Abstract
In this paper, the Lidov–Kozai mechanism was studied in the region of the Hilda group and Jupiter Trojans. Asteroids of these populations move in 3:2 and 1:1 orbital resonances with Jupiter. The study was carried out using numerical integration of real asteroids’ equations of motion. A simplified dynamical model was adopted. Perturbations from only Jupiter moving in a fixed elliptical orbit were taken into account. Classical secular perturbations were excluded from osculating elements at every print step, and derived orbital inclinations and eccentricities were plotted versus a perihelion argument \(\omega \). As a result, it was found that usual positions of a maximum of the eccentricity and, accordingly, a minimum of the inclination (\(\omega = 90^{\circ }\), \(270^{\circ }\)) are shifted in these resonant regions. For Hildas, the maximum of the eccentricity is achieved with perihelion argument values \(\omega =0^{\circ }\), \(180^{\circ }\). For L4 Trojans, it is achieved with \(\omega = 30^{\circ }\), \(210^{\circ }\), and for L5 Trojans—with \(\omega = 150^{\circ }\), \(330^{\circ }\).
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References
Brouwer, D., van Woerkom, A.J.J.: The secular variations of the orbital elements of the principal planets. Astron. Pap. Am. Ephem. Naut. Almanac 13, 81 (1950)
Brož, M., Vokrouhlický, D.: Asteroid families in the first-order resonances with Jupiter. MNRAS 390, 715 (2008)
Everhart, E.: An efficient integrator that uses Gauss–Radau spacings. IAU Colloq. 83, 185–202 (1985)
Hirayama, K.: Groups of asteroids probably of common origin. A J 31, 185–188 (1918)
Knežević, Z., Lemaître, A., Milani, A.: The determination of asteroid proper elements. In: Asteroids III, pp. 603–612. University of Arizona Press (2002)
Kozai, Y.: Secular perturbations of asteroids with high inclination and eccentricity. A J 67, 591 (1962)
Kozai, Y.: Secular perturbations of resonant asteroids. Cel. Mech. Dyn. Astron. 36(1), 47 (1985)
Lidov M.L.: Artificial satellites of the earth, 5 (in Russian) (1961)
Lidov, M.L.: The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies. Planet. Space Sci. 9, 719 (1962)
Schubart, J.: Numerical determination of proper inclinations of Hilda-type asteroids. Cel. Mech. Dyn. Astron. 28, 189–194 (1982)
Vinogradova, T.A.: Identification of asteroid families in Trojans and Hildas. MNRAS 454, 2436 (2015)
Vinogradova, T.A.: Amplitude of the Lidov–Kozai i- and e-oscillations in asteroid families. MNRAS 468, 4719 (2017)
Vinogradova, T.A.: Empirical method of proper elements calculation and identification of asteroid families. MNRAS 484, 3755 (2019)
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Vinogradova, T.A. Lidov–Kozai mechanism in Hildas and Jupiter Trojans. Celest Mech Dyn Astron 136, 17 (2024). https://doi.org/10.1007/s10569-024-10190-7
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DOI: https://doi.org/10.1007/s10569-024-10190-7