Kozai mechanism
This effect causes the orbit's argument of pericenter to oscillate about a constant value, which in turn leads to a periodic exchange between its eccentricity and inclination.
[2]It was described in 1961 by Mikhail Lidov while analyzing the orbits of artificial and natural satellites of planets.
[3] In 1962, Yoshihide Kozai published this same result in application to the orbits of asteroids perturbed by Jupiter.
[1]: vi It was pointed out in 2019 by Takashi Ito and Katsuhito Ohtsuka that the Swedish astronomer Edvard Hugo von Zeipel had also studied this mechanism in 1909, and his name is sometimes now added.
In general, the behaviour of a three-body system over long periods of time is enormously sensitive to any slight changes in the initial conditions, including even small uncertainties in determining the initial conditions, and rounding-errors in computer floating point arithmetic.
The practical consequence is that, the three-body problem cannot be solved analytically for an indefinite amount of time, except in special cases.
, defined as the ratio of the semi-major axes of the inner and the outer binary and hence small in a hierarchical system.
[9] Since the perturbative series converges rapidly, the qualitative behaviour of a hierarchical three-body system is determined by the initial terms in the expansion, referred to as the quadrupole (
[11] The Lidov–Kozai mechanism is a secular effect, that is, it occurs on timescales much longer compared to the orbital periods of the inner and the outer binary.
In order to simplify the problem and make it more tractable computationally, the hierarchical three-body Hamiltonian can be secularised, that is, averaged over the rapidly varying mean anomalies of the two orbits.
[10]: 4 The simplest treatment of the von Zeipel-Lidov–Kozai mechanism assumes that one of the inner binary's components, the secondary, is a test particle – an idealized point-like object with negligible mass compared to the other two bodies, the primary and the distant perturber.
Since increasing eccentricity while keeping the semimajor axis constant reduces the distance between the objects at periapsis, this mechanism can cause comets (perturbed by Jupiter) to become sungrazing.
The von Zeipel-Lidov–Kozai mechanism causes the argument of pericenter (ω) to librate about either 90° or 270°, which is to say that its periapse occurs when the body is farthest from the equatorial plane.
This effect is part of the reason that Pluto is dynamically protected from close encounters with Neptune.
[14] A number of moons have been found to be in the Lidov–Kozai resonance with their planet, including Jupiter's Carpo and Euporie,[15] Saturn's Kiviuq and Ijiraq,[1]: 100 Uranus's Margaret,[16] and Neptune's Sao and Neso.
[17] Some sources identify the Soviet space probe Luna 3 as the first example of an artificial satellite undergoing Lidov–Kozai oscillations.
Launched in 1959 into a highly inclined, eccentric, geocentric orbit, it was the first mission to photograph the far side of the Moon.
[1]: 9–10 However, according to Gkolias et al.. (2016) a different mechanism must have driven the decay of the probe's orbit since the Lidov–Kozai oscillations would have been thwarted by effects of the Earth's oblateness.
[23] The mechanism is thought to affect the growth of central black holes in dense star clusters.
[24] The effect was first described in 1909 by the Swedish astronomer Hugo von Zeipel in his work on the motion of periodic comets in Astronomische Nachrichten.
[25][5] In 1961, the Soviet space scientist Mikhail Lidov discovered the effect while analyzing the orbits of artificial and natural satellites of planets.
[3][26]: 88 Lidov first presented his work on artificial satellite orbits at the Conference on General and Applied Problems of Theoretical Astronomy held in Moscow on 20–25 November 1961.
