How does the Lidov&#8211;Kozai mechanism protect Quadrantids meteoroid stream from close encounters with Jupiter?
Authors: Sambarov Georgy E. , Galushina Tatyana Yu. , Syusina Olga M. 
Published: October 2020

The dynamical evolution of simulated meteoroid stream of the Quadrantids ejected from the parent body of the asteroid (196256) 2003 EH1 expects possible scenario for resonant motion. We found a peculiar behavior for this stream. Here, we show that the orbits of some ejected particles are strongly affected by the Lidov&#8211;Kozai mechanism that protects them from close encounters with Jupiter. Lack of close encounters with Jupiter leads to a rather smooth growth in the parameter MEGNO (Mean Exponential Growth factor of Nearby Orbits) and the behavior imply the stable motion of simulation particles of the Quadrantids meteoroid stream. A rather smooth path with nearly constant semi-major axis is obtained due to lack of close encounters with Jupiter. The coupled oscillation of the three orbital parameters, e, i, and &#969;, for stable ejected particles is observed.However, close encounters with Jupiter are not treated by the Kozai formalism and can transfer particles away from the Kozai trajectories for unstable ejected particles over time. Other ejected particles have chaotic motion from simulations of the orbit of meteoroids are not affected by the Lidov &#8211; Kozai mechanism. We suppose that the reasons are the frequent close approaches of the ejected particles with Jupiter and they located near mean motion resonance 2:1J with Jupiter. The motion of these objects has considered to be chaotic in a long-time scale, and the close encounters with Jupiter are supposed to be the cause of the faster chaos. Another reason is that a non-resonant state near the mean motion resonance 2:1J has a strong influence on the motion of the Quadrantid meteor stream. This &#8220;weak chaos&#8221; is largely confined to the true anomaly. Consequently, the shape of the orbit can be computed reliably over much longer time scales than can the body&#8217;s position within the orbit. High value of the parameter MEGNO are due to frequent changes in semimajor axis induced by multiple close encounters with Jupiter near Hill sphere. We finally note that the chaotic behavior of the simulation particles of meteor stream may be caused not only by close encounter with planets but also by unstable mean motion or secular resonances.We conjecture that the reasons of chaos are the overlap of stable secular resonances and unstable mean motions resonances and close and/or multiple close encounters with the major planets. The orbits of some ejected particles are strongly affected by the Lidov&#8211;Kozai mechanism that protects them from close encounters with Jupiter that leads to a rather smooth growth in the parameter MEGNO and the behavior imply the stable motion of simulation particles of the Quadrantids meteoroid stream.The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation (theme No. 0721-2020-0049)&#160;ReferencesAbedin, A., Spurn&#253;, P., Wiegert, P., Pokorn&#253;, P., Borovi cka, J., Brown, P., 2015. On the age and formation mechanism of the core of the Quadrantid meteoroid stream. Icarus 261, 100&#8211;117.Cincotta, P.M., Girdano, C.M., Simo, C., 2003. Phase space structure of multi-dimensional systems by means of the mean exponential growth factor of nearby orbits. Phys. Nonlinear Phenom. 182 (3&#8211;4), 151&#8211;178.Chirikov, B.V., 1979. A universal instability of many-dimensional oscillator systems. Phys. Rep. 52 (5), 263&#8211;379.Galushina, T.Yu, Sambarov, G.E., 2017. The dynamical evolution and the force model for asteroid (196256) 2003 EH1. Planet. Space Sci. 142, 38.Galushina, T.Yu, Sambarov, G.E., 2019. Dynamics of asteroid 3200 Phaethon under overlap of different resonances. Sol. Syst. Res. 53 (3), 215&#8211;223.Gonczi, R., Rickman, H., Froeschle, C., 1992. The connection between Comet P/Machholz and the Quadrantid meteor. Mon. Not. Roy. Astron. Soc. 254, 627.Hughes, D.W., Taylor, I.W., 1977. Observations of overdense Quadrantid radio meteors and the variation of the position of stream maxima with meteor magnitude. Mon. Not. Roy. Astron. Soc. 181, 517.Kozai, Y., 1962. Secular perturbations of asteroids with high inclination and eccentricity. Astron. J. 67, 591&#8211;598.Lidov, M.L., 1962. The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies. Planet. Space Sci. 9, 719.Williams, I.P., Ryabova, G.O., Baturin, A.P., Chernitsov, A.M., 2004a. The parent of the Quadrantid meteoroid stream and asteroid 2003 EH1. Mon. Not. Roy. Astron. Soc. 355 (4), 1171&#8211;1181.