Longitude of periapsis

ϖ is the sum of the longitude of ascending node Ω (measured on ecliptic plane) and the argument of periapsis ω (measured on orbital plane): \varpi = \Omega + \omega which are derived from the orbital state vectors. ==Derivation of ecliptic longitude and latitude of perihelion for inclined orbits==

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) for the hypothetical Planet 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). ==References==