Precessional Motion Emerging from Relativistic Component of External Force
Published on: 25th October, 2024
The external force in the relativistic equation of motion can be separated into two components: Fr and Fp. The first is expressed by the physical force divided by the square of the relativistic Lorentz factor, i.e γ2. This force dominates for non-relativistic velocities and vanishes for velocities approaching the speed of light c. On the other hand, the second term increases from zero with increasing velocity and dominates for velocities close to c. It is then a purely relativistic component. The characteristic feature of this component is its zero power, Fp ⋅ v = 0, but it is responsible for the relativistic precession. The effect was confirmed by numerical solutions of the equation of motion. Relativistic formulas for the precession frequency for point objects moving in selected fields of central forces were also derived analytically. It has been shown that for weak gravitational interactions, the correction for relativistic precession is small, negligibly small for Earth, and relatively small, though measurable, for Mercury. In turn, for the microworld and electrostatic forces (e.g., for the hydrogen atom), relativistic precession can fundamentally affect the movement of the electron.
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