World Library  
Flag as Inappropriate
Email this Article

Argument of periapsis

Article Id: WHEBN0000975450
Reproduction Date:

Title: Argument of periapsis  
Author: World Heritage Encyclopedia
Language: English
Subject: Infobox planet/testcases, Orbital elements, Orbital mechanics, 2015 ER61, Molniya orbit
Collection: Orbits
Publisher: World Heritage Encyclopedia

Argument of periapsis

The argument of periapsis (also called argument of perifocus or argument of pericenter), symbolized as ω, is one of the orbital elements of an orbiting body. Specifically, ω is the angle from the body's ascending node to its periapsis, measured in the direction of motion. For specific types of orbits, words such as perihelion (for Sun-centered orbits), perigee (for Earth-centered orbits), periastron (for orbits around stars) and so on may replace the word periapsis. 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".

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


  • Calculation 1
  • See also 2
  • References 3
  • External links 4


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 \omega = 2 \pi - \omega\,)


  • \mathbf{n} is a vector pointing towards the ascending node (i.e. the z-component of \mathbf{n} is zero),
  • \mathbf{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 = \arctan2({e_y}, {e_x})
(if the orbit is clockwise (i.e. ( \mathbf{r} \times \mathbf{v} )_z < 0) then \omega = 2 \pi - \omega\,)


  • e_x\, and e_y\, are the x and y components of the eccentricity vector \mathbf{e }.\,

In the case of circular orbits it is often assumed that the periapsis is placed at the ascending node and therefore ω=0.

See also


External links

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.