**34th Meeting of the AAS Division on Dynamical Astronomy, May 2003**

* 6 Poster Papers*

Posters, Monday, May 5, 2003, 8:00pm,
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## [6.04] A Method of Non-linear Harmonic Analysis and its Application to Determination of Planetary Precession in DE405

*T. Fukushima (NAOJ), W. Harada (Tokyo Univ.)*

We developed a method of non-linear harmonic analysis. The
algorithm determines (1) the coefficients of a quadratic
polynomial representing the secular variation, the
amplitudes and phases of Fourier terms, and the other linear
parameters by the usual linear least square method, (2) the
frequencies of Fourier terms and the other non-linear
parameters by the BFGS algorithm of the quasi-Newton method
(Broyden 1967), and (3) the number of the non-linear
parameters by increasing it one by one from zero until the
residual root mean square (RMS) becomes smaller than the
required level for the noiseless data or until its
decreasing manner becomes approximately flat for the noisy
data. We accelerated the convergence of the algorithm by
expanding the set of base functions so as to include the
so-called mixed secular terms, namely the product of Fourier
terms and a linear function. In order to find suitable
initial guesses for the search in the quasi-Newton method,
we extended the concept of periodogram to the case of mixed
secular terms. As an application of the developed algorithm,
we analysed the motion of the unit vector of the
heliocentric orbital angular momentum of the Earth-Moon
barycenter in the latest lunar/planetary ephemeris, DE405,
as Standish (1982) did for DE102. After dropping 86 Fourier
terms and 4 mixed secular terms detected, we determined the
secular variation of two angles specifying the unit vector
in the form of quadratic polynomials as \gamma = (-0.05240
±0.00014) + (10.55318 ±0.00011) t + (0.49318 ±
0.00004) t^{2}, \varphi = (84381.41127 ±0.00006) +
(-46.81265 ±0.00004) t + (0.04843 ±0.00002) t^{2} where
the unit is arc second and t is the time since J2000.0
measured in Julian century. This is the latest determination
of planetary precession formula in the inertial sense and
referred to the ICRF.

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Bulletin of the American Astronomical Society, **35** #4

© 2003. The American Astronomical Soceity.