Gyroscope deviation from geodesic motion: quasiresonant oscillations on a circular orbit

TL;DR

This paper investigates how relativistic spin-orbit interactions cause measurable quasiresonant oscillations of a gyroscope's mass center in orbit, influenced by Earth's oblateness and precession effects.

Contribution

It introduces a detailed analysis of gyroscope oscillations caused by relativistic effects, including the impact of Earth's oblateness on amplitude and frequency.

Findings

Oscillation amplitude reaches detectable levels within practical times.

Oblateness decreases amplitude and increases modulation frequency.

Quadrupole precession period allows for measurable oscillation amplitudes.

Abstract

General relativistic spin-orbit interaction leads to the quasiresonant oscillation of the gyroscope mass center along the orbital normal. The beating amplitude does not include the speed of light and equals the ratio of the intrinsic momentum of the gyroscope to its orbital momentum. The modulation frequency equals the angular velocity of the geodetic precession that prevents the oscillation from resonance. The oscillation represents the precession of the gyroscope orbital momentum. Within an acceptable time the oscillation amplitude reaches the values that are amenable to being analyzed experimentally. Taking into account the source oblateness decreases the beating amplitude and increases the modulation frequency by the factor that is equal to the ratio of the quadrupole precession velocity to the geodetic precession velocity. The period of the quadrupole precession turns out to be a quite sufficient time to form a measurable amplitude of the oscillation.