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The orbital period (also revolution period) is the amount of time a given
astronomical object An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often u ...
takes to complete one
orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...
around another object. In
astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
, it usually applies to
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
s or
asteroid An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. ...
s orbiting the Sun,
moons A natural satellite is, in the most common usage, an astronomical body that orbits a planet, dwarf planet, or small Solar System body (or sometimes another natural satellite). Natural satellites are often colloquially referred to as ''moons'' ...
orbiting planets,
exoplanet An exoplanet or extrasolar planet is a planet outside the Solar System. The first possible evidence of an exoplanet was noted in 1917 but was not recognized as such. The first confirmation of detection occurred in 1992. A different planet, init ...
s orbiting other
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s, or
binary star A binary star is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved using a telescope as separate stars, in ...
s. For celestial objects in general, the sidereal period (
sidereal year A sidereal year (, ; ), also called a sidereal orbital period, is the time that Earth or another planetary body takes to orbit the Sun once with respect to the fixed stars. Hence, for Earth, it is also the time taken for the Sun to return to t ...
) is referred to by the orbital period, determined by a 360° revolution of one body around its
primary Primary or primaries may refer to: Arts, entertainment, and media Music Groups and labels * Primary (band), from Australia * Primary (musician), hip hop musician and record producer from South Korea * Primary Music, Israeli record label Works ...
, e.g. Earth around the Sun, relative to the
fixed stars In astronomy, fixed stars ( la, stellae fixae) is a term to name the full set of glowing points, astronomical objects actually and mainly stars, that appear not to move relative to one another against the darkness of the night sky in the backgro ...
projected in the sky. Orbital periods can be defined in several ways. The tropical period is more particularly about the position of the parent star. It is the basis for the
solar year A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky of a celestial body of the Solar System such as the Earth, completing a full cycle of seasons; for example, the time f ...
, and respectively the calendar
year A year or annus is the orbital period of a planetary body, for example, the Earth, moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the h ...
. The synodic period incorporates not only the orbital relation to the parent star, but also to other celestial objects, making it not a mere different approach to the orbit of an object around its parent, but a period of orbital relations with other objects, normally Earth and their orbits around the Sun. It applies to the elapsed time where planets return to the same kind of phenomena or location, such as when any planet returns between its consecutive observed conjunctions with or
oppositions ''Oppositions'' was an architectural journal produced by the Institute for Architecture and Urban Studies from 1973 to 1984. Many of its articles contributed to advancing architectural theory and many of its contributors became distinguished practi ...
to the Sun. For example,
Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousand ...
has a synodic period of 398.8 days from Earth; thus, Jupiter's opposition occurs once roughly every 13 months. Periods in astronomy are conveniently expressed in various units of time, often in hours, days, or years. They can be also defined under different specific astronomical definitions that are mostly caused by the small complex external gravitational influences of other celestial objects. Such variations also include the true placement of the centre of gravity between two astronomical bodies (
barycenter In astronomy, the barycenter (or barycentre; ) is the center of mass of two or more bodies that orbit one another and is the point about which the bodies orbit. A barycenter is a dynamical point, not a physical object. It is an important con ...
),
perturbation Perturbation or perturb may refer to: * Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly * Perturbation (geology), changes in the nature of alluvial deposits over time * Perturbat ...
s by other planets or bodies,
orbital resonance In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relationsh ...
,
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, etc. Most are investigated by detailed complex astronomical theories using
celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, ...
using precise positional observations of celestial objects via
astrometry Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way. Hist ...
.


