Astronomy and Astrophysics – Astrophysics
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26a...293..605k&link_type=abstract
Astronomy and Astrophysics 293, 605-612 (1995)
Astronomy and Astrophysics
Astrophysics
7
Celestial Mechanics, Minor Planets, Asteroids
Scientific paper
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).
Froeschlé Ch.
Knezevic Zoran
Lemaître Aristide
Milani Andrea
Morbidelli Alessandro
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