Incelestial mechanics, thelongitude of the periapsis, also calledlongitude of the pericenter, of an orbiting body is thelongitude (measured from the point of the vernal equinox) at which theperiapsis (closest approach to the central body) would occur if the body's orbitinclination were zero. It is usually denotedϖ.
For the motion of a planet around the Sun, this position is calledlongitude of perihelion ϖ, which is the sum of the longitude of the ascending node Ω, and theargument of perihelion ω.[1][2]
The longitude of periapsis is a compound angle, with part of it being measured in theplane of reference and the rest being measured in the plane of theorbit. Likewise, any angle derived from the longitude of periapsis (e.g.,mean longitude andtrue longitude) will also be compound.
Sometimes, the termlongitude of periapsis is used to refer toω, the angle between the ascending node and the periapsis. That usage of the term is especially common in discussions of binary stars and exoplanets.[3][4] However, the angle ω is less ambiguously known as theargument of periapsis.
ϖ is the sum of thelongitude of ascending node Ω (measured on ecliptic plane) and theargument of periapsisω (measured on orbital plane):
which are derived from theorbital state vectors.
Define the following:
Then:
The right ascension α and declination δ of the direction of perihelion are:
If A < 0, add 180° to α to obtain the correct quadrant.
The ecliptic longitude ϖ and latitude b of perihelion are:
If cos(α) < 0, add 180° to ϖ to obtain the correct quadrant.
As an example, using the most up-to-date numbers from Brown (2017)[5] for the hypotheticalPlanet Nine with i = 30°, ω = 136.92°, and Ω = 94°, then α = 237.38°, δ = +0.41° and ϖ = 235.00°, b = +19.97° (Brown actually provides i, Ω, and ϖ, from which ω was computed).
