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The argument of periapsis (also called argument of perifocus or argument of pericenter), symbolized as ''ω'', is one of the
orbital element Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same ...
s of an
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 a p ...
ing body. Parametrically, ''ω'' is the angle from the body's
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 reference ...
to its
periapsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary (astronomy), primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two ...
, measured in the direction of motion. For specific types of orbits, terms such as argument of perihelion (for
heliocentric orbit A heliocentric orbit (also called circumsolar orbit) is an orbit around the barycenter of the Solar System, which is usually located within or very near the surface of the Sun. All planets, comets, and asteroids in the Solar System, and the Sun i ...
s), argument of perigee (for
geocentric orbit A geocentric orbit or Earth orbit involves any object orbiting Earth, such as the Moon or artificial satellites. In 1997, NASA estimated there were approximately 2,465 artificial satellite payloads orbiting Earth and 6,216 pieces of space debris ...
s), argument of periastron (for orbits around stars), and so on, may be used (see
apsis 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 ellip ...
for more information). An argument of periapsis of 0° means that the orbiting body will be at its closest approach to the central body at the same moment that it crosses the plane of reference from South to North. An argument of periapsis of 90° means that the orbiting body will reach periapsis at its northmost distance from the plane of reference. Adding the argument of periapsis to the
longitude of the ascending node The longitude of the ascending node (☊ or Ω) is one of the orbital elements used to specify the orbit of an object in space. It is the angle from a specified reference direction, called the ''origin of longitude'', to the direction of the asce ...
gives the
longitude of the periapsis In celestial mechanics, the longitude of the periapsis, also called longitude of the pericenter, of an orbiting body is the longitude (measured from the point of the vernal equinox) at which the periapsis (closest approach to the central body) woul ...
. However, especially in discussions of binary stars and exoplanets, the terms "longitude of periapsis" or "longitude of periastron" are often used synonymously with "argument of periapsis".


Calculation

In
astrodynamics Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of ...
the argument of periapsis ''ω'' can be calculated as follows: :\omega = \arccos ::If ''ez'' < 0 then ''ω'' → 2 − ''ω''. where: * n is a vector pointing towards the ascending node (i.e. the ''z''-component of n is zero), * e is the
eccentricity vector In celestial mechanics, the eccentricity vector of a Kepler orbit is the dimensionless vector with direction pointing from apoapsis to periapsis and with magnitude equal to the orbit's scalar eccentricity. For Kepler orbits the eccentricity vector i ...
(a vector pointing towards the periapsis). In the case of
equatorial orbit A near-equatorial orbit is an orbit that lies close to the equatorial plane of the object orbited. Such an orbit has an inclination near 0°. On Earth, such orbits lie on the celestial equator, the great circle of the imaginary celestial sphere on ...
s (which have no ascending node), the argument is strictly undefined. However, if the convention of setting the longitude of the ascending node Ω to 0 is followed, then the value of ''ω'' follows from the two-dimensional case: :\omega = \arctan2\left(e_y, e_x\right) ::If the orbit is clockwise (i.e. (r × v)''z'' < 0) then ''ω'' → 2 − ''ω''. where: *''ex'' and ''ey'' are the ''x''- and ''y''-components of the eccentricity vector e. In the case of circular orbits it is often assumed that the periapsis is placed at the ascending node and therefore ''ω'' = 0. However, in the professional exoplanet community, ''ω'' = 90° is more often assumed for circular orbits, which has the advantage that the time of a planet's inferior conjunction (which would be the time the planet would transit if the geometry were favorable) is equal to the time of its periastron.


See also

*
Apsidal precession In celestial mechanics, apsidal precession (or apsidal advance) is the precession (gradual rotation) of the line connecting the apsides (line of apsides) of an astronomical body's orbit. The apsides are the orbital points closest (periapsi ...
*
Kepler orbit Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
*
Orbital mechanics Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of ...
*
Orbital node An orbital node is either of the two points where an orbit intersection (Euclidean geometry), intersects a plane of reference to which it is inclined. A non-inclined orbit, which is coplanarity, contained in the reference plane, has no nodes. P ...


References


External links


Argument Of Perihelion
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Swinburne University Astronomy
Website {{orbits Orbits