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XVIII conference

Orbits in problem three bodies

Yakovenko G.N.

Yakovenko_G@mtu-net.ru

The Interest to system, subject to power of the worldwide gravity Newton, justified that that surrounding us world — the Sun, the Earth, the Moon, planets of the Solar system, starry concourses — make mechanical motion under the action of these power and available observation. To persisting moment full clarity there is to orbit two gravitating point masses [1]: in system, which moves onward together with the centre of the inertias two masses, points move on ellipse, parabola or hyperbole. In the event of three point masses situation distant from full understanding, but occasionly decision of the concrete problem disagrees the good sense. For instance, in Pifagor–problem [2] three masses at initial moment of time still, but then begin to move under the action of power of the mutual gravity. In total two masses form the double star, which rushes on infinity. The third mass also strives on infinity in opposite side.

In report are discussed some orbital particularities to final stage of the problem three bodies [3]: exchange, seizure, oscilllating motions. On example three bodies are considered also nonklassical aspects motion [4]: strange attractors, chaos.

References.

1. Yakovenko G.N. The Short course theoretical mechanical engineers — M.: BINOM. Laboratory of the knowledges, 2006. — 116 p.

2. Arnolid V.I., Kozlov V.V., Neyshtadt A.I. The mathematical aspects classical and celestial mechanics. — M.: Editorial URSS, 2002. — 416 p.

3. Alexeev V.M. The Lectures on celestial mechanics. — Izhevsk: Izhevsk’s republican printing house, 1999. 160 p.

4. Kolesov A.YU., Rosov N.H. To question about determination of the chaos // Successes of the mathematical sciences, 2009, July-August, t. 64, drink. 4 (388). P. 125–172

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