By Ivan I. Shevchenko
This ebook offers with an impression in celestial mechanics that has turn into fairly very important in exoplanet examine. The Lidov-Kozai impression finds itself in coherent periodic diversifications (which could be very huge) of the inclination and eccentricity of an orbiting physique within the presence of an vulnerable perturber. The impact is understood to be very important within the movement of many asteroids and planetary satellites. what's extra, now it draws a growing number of curiosity within the astronomical and astrophysical neighborhood because of its relevance for lots of exoplanetary structures. fresh years witnessed significant developments in its concept. it'd be no exaggeration to assert that these days the Lidov-Kozai impression turns into some of the most studied astrophysical results. This publication covers the multitude of the Lidov-Kozai effect’s smooth purposes and its thought advancements. it will likely be helpful for researchers and scholars operating in astrophysics, celestial mechanics, stellar dynamics, theoretical mechanics, house missions layout, looking on the pursuits of the reader. The e-book is self-contained. It offers the whole unique insurance of the effect’s idea and applications.
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Additional resources for The Lidov-Kozai Effect - Applications in Exoplanet Research and Dynamical Astronomy
What is more, the crucial advantage of the Hori–Deprit method consists in its practical recursiveness: it is based on recurrent explicit formulas, which reduce the normalization in every successive order to a standard mathematical procedure. 42) where n is the number of degrees of freedom. 0//. 47) is called the Lie series of a function f along the flow S. 47) can be interpreted as an operator applied to f . As such, it is henceforth designated LtS f . Recall that a transformation of variables is called canonical, if it preserves the Hamiltonian form of equations.
As soon as, in any real problem, a=apert is not zero, icrit is less than the classical value. The critical inclination diminishes with increasing a=apert . , if a=apert D 0:5 then icrit 32ı , as follows from figure 1 in Kozai (1962). 1 e2 /1=2 cos i is close to unity, the particle’s eccentricity and inclination suffer only small variations. Large variations become possible only if c1 < 3=5, because the LK-resonance is then possible. If the system is in LK-resonance, the secular e and i vary periodically; the maximum eccentricity is achieved at i D 0, and the maximum inclination at e D 0.
The osculating elements were used in both integrations, but the results were averaged to provide a better comparison with the analytical solution. Nevertheless, in both cases, the averaging-out of the short-periodic terms induced differences between the osculating and mean elements, thus causing inevitable differences between the analytical and numerical solutions. This factor dominated the (small) inaccuracy of the analytical solution in case of Laomedeia. In case of (3040) Kozai, another circumstance produced a greater inaccuracy.