Argument of periapsis - Misplaced Pages

(Redirected from Argument of the perihelion) Specifies the orbit of an object in space

Fig. 1: Diagram of orbital elements, including the argument of periapsis (ω).

Astrodynamics
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Orbital elements Apsis Argument of periapsis Eccentricity Inclination Mean anomaly Orbital nodes Semi-major axis True anomaly
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v t e

The argument of periapsis (also called argument of perifocus or argument of pericenter), symbolized as ω (omega), is one of the orbital elements of an orbiting body. Parametrically, ω is the angle from the body's ascending node to its periapsis, measured in the direction of motion.

For specific types of orbits, terms such as argument of perihelion (for heliocentric orbits), argument of perigee (for geocentric orbits), argument of periastron (for orbits around stars), and so on, may be used (see apsis 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 gives the longitude of the periapsis. 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 the argument of periapsis ω can be calculated as follows:

\omega =\arccos {{\mathbf {n} \cdot \mathbf {e} } \over {\mathbf {\left|n\right|} \mathbf {\left|e\right|} }}

If e_z < 0 then ω → 2π − 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 (a vector pointing towards the periapsis).

In the case of equatorial orbits (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: $\omega =\mathrm {atan2} \left(e_{y},e_{x}\right)$

If the orbit is clockwise (i.e. (r × v)_z < 0) then ω → 2π − 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

Iglesias-Marzoa, Ramón; López-Morales, Mercedes; Jesús Arévalo Morales, María (2015). "Thervfit Code: A Detailed Adaptive Simulated Annealing Code for Fitting Binaries and Exoplanets Radial Velocities". Publications of the Astronomical Society of the Pacific. 127 (952): 567–582. arXiv:1505.04767. Bibcode:2015PASP..127..567I. doi:10.1086/682056.
Kreidberg, Laura (2015). "Batman: BAsic Transit Model cAlculatioN in Python". Publications of the Astronomical Society of the Pacific. 127 (957): 1161–1165. arXiv:1507.08285. Bibcode:2015PASP..127.1161K. doi:10.1086/683602. S2CID 7954832.
Eastman, Jason; Gaudi, B. Scott; Agol, Eric (2013). "EXOFAST: A Fast Exoplanetary Fitting Suite in IDL". Publications of the Astronomical Society of the Pacific. 125 (923): 83. arXiv:1206.5798. Bibcode:2013PASP..125...83E. doi:10.1086/669497. S2CID 118627052.

External links

Argument Of Perihelion in Swinburne University Astronomy Website

Gravitational orbits

Types

General	Box Capture Circular Elliptical / Highly elliptical Escape Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic trajectory Parking Prograde / Retrograde Synchronous semi sub Transfer orbit
Geocentric	Geosynchronous Geostationary Geostationary transfer Graveyard High Earth Low Earth Medium Earth Molniya Near-equatorial Orbit of the Moon Polar Sun-synchronous Transatmospheric Tundra Very low Earth
About other points	Mars Areocentric Areosynchronous Areostationary Lagrange points Distant retrograde Halo Lissajous Libration Lunar Sun Heliocentric Earth's orbit Mars cycler Heliosynchronous Other Lunar cycler

Parameters

Shape Size	e Eccentricity a Semi-major axis b Semi-minor axis Q, q Apsides
Orientation	i Inclination Ω Longitude of the ascending node ω Argument of periapsis ϖ Longitude of the periapsis
Position	M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude
Variation	T Orbital period n Mean motion v Orbital speed t₀ Epoch

Maneuvers

Orbital
mechanics

List of orbits

Categories:

Calculation

See also

References

External links