Related periods

There are many periods related to the orbits of objects, each of which are often used in the various fields of
astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
and
astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the h ...
, particularly they must not be confused with other revolving periods like rotational periods. Examples of some of the common orbital ones include the following: * The sidereal period is the amount of time that it takes an object to make a full orbit, relative to the
fixed stars In astronomy, fixed stars ( la, stellae fixae) is a term to name the full set of glowing points, astronomical objects actually and mainly stars, that appear not to move relative to one another against the darkness of the night sky in the backgro ...
, the
sidereal year A sidereal year (, ; ), also called a sidereal orbital period, is the time that Earth or another planetary body takes to orbit the Sun once with respect to the fixed stars. Hence, for Earth, it is also the time taken for the Sun to return to t ...
. This is the orbital period in an inertial (non-rotating)
frame of reference In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both math ...
. * The synodic period is the amount of time that it takes for an object to reappear at the same point in relation to two or more other objects. In common usage, these two objects are typically Earth and the Sun. The time between two successive
oppositions ''Oppositions'' was an architectural journal produced by the Institute for Architecture and Urban Studies from 1973 to 1984. Many of its articles contributed to advancing architectural theory and many of its contributors became distinguished practi ...
or two successive conjunctions is also equal to the synodic period. For celestial bodies in the solar system, the synodic period (with respect to Earth and the Sun) differs from the tropical period owing to Earth's motion around the Sun. For example, the synodic period of the
Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
's orbit as seen from
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
, relative to the Sun, is 29.5 mean solar days, since the Moon's phase and position relative to the Sun and Earth repeats after this period. This is longer than the sidereal period of its orbit around Earth, which is 27.3 mean solar days, owing to the motion of Earth around the Sun. * The draconitic period (also draconic period or nodal period), is the time that elapses between two passages of the object through its ascending node, the point of its orbit where it crosses the
ecliptic The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic agains ...
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 In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured. The moment of epoch is usually decided ...
, the orbital plane of the object still precesses, causing the draconitic period to differ from the sidereal period. * 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 The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
, called the
perihelion An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any elli ...
), the point of its closest approach to the attracting body. It differs from the sidereal period because the object's
semi-major axis In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the lon ...
typically advances slowly. * Also, the tropical period of Earth (a
tropical year A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky of a celestial body of the Solar System such as the Earth, completing a full cycle of seasons; for example, the time ...
) is the interval between two alignments of its rotational axis with the Sun, also viewed as two passages of the object at a
right ascension Right ascension (abbreviated RA; symbol ) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the ( hour circle of the) point in question above the earth. When pair ...
of 0 hr. One Earth
year A year or annus is the orbital period of a planetary body, for example, the Earth, moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the h ...
is slightly shorter than the period for the Sun to complete one circuit along the
ecliptic The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic agains ...
(a
sidereal year A sidereal year (, ; ), also called a sidereal orbital period, is the time that Earth or another planetary body takes to orbit the Sun once with respect to the fixed stars. Hence, for Earth, it is also the time taken for the Sun to return to t ...
) because the inclined axis and equatorial plane slowly
precess Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...
(rotate with respect to reference stars), realigning with the Sun before the orbit completes. This cycle of axial precession for Earth, known as ''precession of the equinoxes'', recurs roughly every 25,772 years.


Small body orbiting a central body

According to
Kepler's Third Law In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbi ...
, the orbital period ''T'' of two point masses orbiting each other in a circular or
elliptic orbit In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, i ...
is: :T = 2\pi\sqrt where: * ''a'' is the orbit's
semi-major axis In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the lon ...
* ''μ'' = ''GM'' is the
standard gravitational parameter In celestial mechanics, the standard gravitational parameter ''μ'' of a celestial body is the product of the gravitational constant ''G'' and the mass ''M'' of the bodies. For two bodies the parameter may be expressed as G(m1+m2), or as GM whe ...
** ''G'' is the
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
, ** ''M'' is the mass of the more massive body. For all ellipses with a given semi-major axis the orbital period is the same, regardless of eccentricity. Inversely, for calculating the distance where a body has to orbit in order to have a given orbital period: :a = \sqrt /math> where * ''a'' is the orbit's semi-major axis, * ''G'' is the gravitational constant, * ''M'' is the mass of the more massive body, * ''T'' is the orbital period. For instance, for completing an orbit every 24 
hour An hour (symbol: h; also abbreviated hr) is a unit of time conventionally reckoned as of a day and scientifically reckoned between 3,599 and 3,601 seconds, depending on the speed of Earth's rotation. There are 60 minutes in an hour, and 24 ...
s around a mass of 100  kg, a small body has to orbit at a distance of 1.08 
meters The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pr ...
from the central body's
center of mass In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...
. In the special case of perfectly circular orbits, the orbital velocity is constant and equal (in m/s) to : v_\text = \sqrt where: * ''r'' is the circular orbit's radius in meters, * ''G'' is the gravitational constant, * ''M'' is the mass of the central body. This corresponds to times (≈ 0.707 times) the
escape velocity In celestial mechanics, escape velocity or escape speed is the minimum speed needed for a free, non- propelled object to escape from the gravitational influence of a primary body, thus reaching an infinite distance from it. It is typically ...
.


