Mathematics  Physics

Comparison of Newtonian and SpecialRelativistic Trajectories with the GeneralRelativistic Trajectory for a LowSpeed WeakGravity System
Published:
Thursday, April 19, 2012
Author:
ShiuanNi Liang et al.
by ShiuanNi Liang, Boon Leong Lan
We show, contrary to expectation, that the trajectory predicted by generalrelativistic mechanics for a lowspeed weakgravity system is not always wellapproximated by the trajectories predicted by specialrelativistic 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 nondissipative, the breakdown of agreement occurs for chaotic trajectories and nonchaotic trajectories. The agreement breaks down slowly for nonchaotic trajectories but rapidly for chaotic trajectories. When the predictions are different, generalrelativistic mechanics must therefore be used, instead of specialrelativistic mechanics (Newtonian mechanics), to correctly study the dynamics of a weakgravity system (a lowspeed weakgravity system).
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