Chaotic motions in Newton's gravity field revealed from energy flow investigations

Abstract

Mathematicians have searched the evidence for motion stabilities in Solar System. A predication indicated “Earth’s orbit can become chaotic”. Until now, It have not been found any theoretical / numerical results on chaotic motion orbits in Newton’s gravity field. Newton’s gravity field is one of central-force fields like electromagnetic / quantum ones, so its motion characteristics revealed can be applied to research of quantum systems. This paper intends to tackle this historic problem based on the energy flow numerical investigations. we have shown some chaotic motions in Newton’s gravity field. Depending on initial conditions, mechanical-energy H and angular-momentum, particle motion-paths are hyperbolas (H > 0) or parabolas (H = 0) as infinite motions. Negative energies (H < 0) show ellipse orbits of periodical motions with constant time-averaged potential / kinetic energies and zero-time averaged energy flows. Chaotic motion, appearing when H < 0 due to small disturbances / initial conditions, behaves periodical one of infinite period: a repeating motion between the two zero-radial-speed circles, and its starting and ending points never coinciding, and the characteristics of time averaged energy-flow variables are same as the periodical ones when the average time tends infinite. Therefore, the revealed chaotic motion is a stable infinite long period periodical motion restricted in a finite space. This result can address the predication of chaotic Earth’ orbit. New findings will benefit to tackle particle motions in central-force fields of modern physics. The energy-flow theory provides a generalised means to reveal hidden nonlinear phenomena of nature.

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ORCID for Jing Tang Xing: orcid.org/0000-0003-3992-5265

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