USNO Circular 181
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Nutation Series Evaluation in NOVAS 3.0

George H. Kaplan
U.S. Naval Observatory
December 2009


This circular describes the computation of nutation in the Naval Observatory Vector Astrometry Software (NOVAS), versions 3.0 and 3.1. The user's guides to the Fortran and C editions of NOVAS 3.1 provide a detailed description of current software, which supersedes NOVAS 3.0 described by USNO Circular 180.

Nutation is a small periodic oscillation of the Earth's axis with respect to a space-fixed reference system ("inertial space") caused by the torque of the Sun and Moon — and to a lesser extent, the other planets — on the Earth's equatorial bulge. Nutation is usually modeled by lengthy trigonometric series that, when evaluated for a specific date and time, yield the values of two ecliptic angles: the nutation in longitude, Δ ψ, and the nutation in obliquity, Δ ε. The evaluation of the nutation series is generally the most computationally intensive part of calculating the positions of celestial objects with respect to the traditional celestial coordinate system defined by the true equator and equinox of date. NOVAS provides several nutation series with different numbers of terms, which the user can select depending on the accuracy requirements.

This circular also applies to NOVAS 3.1, which was released in March 2011. No significant changes occurred in the nutation series or their handling between NOVAS 3.0 and 3.1.

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