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Precession Theory Using the Invariable Plane of the Solar System

Published online by Cambridge University Press:  12 April 2016

W.M. Owen Jr.
W.M. Owen Jr.*
Affiliation:
Jet Propulsion Laboratory, University of Florida , California Institute of TechnologyGainesville, Florida Pasadena, California;

Abstract

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Standard precession theory builds up the precession matrix P, which rotates coordinates from the mean equator and equinox of epoch to the mean equator and equinox of date, by a sequence of three elementary rotations by the accumulated Euler angles ϚA, θA and zA: P = R3(−zA)R2(θA)R3(−ϚA). This scheme works well provided both the epoch and the date are within a few centuries of J2000. For long-term applications, the alternative formulation using the accumulated luni-solar and planetary precession, P = R3(ᵡA)R1(−ѡA)R3(−ψA)R1(ɛ), is more stable.

Yet another formulation for P is possible, using the invariable plane of the Solar System as an intermediate plane: P = R3(−L) R1(−I) R3(−Δ) R1(I0) R3(L0). The angles I0 and L0 are the inclination and ascending node of the invariable plane at epoch; I and L are the same quantities at the date. Only the angle Δ is a function of both times. This scheme works for both short-term and long-term applications.

For the short term, polynomial coefficients for I, L, and Δ are derived from the currently-accepted coefficients of the angles ϚA, θA and zA. For the long term, these angles are expressed as sums of Chebyshev polynomials obtained from analysis of a million-year numerical integration.

If the intersection of the mean equator and the invariable plane were adopted as the origin of right ascensions, the theory would be simplified further: since L0 and L would no longer be required, P would again consist of the minimum three rotations.

Type
Part 2. Poster Papers
Information
International Astronomical Union Colloquium , Volume 127: Reference Systems , 1991 , pp. 323 - 326
Copyright
Copyright © United States Naval Observatory 1991

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