs; also /ˈdiːməs/ 2648 days, 0. 18% longer than Deimos' sidereal period of 1. 2624 d.

Calculation

Small body orbiting a central body

In astrodynamics the orbital period (in seconds) of a small body orbiting a central body in a circular or elliptical orbit is:

Using the Law of Exponents, this equation can also be written as (rmfr):

and

(standard gravitational parameter)

where:

• is length of orbit's semi-major axis (km),
• is the standard gravitational parameter,
• is the gravitational constant,
• the mass of the central body (kg). Orbital mechanics or astrodynamics is the application of Celestial mechanics to the practical problems concerning the motion of Rockets and other Spacecraft Small body orbiting a central body Under Standard assumptions in astrodynamics we have m where m \ is the mass In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae Small body orbiting a central body Under Standard assumptions in astrodynamics we have m where m \ is the mass The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass

Note that for all ellipses with a given semi-major axis, the orbital period is the same, regardless of eccentricity.

Orbital period as a function of central body's density

For the Earth (and any other spherically symmetric body with the same average density) as central body we get

and for a body of water

T in hours, with R the radius of the body.

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. A time standard

For the Sun as central body we simply get

T in years, with a in astronomical units. The astronomical unit ( AU or au or au or sometimes ua) is a unit of Length based on the distance from the Earth to the This is the same as Kepler's Third Law

Two bodies orbiting each other

In celestial mechanics when both orbiting bodies' masses have to be taken into account the orbital period can be calculated as follows:

where:

• is the sum of the 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),
• and are the masses of the bodies,
• is the gravitational constant. In Astronomy, Kepler's Laws of Planetary Motion are three mathematical laws that describe the motion of Planets in the Solar System. Celestial mechanics is the branch of Astrophysics that deals with the motions of Celestial objects The field applies principles of Physics, historically In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass

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 Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star

In a parabolic or hyperbolic trajectory the motion is not periodic, and the duration of the full trajectory is infinite.

Earth orbits

See also

• Geosynchronous orbit derivation
• Sidereal time
• Sidereal year

• Opposition (astronomy)