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<p>Asteroid proper elements can be computed by means of several methods, among which a purely numerical, synthetic method (Knežević, Z., Milani, A.: Synthetic proper elements for outer main belt asteroids. Celest. Mech. Dyn. Astron. <b>78</b>, 17–46 (2000), Knežević, Z., Milani, A.: Proper element catalogs and asteroid families. Astron. Astrophys. <b>403</b>, 1165–1173 (2003) ) is considered to be the most accurate one, widely applicable to the asteroids with very different orbits and in various dynamical circumstances. The proper element catalogs nowadays typically contain data sets for more than a million asteroids, and are available from different sources. The computation of proper elements fails in some cases, which were hitherto neither reported nor thoroughly investigated. The purpose of this paper is to draw attention to these comparatively seldom failures, with a goal to recognize their forms and to point out the dynamical or computational causes of the failure (like resonances or close approaches to perturbing planets). We analyze these cases, assess their significance in the overall proper elements statistics, and show some typical examples of the failed computations, discussing the dynamical mechanisms giving rise to failures. The analysis confirmed that most of the failures occur in or near strong mean motion resonances, which pump up the eccentricities until asteroid undergoes close approaches to the major planets, eventually ending up as a hyperbolic escapee, or in a seriously disturbed, chaotic orbit. Next, we confront the current practices in computation of synthetic proper elements, comparing the resulting elements and frequencies, as well as their errors, computed by using a shorter or longer orbital integration, and by using an optimized choice of dynamical model in different parts of the asteroid main belt, or a more complete model uniformly applied throughout the belt. It has been shown that the more complex and computer time demanding approach does not bring any significant improvement and that, from the point of view of classification of asteroids into families, proper elements computed either way can be considered practically equal.</p>

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Failures and optimization in computation of asteroid synthetic proper elements

  • 期刊论文

  • 发表日期：

    2025年12月3日

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  • Zoran Knežević

摘要

Asteroid proper elements can be computed by means of several methods, among which a purely numerical, synthetic method (Knežević, Z., Milani, A.: Synthetic proper elements for outer main belt asteroids. Celest. Mech. Dyn. Astron. 78, 17–46 (2000), Knežević, Z., Milani, A.: Proper element catalogs and asteroid families. Astron. Astrophys. 403, 1165–1173 (2003) ) is considered to be the most accurate one, widely applicable to the asteroids with very different orbits and in various dynamical circumstances. The proper element catalogs nowadays typically contain data sets for more than a million asteroids, and are available from different sources. The computation of proper elements fails in some cases, which were hitherto neither reported nor thoroughly investigated. The purpose of this paper is to draw attention to these comparatively seldom failures, with a goal to recognize their forms and to point out the dynamical or computational causes of the failure (like resonances or close approaches to perturbing planets). We analyze these cases, assess their significance in the overall proper elements statistics, and show some typical examples of the failed computations, discussing the dynamical mechanisms giving rise to failures. The analysis confirmed that most of the failures occur in or near strong mean motion resonances, which pump up the eccentricities until asteroid undergoes close approaches to the major planets, eventually ending up as a hyperbolic escapee, or in a seriously disturbed, chaotic orbit. Next, we confront the current practices in computation of synthetic proper elements, comparing the resulting elements and frequencies, as well as their errors, computed by using a shorter or longer orbital integration, and by using an optimized choice of dynamical model in different parts of the asteroid main belt, or a more complete model uniformly applied throughout the belt. It has been shown that the more complex and computer time demanding approach does not bring any significant improvement and that, from the point of view of classification of asteroids into families, proper elements computed either way can be considered practically equal.