True longitude

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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 direction from the central object at which the body would be located at a particular time.

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

Calculation

The true longitude l can be calculated as follows: [1] [2] [3]

l = ν + ϖ

where:

True anomaly angular parameter that defines the position of a body moving along a Keplerian orbit; angle between the direction of periapsis and the current position of the body, as seen from the main focus of the ellipse (the point around which the object orbits)

In celestial mechanics, true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between the direction of periapsis and the current position of the body, as seen from the main focus of the ellipse.

Longitude of the periapsis longitude (measured from the point of the vernal equinox) at which the periapsis (closest approach to the central body) would occur if the bodys inclination were zero

In celestial mechanics, the longitude of the periapsis, also called longitude of the pericenter, of an orbiting body is the longitude at which the periapsis would occur if the body's orbit inclination were zero. It is usually denoted ϖ.

Argument of periapsis one of the orbital elements used to specify the orbit of an object in space

The argument of periapsis, symbolized as ω, is one of the orbital elements of an orbiting body. Parametrically, ω is the angle from the body's ascending node to its periapsis, measured in the direction of motion.

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In celestial mechanics, the plane of reference 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 inclination and the longitude of the ascending node.

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Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities. Those Greek letters which have the same form as Latin letters are rarely used: capital A, B, E, Z, H, I, K, M, N, O, P, T, Y, X. Small ι, ο and υ are also rarely used, since they closely resemble the Latin letters i, o and u. Sometimes font variants of Greek letters are used as distinct symbols in mathematics, in particular for ε/ϵ and π/ϖ. The archaic letter digamma (Ϝ/ϝ/ϛ) is sometimes used.

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In celestial mechanics, the argument of latitude is an angular parameter that defines the position of a body moving along a Kepler orbit. It is the angle between the ascending node and the body.

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References

  1. Multon, F. R. (1970). An Introduction to Celestial Mechanics (2nd ed.). New York, NY: Dover. pp. 182–183.
  2. Roy, A. E. (1978). Orbital Motion. New York, NY: John Wiley & Sons. p. 174. ISBN   0-470-99251-4.
  3. Brouwer, D.; Clemence, G. M. (1961). Methods of Celestial Mechanics. New York, NY: Academic Press. p. 45.