Effect of central body's density

For a perfect sphere of uniform
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
, it is possible to rewrite the first equation without measuring the mass as: :T = \sqrt where: * ''r'' is the sphere's radius * ''a'' is the orbit's semi-major axis in metres, * ''G'' is the gravitational constant, * ''ρ'' is the density of the sphere in kilograms per cubic metre. For instance, a small body in circular orbit 10.5 cm above the surface of a sphere of
tungsten Tungsten, or wolfram, is a chemical element with the symbol W and atomic number 74. Tungsten is a rare metal found naturally on Earth almost exclusively as compounds with other elements. It was identified as a new element in 1781 and first isol ...
half a metre in radius would travel at slightly more than 1 mm/ s, completing an orbit every hour. If the same sphere were made of
lead Lead is a chemical element with the symbol Pb (from the Latin ) and atomic number 82. It is a heavy metal that is denser than most common materials. Lead is soft and malleable, and also has a relatively low melting point. When freshly cut, ...
the small body would need to orbit just 6.7 mm above the surface for sustaining the same orbital period. 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 ) :T = \sqrt Thus the orbital period in low orbit depends only on the density of the central body, regardless of its size. So, for the Earth as the central body (or any other spherically symmetric body with the same mean density, about 5,515 kg/m3, e.g. Mercury with 5,427 kg/m3 and
Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never f ...
with 5,243 kg/m3) we get: :''T'' = 1.41 hours and for a body made of water (''ρ'' ≈ 1,000 kg/m3), or bodies with a similar density, e.g. Saturn's moons
Iapetus In Greek mythology, Iapetus (; ; grc, Ἰαπετός, Iapetós), also Japetus, is a Titan, the son of Uranus and Gaia and father of Atlas (mythology), Atlas, Prometheus, Epimetheus (mythology), Epimetheus, and Menoetius (mythology), Menoetius. ...
with 1,088 kg/m3 and Tethys with 984 kg/m3 we get: :''T'' = 3.30 hours Thus, as an alternative for using a very small number like ''G'', the strength of universal gravity can be described using some reference material, such as 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 unit of time is any particular time interval, used as a standard way of measuring or expressing duration. The base unit of time in the International System of Units (SI) and by extension most of the Western world, is the second, defined as a ...
if we have a unit of mass, a unit of length, and a unit of density.


Two bodies orbiting each other

In
celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, ...
, when both orbiting bodies' masses have to be taken into account, the orbital period ''T'' can be calculated as follows: :T= 2\pi\sqrt where: * ''a'' 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), * ''M''1 + ''M''2 is the sum of the masses of the two bodies, * ''G'' is the
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
. Note that the orbital period is independent of size: for a scale model it would be the same, when densities are the same, as ''M'' scales linearly with ''a''3 (see also ). In a parabolic or hyperbolic trajectory, the motion is not periodic, and the duration of the full trajectory is infinite.


Synodic period

One of the observable characteristics of two bodies which orbit a third body in different orbits, and thus have different orbital periods, is their synodic period, which is the time between conjunctions. An example of this related period description is the repeated cycles for celestial bodies as observed from the Earth's surface, the synodic period, applying to the elapsed time where planets return to the same kind of phenomenon or location. For example, when any planet returns between its consecutive observed conjunctions with or
oppositions ''Oppositions'' was an architectural journal produced by the Institute for Architecture and Urban Studies from 1973 to 1984. Many of its articles contributed to advancing architectural theory and many of its contributors became distinguished practi ...
to the Sun. For example,
Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousand ...
has a synodic period of 398.8 days from Earth; thus, Jupiter's opposition occurs once roughly every 13 months. If the orbital periods of the two bodies around the third are called ''T''1 and ''T''2, so that ''T''1 < ''T''2, their synodic period is given by: :\frac = \frac - \frac


Examples of sidereal and synodic periods

Table of synodic periods in the Solar System, relative to Earth: In the case of a planet's
moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
, 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 Deimos, a Greek word for ''dread'', may refer to: * Deimos (deity), one of the sons of Ares and Aphrodite in Greek mythology * Deimos (moon), the smaller and outermost of Mars' two natural satellites * Elecnor Deimos, a Spanish aerospace company * ...
's synodic period is 1.2648 days, 0.18% longer than Deimos's sidereal period of 1.2624 d.


Synodic periods relative to other planets

The concept of synodic period applies not just to the Earth, but also to other planets as well, and the formula for computation is the same as the one given above. Here is a table which lists the synodic periods of some planets relative to each other:


Binary stars


See also

*
Geosynchronous orbit derivation A geostationary orbit, also referred to as a geosynchronous equatorial orbit''Geostationary orbit'' and ''Geosynchronous (equatorial) orbit'' are used somewhat interchangeably in sources. (GEO), is a circular geosynchronous orbit in altitude ...
*
Rotation period The rotation period of a celestial object (e.g., star, gas giant, planet, moon, asteroid) may refer to its sidereal rotation period, i.e. the time that the object takes to complete a single revolution around its axis of rotation relative to the ...
– time that it takes to complete one revolution around its axis of rotation * Satellite revisit period *
Sidereal time Sidereal time (as a unit also sidereal day or sidereal rotation period) (sidereal ) is a timekeeping system that astronomers use to locate celestial objects. Using sidereal time, it is possible to easily point a telescope to the proper coor ...
*
Sidereal year A sidereal year (, ; ), also called a sidereal orbital period, is the time that Earth or another planetary body takes to orbit the Sun once with respect to the fixed stars. Hence, for Earth, it is also the time taken for the Sun to return to t ...
*
Opposition (astronomy) In positional astronomy, two astronomical objects are said to be in opposition when they are on opposite sides of the celestial sphere, as observed from a given body (usually Earth). A planet (or asteroid or comet) is said to be "in opposition" ...
* List of periodic comets


Notes


Bibliography

*


External links

{{DEFAULTSORT:Orbital Period Time in astronomy Period