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Tidal effect on the gyroscopic precession around a compact star

General relativistic effects in the spacetime around the massive astrophysical objects can be captured using a spinning test gyro orbiting around the object in a circular geodesic. This article discusses how the tidal disruption due to a companion object affects the precession frequency of a spinning gyro orbiting around a compact astrophysical object. The precession frequency is studied in a region of space around the central object using a perturbative approach. In this study, the central object is either a neutron star or a white dwarf. The gyro is any planetary or asteroid-like object orbiting the neutron star or a white dwarf. Moreover, the companion object that causes the tidal field can be a neutron star, white dwarf, a black hole, or a main-sequence star. The tidal effect significantly affects the spacetime around the host star, which affects the gyro precession frequency. The gyro's precession frequency increases with the mass of the companion object and decreases as the separation between the host star and the companion star increases. The tidal effect also varies with the stiffness of the equation of state of matter describing the neutron star. We also find that the tidal field affects the spacetime around a white dwarf more than that of the neutron star.