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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
The motion of asteroids at the 5:2 resonance with
Jupiter
T. Yu. Galushina
Tomsk State University, Tomsk, Russia
The present work is devoted to investigation of Near­Earth asteroids (NEAs)
motion at the 5:2 resonance with Jupiter. The motion of these objects has some
peculiarities such as close approaches to the inner major planets and Jupiter, large
eccentricities and so on. These features render the motion of many considered
asteroids unstable.
First, all NEAs at the 5:2 resonance with Jupiter have been revealed. The
initial parameters of orbits were taken from Bowell catalog on January 26, 2002
(ftp://ftp.lowell.edu/pub/elgb/astorb.dat). For each investigated object a set of
100 clones has been constructed in such a way [3]. We begin from the analysis of
observations and improvement of the initial parameters of every orbit by the least­
squares method. In Ph.D. dissertation of Yu. D. Medvedev and paper [4] it was
shown that the conditionality of the problem of orbits improvement by the least­
squares method depends on the choice of initial epoch. Therefore the study of the
condionality of the normal equations matrix for different initial epochs has been
made. The epoch with minimal conditionality has been chosen for construction
of particles ensemble. The initial set of orbits has been generated using a random
number generator on the basis of the normal law and corresponding covariation
matrix.
The ensemble evolution has been followed up for 6000 years. The regions of
possible motion where orbital resonance continues to exist have been determined.
Moreover the possibility of approaches of asteroids and clones to the inner major
planets and Jupiter has been considered.
The differential equations in form suggested in [1] have been used. The as­
teroid motion has been considered in rectangular heliocentric coordinate frame
related to ecliptic and equinox 2000.0. The equations of motion have been inte­
grated numerically by Everhart procedure of the 19th order [2]. Perturbations
from planets and the Moon have been taken into account using the planets posi­
tions given by DE406.
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The asteroids falling into the vicinity of the resonance have been determined
by means of numerical estimation of the resonance band ff = 2n a \Gamma 5n J , where
n a , n J are the mean motions of an asteroid and Jupiter correspondingly. The
objects passing through exact commensurability (ff = 0) have been revealed. The
evolution of these orbits has been investigated at the several thousand years time
interval. The accuracy of integration was estimated by comparing the results
of toward--and--backward integration for each asteroid. Time interval has been
chosen for each asteroid from the point of view of preserving the admissible
accuracy.
Thus, we made a list of asteroids moving in vicinity of resonance 5:2 with
Jupiter on time interval of several thousand years. For each investigated object
an ensemble of 100 clones has been constructed. The results of investigation of
asteroids 6178 1986 DA and 1985 WA are cited as an example.
References
1. Bordovitsyna T. V, Avdyushev V. A., Titarenko V. P. Numerical integration
in the general three--bodies problem. Research in Ballistics and Contiguous
Problems of Dynamics, Tomsk: Tomsk State University Publishers, 1998, 2,
164--168 (in Russian).
2. Everhart E. An efficient integrator that uses Gauss­Radau spacing. In Dy­
namics of comets: their origin and evolution (A. Carusi and G. B. Valsecchi,
Eds.), Dordrecht: Reidel, 1985, 185--202.
3. Bykova L. E. and Galushina T. Yu. Orbital evolution of near--Earth asteroids
close to mean motion resonances. Cel. Mech. & Dyn. Astron. 2002, 82, 265--
284.
4. Bykova L. E., Parfenov E. V. About problem of conditionality of problem of
determination of orbits of near--Earth asteroids. Research in Ballistics and
Contiguous Problems of Dynamics, Tomsk: Tomsk State University Publish­
ers, 1999, 3, 136--137 (in Russian).
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