Optimized Chebyshev Polynomial Representations of Ephemerides
Abstract
Highprecision planetary ephemerides have accuracies of about one part in 10(10}10({12)) , and span several centuries. This leads to a storage space problem for these ephemerides. We developed a computer program to optimize conversion of orbital ephemerides from tabular form to Chebyshev polynomials (see Newhall, X X 1989, Celest. Mech., 45, 305310) for compact storage and speedy interpolation. This program was used to numerically determine the optimal mean anomaly segment length for an orbit. Each segment is fitted with the Chebyshev polynomial of minimum order needed to yield a specified precision. At the level of precision needed for high precision ephemerides, the file size increases by about 10% when the precision of the Chebyshev polynomials is increased by an order of magnitude, regardless of segment length. File sizes continuously shrink as segment length is increased for loweccentricity Keplerian orbits (e < 0.5). At higher eccentricities, Keplerian orbit file sizes reach local minima near segment lengths that are simple fractions of a complete orbit. For ephemerides of 15 asteroids, the file size becomes approximately constant for segment lengths greater than about 90 degrees. The file size is independent of the orbital eccentricity and depends linearly on the semimajor axis. The file sizes for the outer planets, Saturn through Pluto, also become constant, but for segment lengths greater than about 45 degrees. Also, the file sizes increase linearly with semimajor axis, but the slope of the increase is lower. Dynamical studies using fictitious bodies are currently being conducted to understand this behavior. The file sizes for the Moon and Venus are similar to those of Keplerian orbits of eccentricity 0.1, while the remaining planets produce optimized file sizes intermediate between the lunar and outer planet extremes.
 Publication:

AAS/Division of Dynamical Astronomy Meeting
 Pub Date:
 September 1999
 Bibcode:
 1999DDA....30.1102H