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Gyroscopic precession in non-circular orbits: a phase-locked tetrad approach

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Abstract

We deduce the explicit form of a phase-locked (PL) tetrad, adapted to a small spinning particle (a test gyroscope) following an arbitrary geodesic orbit in the Schwarzschild geometry of a gravitational source. We subsequently obtain the analytic expression of the gyroscopic precessional velocity Ω in a non-circular orbit, by means of the Fermi rotation coefficients related to the tetrad’s transport law. As an application, we compute the orbital shift in the spin vector, considering a spinning test particle (the gyroscope) in a slightly non-circular orbital motion in the weak gravitational field limit. We compare our results with those of other previous works.

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Authors and Affiliations

  1. Dipartimento di Fisica Università di Padova, I.N.F.N. Università di Padova, 35131, Padova, Italy

    Francesco Sorge & Silvio Zilio

Authors
  1. Francesco Sorge
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  2. Silvio Zilio
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Correspondence to Francesco Sorge.

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Sorge, F., Zilio, S. Gyroscopic precession in non-circular orbits: a phase-locked tetrad approach. Gen Relativ Gravit 39, 957–964 (2007). https://doi.org/10.1007/s10714-007-0432-4

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  • DOI: https://doi.org/10.1007/s10714-007-0432-4

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