Title:

                  Comparison between two theories of asteroid proper elements.
 Authors:

                  Knezevic, Z.; Froeschle, C.; Lemaitre, A.; Milani, A.; Morbidelli, A.
 Journal:

                  Astron. Astrophys. 293, 605-612 (1995) (A&A Homepage)
 Publication Date:

                  01/1995
 Origin:

                  A&A via CDS; KNUDSEN
 A&A Keywords:

                  CELESTIAL MECHANICS, MINOR PLANETS, ASTEROIDS
 Abstract Copyright:

                  (c) 1995: Astronomy & Astrophysics
 Bibliographic Code:

                  1995A&A...293..605K
 

                                            Abstract

A comparison between two theories for the calculation of proper elements is presented in this paper; the first theory, purely
analytical, has been developed by Milani & Knezevic (1990, 1992, 1994); the second one, a semi-numerical approach, is due to
Lemaitre & Morbidelli (1994). The analytical theory, based on series expansions in eccentricity and inclination, is particularly
suitable for low inclination and low eccentricity orbits, while the semi-numerical one is devoted to orbits with either large
eccentricities or large inclinations. The orbits of the minor planets 3710, 1021, 387, 980, 185 have been computed numerically for
4.5Myrs, and the proper elements have been derived with both algorithms. The RMS values of the changes with time of the proper
elements are taken as a measure of the instability. The results confirm the theoretical predictions, namely the Milani and Knezevic
proper elements are more stable at low e and I, while the stability of the Lemaitre & Morbidelli proper elements depends very
little upon eccentricity and inclination. As a result, the MK elements should be used below about 15deg of inclination, and the LM
elements should be used above about 17deg of inclination. The region between 15deg and 17deg should be considered as a
transition region where both methods have roughly the same stability; therein the use of both data sets and the comparison of the
results is recommended. The small values of the instabilities confirm that our long term research program, aimed at providing
proper elements for the purpose of asteroid family identification, has been successful, to the point that reliable proper elements are
now available for all the regions of the asteroid main belt (and also beyond the main belt, taking into account other available
results by ourselves and by others).