34th Meeting of the AAS Division on Dynamical Astronomy, May 2003
6 Poster Papers
Posters, Monday, May 5, 2003, 8:00pm,

## [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) t2, \varphi = (84381.41127 ±0.00006) + (-46.81265 ±0.00004) t + (0.04843 ±0.00002) t2 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.

Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.