Post 3
The Kozai-Lidov effect was first studied by Russian astronomer Mikhail Lidov, not in asteroids, but in artificial satellites orbiting the Earth. He found that for satellites in specific orbits, the Moon’s gravity would tug at them in such a way as to stretch and squish their orbits in a cycle that would repeat itself every hundred thousand years or so (Lidov, 1962). Later that same year, Japanese astronomer Yoshihide Kozai found that the same effect could occur in asteroids affected by the gravity of Jupiter (Kozai, 1962).
The Kozai-Lidov effect has interesting implications for the stability of asteroid orbits. Most secular resonances involve a one-way drifting of the asteroid’s orbit; once an asteroid enters a secular resonance, it will drift to other orbits and never come back. This aperiodic resonance is called circulation. However, the Kozai-Lidov effect is a cyclical resonance, meaning that the orbit drifts in such a way that the asteroid eventually returns to its initial orbit. This kind of periodic resonance is generally called libration. The Kozai-Lidov effect is a stable libration; any asteroid caught in the Kozai-Lidov resonance is likely to remain in the resonance for a long period of time. The one exception to this rule is if the drifting of the orbit brings the asteroid into the vicinity of a planet, in which case the gravity of that planet will eject the asteroid from its orbit and out of the resonance. However, because the Kozai-Lidov effect causes libration of the orbit instead of circulation, there is only a small range of orbits that the asteroid will occupy during one libration cycle, which significantly reduces the chance that the asteroid will encounter a planet. The seminal paper on near-Earth asteroids by Milani and coauthors calls the Kozai-Lidov effect a protection mechanism, since it protects the asteroid from being thrown out of its orbit entirely (Milani et al., 1989). Therefore, when studying the asteroid belt for asteroids that are in danger of being thrown into the inner solar system, knowing which asteroids are trapped in the Kozai-Lidov resonance tells us which asteroids are safe from ejection and therefore pose no threat to us.There is a gap in the literature pertaining to which asteroids in the main asteroid belt are in a Kozai-Lidov resonance, and we have the tools needed to answer that question. My goal in this paper is to comprehensively map the Kozai-Lidov effect in the asteroid belt using the more accurate computer modeling approach, and find which groups of asteroids are subject to the resonance.
Works Cited
Kozai, Y. (1962). Secular perturbations of asteroids with high inclination and eccentricity. The Astronomical Journal, 67, 591-598.
Milani, A., Carpino, M., Hahn, G., & Nobili, A. M. (1989). Dynamics of planet-crossing asteroids: Classes of orbital behavior: Project SPACEGUARD. Icarus, 78(2), 212-269.