Asteroid Mean Elements: Higher Order and Iterative Theories |
| |
| Authors: | Andrea Milani Zoran Kne?evi? |
| |
| Institution: | (1) Space Mechanics Group, Department of Mathematics, Pisa University, Italy;(2) Astronomska opservatorija, Beograd, Yugoslavia |
| |
| Abstract: | Mean orbital elements are obtained from osculating ones by removing the short periodic perturbations. Large catalogues of
asteroid mean elements need to be computed, as a first step in the computation of proper elements, used to study asteroid
families. The algorithms for this purpose available so far are only accurate to first order in the masses of the perturbing
planet; the mean elements have satisfactory accuracy for most of the asteroid belt, but degraded accuracy in the neighbourhoods
of the main mean motion resonances, especially the 2:1. We investigate a number of algorithms capable of improving this approximation;
they belong to the two classes of Breiter-type methods and iterative methods. The former are obtained by applying some higher
order numerical integration scheme, such as Runge–Kutta, to the differential equation whose solution is a transformation removing
the fast angular variables from the equations; they can be used to compute a full second order theory, however, only if the
full second order determining function is explicitly computed, and this is computationally too cumbersome for a complicated
problem such as the N-body. The latter are fixed point iterative schemes, with the first order theory as an iteration step,
used to compute the inverse map from mean to osculating elements; formally the method is first order, but because they implement
a fixed frequency perturbation theory, they are more accurate than conventional single iteration methods; a similar method
is already in use in our computation of proper from mean elements. Many of these methods are tested on a sample of asteroid
orbits taken from the Themis family, up to the edge of the 2:1 resonance, and the dispersion of the values of the computed
mean semimajor axis over 100 000 years is used as quality control. The results of these tests indicate that the iterative
methods are superior, in this specific application, to the Breiter methods, in accuracy and reliability. This is understood
as the result of the cancellations occurring between second order perturbation terms: the incomplete second order theory,
resulting from the use of a Breiter method with the first order determining function only, can be less accurate than complete,
fixed frequency theories of the first order. We have therefore computed new catalogues of asteroid mean and proper elements,
incorporating an iterative algorithm in both steps (osculating to mean and mean to proper elements). This new data set, significantly
more reliable even in the previously degraded regions of Themis and Cybele, is in the public domain.
This revised version was published online in July 2006 with corrections to the Cover Date. |
| |
| Keywords: | asteroids mean elements Lie series short periodic perturbations mean motion resonances analytical theories iterative methods Runge– Kutta Themis family |
| 本文献已被 SpringerLink 等数据库收录！ |
|
