The argument of periapsis (also called argument of perifocus or argument of pericenter), symbolized as ''ω (

omega Omega (, ; uppercase Ω, lowercase ω; Ancient Greek ὦ, later ὦ μέγα, Modern Greek ωμέγα) is the twenty-fourth and last letter in the Greek alphabet. In the Greek numerals, Greek numeric system/isopsephy (gematria), it has a value ...

)'', 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 (also known as orbital revolution) 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 ...

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 referenc ...

to its

periapsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides perta ...

, 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 ...

s), argument of perigee (for

geocentric orbit A geocentric orbit, Earth-centered 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 6,21 ...

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. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides perta ...

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, also known as the right ascension of the ascending node, is one of the orbital elements used to specify the orbit of an object in space. Denoted with the symbol Ω, it is the angle from a specified reference d ...

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

astrodynamics Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the Newton's law of univ ...

the argument of periapsis ''ω'' can be calculated as follows: :

\omega = \arccos

::If ''e_z'' < 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 ...

(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 primary body orbited. Such an orbit has an inclination near 0°. On Earth, such orbits lie near the celestial equator, the great circle of the imaginary celestial s ...

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 = \mathrm\left(e_y, e_x\right)

::If the orbit is clockwise (i.e. (r × v)_''z'' < 0) then ''ω'' → 2 − ''ω''. where: *''e_x'' and ''e_y'' 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.

References

External links

Argument Of Perihelion
i
Swinburne University Astronomy
Website {{orbits Orbits Angle

Calculation

See also

References

External links