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Comparison of Newtonian and Special-Relativistic Trajectories with the General-Relativistic Trajectory for a Low-Speed Weak-Gravity System

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  • Shiuan-Ni Liang
  • Boon Leong Lan

Abstract

We show, contrary to expectation, that the trajectory predicted by general-relativistic mechanics for a low-speed weak-gravity system is not always well-approximated by the trajectories predicted by special-relativistic and Newtonian mechanics for the same parameters and initial conditions. If the system is dissipative, the breakdown of agreement occurs for chaotic trajectories only. If the system is non-dissipative, the breakdown of agreement occurs for chaotic trajectories and non-chaotic trajectories. The agreement breaks down slowly for non-chaotic trajectories but rapidly for chaotic trajectories. When the predictions are different, general-relativistic mechanics must therefore be used, instead of special-relativistic mechanics (Newtonian mechanics), to correctly study the dynamics of a weak-gravity system (a low-speed weak-gravity system).

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  • Shiuan-Ni Liang & Boon Leong Lan, 2012. "Comparison of Newtonian and Special-Relativistic Trajectories with the General-Relativistic Trajectory for a Low-Speed Weak-Gravity System," PLOS ONE, Public Library of Science, vol. 7(4), pages 1-11, April.
    • Handle: RePEc:plo:pone00:0034720
    DOI: 10.1371/journal.pone.0034720
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    References listed on IDEAS

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    1. Lan, Boon Leong, 2009. "Implications of the disagreement between newtonian and relativistic low-speed trajectories," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 534-537.
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