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 between the orbit's
periapsis (the point of closest approach to the central point) and the orbit's
ascending node (the point where the body crosses the
plane of reference from South to North). The angle is measured in the
orbital plane and 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
In
astrodynamics the
argument of periapsis ω can be calculated as follows:
- (if then )
where:
- is a vector pointing towards the ascending node (i.e. the z-component of is zero),
- 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:
- (if the orbit is clockwise (i.e. ) then )
where:
- and are the x and y components of the eccentricity vector
In the case of circular orbits it is often assumed that the periapsis is placed at the ascending node and therefore
ω=0.
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