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Unusual Lidov–Kozai Perturbation in the Hilda Group

Transactions of IAA RAS, issue 54, 3–10 (2020)

Keywords: celestial mechanics, asteroids, secular perturbations

Abstract

The Lidov–Kozai mechanism was investigated in the region of the Hilda group. The asteroids in this region move in commensurability of the mean motions 3:2 with Jupiter. The study was carried out mainly by means of numerical integration of the equations of real asteroids motion. The simplest dynamic model was used with Jupiter as the only perturbing body moving in a fixed elliptical orbit. After eliminating the classical secular perturbations, it becomes possible to determine the influence of the Lidov–Kozai mechanism on the orbital elements. As a result, it was found that the maximum eccentricity, and, accordingly, the minimum inclination is observed when the argument of perihelion ω = 0º, 180º, whilst usually it takes place at ω = 90º, 270º. On the contrary, there is a minimum eccentricity and a maximum inclination at ω = 90º, 270º. The character of the elements change, which is typical for the Lidov–Kozai perturbation, is preserved for only asteroids with a large amplitude of the semi-major axis libration.

Citation

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T. A. Vinogradova. Unusual Lidov–Kozai Perturbation in the Hilda Group // Transactions of IAA RAS. — 2020. — Issue 54. — P. 3–10.

@article{vinogradova2020,
  abstract = {The Lidov–Kozai mechanism was investigated in the region of the Hilda group. The asteroids in this region move in commensurability of the mean motions 3:2 with Jupiter. The study was carried out mainly by means of numerical integration of the equations of real asteroids motion. The simplest dynamic model was used with Jupiter as the only perturbing body moving in a fixed elliptical orbit. After eliminating the classical secular perturbations, it becomes possible to determine the influence of the Lidov–Kozai mechanism on the orbital elements. As a result, it was found that the maximum eccentricity, and, accordingly, the minimum inclination is observed when the argument of perihelion ω = 0º, 180º, whilst usually it takes place at ω = 90º, 270º. On the contrary, there is a minimum eccentricity and a maximum inclination at ω = 90º, 270º. The character of the elements change, which is typical for the Lidov–Kozai perturbation, is preserved for only asteroids with a large amplitude of the semi-major axis libration.},
  author = {T.~A. Vinogradova},
  doi = {10.32876/ApplAstron.54.3-10},
  issue = {54},
  journal = {Transactions of IAA RAS},
  keyword = {celestial mechanics, asteroids, secular perturbations},
  pages = {3--10},
  title = {Unusual Lidov–Kozai Perturbation in the Hilda Group},
  url = {http://iaaras.ru/en/library/paper/2056/},
  year = {2020}
}

TY  - JOUR
TI  - Unusual Lidov–Kozai Perturbation in the Hilda Group
AU  - Vinogradova, T. A.
PY  - 2020
T2  - Transactions of IAA RAS
IS  - 54
SP  - 3
AB  - The Lidov–Kozai mechanism was investigated in the region of the Hilda
group. The asteroids in this region move in commensurability of the
mean motions 3:2 with Jupiter. The study was carried out mainly by
means of numerical integration of the equations of real asteroids
motion. The simplest dynamic model was used with Jupiter as the only
perturbing body moving in a fixed elliptical orbit. After eliminating
the classical secular perturbations, it becomes possible to determine
the influence of the Lidov–Kozai mechanism on the orbital elements.
As a result, it was found that the maximum eccentricity, and,
accordingly, the minimum inclination is observed when the argument of
perihelion ω = 0º, 180º, whilst usually it takes place at ω = 90º,
270º. On the contrary, there is a minimum eccentricity and a maximum
inclination at ω = 90º, 270º. The character of the elements change,
which is typical for the Lidov–Kozai perturbation, is preserved for
only asteroids with a large amplitude of the semi-major axis
libration.
DO  - 10.32876/ApplAstron.54.3-10
UR  - http://iaaras.ru/en/library/paper/2056/
ER  -