caa a22 4500 467986975 CHVBK 20180323112534.0 cr unu---uuuuu 170328e19901201xx s 000 0 eng 10.1007/BF00049444 doi (NATIONALLICENCE)springer-10.1007/BF00049444 Secular perturbation theory and computation of asteroid proper elements [Elektronische Daten] [Andrea Milani, Zoran Knežević] A new theory for the calculation of proper elements, taking into account terms of degree four in the eccentricities and inclinations, and also terms of order two in the mass of Jupiter, has been derived and programmed in a self contained code. It has many advantages with respect to the previous ones. Being fully analytical, it defines an explicit algorithm applicable to any chosen set of orbits. Unlike first order theories, it takes into account the effect of shallow resonances upon the secular frequencies; this effect is quite substantial, e.g. for Themis. Short periodic effects are corrected for by a rigorous procedure. Unlike linear theories, it accounts for the effects of higher degree terms and can thus be applied to asteroids with low to moderate eccentricity and inclination; secular resonances resulting from the combination of up to four secular frequencies can be accounted for. The new theory is self checking : the proper elements being computed with an iterative algorithm, the behaviour of the iteration can be used to define a quality code. The amount of computation required for a single set of osculating elements, although not negligible, is such that the method can be systematically applied on long lists of osculating orbital elements, taken either from catalogues of observed objects or from the output of orbit computations. As a result, this theory has been used to derive proper elements for 4100 numbered asteroids, and to test the accuracy by means of numerical integrations. These results are discussed both from a quantitative point of view, to derive an a posteriori accuracy of the proper elements sets, and from a qualitative one, by comparison with the higher degree secular resonance theory. Kluwer Academic Publishers, 1990 Asteroids nationallicence Secular perturbations nationallicence Lie series nationallicence Proper elements nationallicence Secular resonances nationallicence Milani Andrea Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, I-56127, Pisa, Italy aut Knežević Zoran Astronomska opservatorija, Volgina 7, 11050, Beograd, Yugoslavia aut Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 49/4(1990-12-01), 347-411 0923-2958 49:4<347 1990 49 10569 https://doi.org/10.1007/BF00049444 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00049444 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Milani Andrea Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, I-56127, Pisa, Italy aut NATIONALLICENCE 700 1- Knežević Zoran Astronomska opservatorija, Volgina 7, 11050, Beograd, Yugoslavia aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 49/4(1990-12-01), 347-411 0923-2958 49:4<347 1990 49 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer