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For this reason (among others), the Solar System is chaotic in the technical sense defined by mathematical chaos theory, [1] and that chaotic behavior degrades even the most precise long-term numerical or analytic models for the orbital motion in the Solar System, so they cannot be valid beyond more than a few tens of millions of years into the ...
The amount of time for which the behavior of a chaotic system can be effectively predicted depends on three things: how much uncertainty can be tolerated in the forecast, how accurately its current state can be measured, and a time scale depending on the dynamics of the system, called the Lyapunov time.
A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field. These systems can be studied in both Hamiltonian mechanics and dynamical systems theory.
Like gravity attracts planetary bodies or an ocean current directs sea creatures, researchers found that there are invisible “attractors” that chaotic systems are drawn to.These attractors ...
A prototypical example of a planetary problem is the Sun–Jupiter–Saturn system, where the mass of the Sun is about 1000 times larger than the masses of Jupiter or Saturn. [18] An approximate solution to the problem is to decompose it into n − 1 pairs of star–planet Kepler problems , treating interactions among the planets as perturbations.
Atomic systems, e.g. atoms, ions, and molecules, can be treated in terms of the quantum n-body problem. Among classical physical systems, the n-body problem usually refers to a galaxy or to a cluster of galaxies; planetary systems, such as stars, planets, and their satellites, can also be treated as n-body systems.
The term "dynamics" came in a little later with Gottfried Leibniz, and over a century after Newton, Pierre-Simon Laplace introduced the term celestial mechanics. Prior to Kepler , there was little connection between exact, quantitative prediction of planetary positions, using geometrical or numerical techniques, and contemporary discussions of ...
Systems science portal; Dynamical systems deals with the study of the solutions to the equations of motion of systems that are primarily mechanical in nature; although this includes both planetary orbits as well as the behaviour of electronic circuits and the solutions to partial differential equations that arise in biology.