Chaotic behaviour in the solar system is very often connected with resonance. Great progresses have been made in the last few years to relate the existence of the Kirkwood gaps with chaos. Uses of mappings have allowed cheap computations over millions of years. Unexpected intermittent increase of orbital eccentricities due to the existence of thin chaotic zone provides a mechanism for planetary close approach. However semi-analytical developments show that at least for the 2/1 resonance the problem remains open. Chaotic rotations of satellites like Hyperion or Miranda and chaotic motion of comets in nearly parabolic orbits are predicted and some physical implications discussed. Both comet Halley and Hyperion appear to be good candidates for real examples of dynamical chaos in the solar system.
The periodic orbits in circular restricted 3-body problem are calculated by different numerical as well as analytical methods. The efficiency of both kinds are compared in this contribution. The improvement of analytical methods can be achieved by an artificial splitting of perturbation term. The analytical approximations are thus sufficiently accurate even for large values of mass ratio μ. The use of these approximations as a zero-order approximation In numerical codes for search for periodic orbits improves their efficiency also.
Přesné informace o počátečních fázích vzniku a vývoje sluneční soustavy nelze získat zpětnou integrací pohybových rovnic, neboť se z dlouhodobého hlediska jedná o ljapunovský nestabilní systém, jehož časový vývoj je na počáteční podmínky extrémně citlivý. Pro modelování primordiálních fází planetárního systému je proto zapotřebí provést několik sad simulací jeho vývoje s různými hodnotami počátečních parametrů a na výsledná data nahlížet statisticky. Pro modelování vývoje sluneční soustavy lze využít symplektických integrátorů, tj. numerických schémat, která aproximují hamiltonovský systém při zachování jeho symplekticity., Jakub Rozehnal., and Obsahuje seznam literatury
Secular variations planetarj' theories constructed at the Bureau des Longitudes use either order by order methods (with respect to the masses) or iterative methods. In all cases, the convergence of the
solutions with respect to the masses is slackened by the upcoming of quasi resonant terms giving-smaller and smaller divisors. This shows how diflicult it is to get very precise solutions over long time spans such as several thousands of years. On another hand, if we locally develop the quasi resonant terms with respect to time, we can get very precise analytical solutions over reduced time spans. We have therefore undertaken an analytical solution for the time span 1950-2050, aiming at a 30 meter precision on the position of the Earth with respect to the barycenter of the solar system. This precision is in fact needed for the comparison to the millisecond pulsar data.
Recent work on resonant motion in the Solar System and in planetary system is presented in a unified way. The physical models used and the underlying mathematical theory is also presented. The relation between resonance and instabiity is studied and the mechanism of generation of instability is discussed and is related to the various parameters of the system.
Resonant motions of systems of mutually gravitating rigid bodies are investigated with the help of the periodic and condltionally periodic solutions for multifreguency nonlinear systems, containing a small parameter. The conditions of existence have been obtained for the periodic solutions of these systems in the principal cases as well as in some degenerate ones. The existence has been proved of the periodic solutions of three kinds In the unrestricted problem of three rigid bodies, possessing quasiconcentric distributions of densities. With the help of the periodic solutions of the first kind of this problem, a posslble explanation has been given to the observed resonance In the Venus´ motlon. Perlodlc solutions have been found In the planetary version of the problem of η + 1 rigid bodies, generalizlng the corresponding periodic solutions of the problem of η + 1 point bodies. It is supposed that the bodies of the system have small dimensions and quasiconcentric distributions of densities.
V astronomické a fyzikální komunitě panuje všeobecné přesvědčení, že dodatečně relativistické stáčení perihelia dráhy Merkuru 43" za století je již dávno a mnohokrát prověřená hodnota, na které není třeba nic měnit. Že je dána rozdílem pozorovaného stáčení perihelia Merkuru a počítaného stáčení pomocí Newtonovy mechaniky. V tomto případě se ale odečítají dvě skoro stejně velká čísla, která jsou navíc zatížena mnoha chybami. Výsledný rozdíl 43" za století je tak nejistý a nemusí odpovídat skutečnosti., The perihelion shift of Mercury's orbit is thought to be one of the fundamental tests of the validity of the general theory of relativity. In the current (astro)physical community, it is generally accepted that the additional relativistic perihelion shift of Mercury is the difference between its observed perihelion shift and the one predicted by Newtonian mechanics, and that this difference equals 43" per century. However, as it results from the subtraction of two quite inexact numbers of almost equal magnitude, it may be subject to cancelation errors. As such, the above accepted value is highly uncertain and may not correspond to reality., Michal Křížek., and Obsahuje seznam literatury