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<p>Mathematicians have searched for evidence of motion stability in the Solar System. A predication indicated “Earth’s orbit can become chaotic”. Until now, no theoretical/numerical results have been found for chaotic motion orbits in Newton’s gravity field. Newton’s gravity field is one of the central-force fields, like electromagnetic/quantum ones, so its motion characteristics revealed can be applied to the 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 <i>H</i>, and angular-momentum, particle motion-paths are hyperbolas (<i>H</i> &gt; 0) or parabolas (<i>H</i> = 0) as infinite motions. Negative energies (<i>H</i> &lt; 0) show ellipse orbits of periodic motions with constant time-averaged potential/kinetic energies and zero-time-averaged energy flows. Chaotic motion, appearing when <i>H</i> &lt; 0 due to small disturbances/initial conditions, behaves periodic one of infinite period: a repeating motion between the two zero-radial-speed circles, and its starting and ending points never coincide, and the characteristics of time-averaged energy-flow variables are the same as the periodical ones when the average time tends to infinity. Therefore, the revealed chaotic motion is a stable infinite long period periodical motion restricted to a finite space. This result can address the prediction of the chaotic Earth’s orbit. New findings will benefit in tackling particle motions in central-force fields of modern physics. The energy-flow theory provides a generalised means to reveal hidden nonlinear phenomena of nature.</p>

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

  • 期刊论文

  • 发表日期：

    2026年5月4日

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  • Jing Tang Xing

摘要

Mathematicians have searched for evidence of motion stability in the Solar System. A predication indicated “Earth’s orbit can become chaotic”. Until now, no theoretical/numerical results have been found for chaotic motion orbits in Newton’s gravity field. Newton’s gravity field is one of the central-force fields, like electromagnetic/quantum ones, so its motion characteristics revealed can be applied to the 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 periodic 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 periodic one of infinite period: a repeating motion between the two zero-radial-speed circles, and its starting and ending points never coincide, and the characteristics of time-averaged energy-flow variables are the same as the periodical ones when the average time tends to infinity. Therefore, the revealed chaotic motion is a stable infinite long period periodical motion restricted to a finite space. This result can address the prediction of the chaotic Earth’s orbit. New findings will benefit in tackling particle motions in central-force fields of modern physics. The energy-flow theory provides a generalised means to reveal hidden nonlinear phenomena of nature.