The orbital period (also revolution period) is the amount of time a given
astronomical object 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
asteroids orbiting the
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
,
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,
exoplanets orbiting other
stars, or
binary stars.
For celestial objects in general, the sidereal period (
sidereal year) is referred to by the orbital period, determined by a 360° revolution of
one body around its
primary, e.g. Earth around the Sun, relative to the
fixed stars 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.
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 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-thousandth t ...
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 ...
),
perturbations 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 using precise positional observations of celestial objects via
astrometry.
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, particularly they must not be confused with other revolving periods like
rotational 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 b ...
s. 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, the
sidereal year. This is the orbital period in an inertial (non-rotating)
frame of reference.
* 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 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 surfa ...
, relative to the
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
, 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
The nodal period (or draconic period) of a satellite is the time interval between successive passages of the satellite through either of its orbital nodes, typically the ascending node. This type of orbital period applies to artificial satellites, ...
), is the time that elapses between two passages of the object through its
ascending node
An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined. A non-inclined orbit, which is contained in the reference plane, has no nodes.
Planes of reference
Common planes of refere ...
, 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
An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined. A non-inclined orbit, which is contained in the reference plane, has no nodes.
Planes of reference
Common planes of refere ...
, 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, 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
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 ...
(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 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 f ...
) 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 of
0 hr. One Earth
year 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) because the
inclined axis and
equatorial plane
The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. This plane of reference bases the equatorial coordinate system. In other words, the celestial equator is an abstract projecti ...
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:
:
where:
* ''a'' is the orbit's
semi-major axis
* ''μ'' = ''GM'' is the
standard gravitational parameter
** ''G'' is the
gravitational constant,
** ''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:
: