celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...

, the longitude of the periapsis, also called longitude of the pericenter, of an orbiting body is the

longitude Longitude (, ) is a geographic coordinate that specifies the east- west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lett ...

(measured from the point of the vernal equinox) at which the

periapsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides perta ...

(closest approach to the central body) would occur if the body's orbit

inclination Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Eart ...

were zero. It is usually denoted '' ϖ''. For the motion of a planet around the Sun, this position is called longitude of perihelion ϖ, which is the sum of the longitude of the ascending node Ω, and the

argument of perihelion 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 ...

ω. The longitude of periapsis is a compound angle, with part of it being measured in the

plane of reference In celestial mechanics, the orbital plane of reference (or orbital reference plane) is the plane used to define orbital elements (positions). The two main orbital elements that are measured with respect to the plane of reference are the inclin ...

and the rest being measured in the plane of the

orbit In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an ...

. Likewise, any angle derived from the longitude of periapsis (e.g.,

mean longitude Mean longitude is the ecliptic longitude at which an orbiting body could be found if its orbit were circular and free of perturbations. While nominally a simple longitude, in practice the mean longitude does not correspond to any one physical ang ...

and

true longitude In celestial mechanics, true longitude is the ecliptic longitude at which an orbiting body could actually be found if its inclination were zero. Together with the inclination and the ascending node, the true longitude can tell us the precise direc ...

) will also be compound. Sometimes, the term ''longitude of periapsis'' is used to refer to ''ω'', the angle between the ascending node and the periapsis. That usage of the term is especially common in discussions of binary stars and exoplanets. However, the angle ω is less ambiguously known as the

argument of periapsis 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 it ...

Calculation from state vectors

''ϖ'' is the sum of the

longitude of ascending node The longitude of the ascending node, also known as the right ascension of the ascending node, is one of the orbital elements used to specify the orbit of an object in space. Denoted with the symbol Ω, it is the angle from a specified reference d ...

Ω (measured on ecliptic plane) and the

''ω'' (measured on orbital plane):

\varpi = \Omega + \omega

which are derived from the

orbital state vectors In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are cartesian coordinate system, Cartesian vectors of position (vector), position (\mathbf) and velocity (\mathbf) that together with their t ...

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)Brown, Michael E. (2017) “Planet Nine: where are you? (part 1)” The Search for Planet Nine. http://www.findplanetnine.com/2017/09/planet-nine-where-are-you-part-1.html for the hypothetical

Planet Nine Planet Nine is a List of hypothetical Solar System objects, hypothetical ninth planet in the outer region of the Solar System. Its gravitational effects could explain the peculiar clustering of orbits for a group of extreme trans-Neptunian obj ...

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

External links

Determination of the Earth's Orbital Parameters
Past and future longitude of perihelion for Earth. {{orbits Orbits