Kozai mechanism

The Kozai effect describes in celestial mechanics, a periodic orbit disorder that causes a change in the eccentricity and orbital inclination (inclination ) of the perturbed object.

The effect was in 1962 by Yoshihide Kozai (古 在 由 秀, Yoshihide Kozai ) described, who analyzed the orbits of asteroids. Since then, the Kozai resonance of some bodies in the solar system ( irregular satellites of the planets, trans-Neptunian objects ) is considered as an important factor in the development of the railways. The also Kozai mechanism mentioned effect is also used to the high number of hot Jupiters among the exoplanets, the frequency of triple systems with a close binary system and circulation periods of less than 5 days near the sun as well as the emergence of Blue stragglers to explain.

Kozai resonance

To explain the mechanism we consider a three-body system consisting of a central body (eg the Sun), a these orbiting relatively large body (eg planet ) and a small body (eg asteroid ), which is also the central body orbits, there. The small body i runs relative to the path of the "planets" around the central body in an elliptical orbit with an eccentricity e and inclination, has orbital elements that are disturbed by the large secular orbiting body. In the perturbative approach, however, the following value is then constant in time:

This constant of the motion opens the possibility that there may be an exchange relationship between the inclination and eccentricity of: increasing the inclination, the eccentricity decreases and vice versa. Nearly circular orbits with high inclination can therefore be changed to very eccentric orbits with low inclination. In certain circumstances, it then comes to a periodic, synchronous variation of the two variables. Since an increase in the eccentricity at the same size constant large semi-major axis causes the periapsis of the web is reduced, this mechanism may, for example, cause the orbits of comets over time are changed so that they fall into the sun.

If the inclination and eccentricity of the small body quite small, we obtain as a result of such failure, however, no resonant exchange between eccentricity and inclination, but only a secular progression of the argument of pericentre, ie a " perihelion ". If the initial inclination but large enough yields instead a libration of the pericentre, ie the argument of the pericentre oscillates around a constant value. At the same time there is a resonant exchange between inclination and eccentricity, which vary periodically between minimum and maximum values ​​. The minimum required initial inclination at first almost circular path, called Kozai angle is dependent on the distance of the disturbing " planet " for the small body. If this distance is very large, one finds:

The transition between the " perihelion " Kozai effect and thus takes place at a value for the constant motion of the

Instead. The detrimental great body is closer to the orbit of the small body increases this limit and corresponding reduction in the Kozai angle.

For retrograde orbiting satellites is important to note that the values ​​of the inclination between 90 ° and 180 ° lie, whereby the fact is taken into account that they run around the central body "backwards". The Kozai angle is a maximum value in this case and is accordingly for distant bluff body at 140.8 °.

Consequences

Kozai the resonance leads to limitations in the possible paths in a system, for example:

  • For regular Monde: is the path of a moon strongly inclined to his planet, the eccentricity of the lunar orbit increases as long as the moon is to be destroyed by tidal forces.
  • For irregular moons: only that the increasing eccentricity leads as above to a collision with a regular Moon or to the ejection of the satellite from the Hill sphere.

Sources and Literature

  • Y. Kozai, Secular perturbations of asteroids with high inclination and eccentricity, Astronomical Journal 67, 591 (1962 ) ADS
  • C. Murray and S. Dermott Solar System Dynamics, Cambridge University Press, ISBN 0-521-57597-4
  • Innanen et al. The Kozai Mechanism and the stability of planetary orbits in binary star systems, The Astronomical Journal, 113 (1997).
  • BENJAMIN J. SHAPPEE AND TODD A. THOMPSON: THE MASS -LOSS INDUCED ECCENTRIC Kozai MECHANISM: A NEW CHANNEL FOR THE PRODUCTION OF CLOSE COMPACT STELLAR OBJECT- BINARIES .. In: Astrophysics. Solar and Stellar Astrophysics. 2012, arXiv: 1204.1053v1.
  • Celestial mechanics
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