This paper investigates one of the most interesting effects associated with the rotation of astrophysical objects (the Sagnac effect). The effect was first confirmed in laboratory experiments by Georges Sagnac with a rotating ring interferometer in 1913. Later, the effect was also confirmed within the framework of the Earth in the "Around-the-World" experiment conducted by J. Hafele and R. Kitting, in which they twice circled the Earth with an atomic cesium clock on board and compared the "flying" clock with those remaining static on the Earth. As a result, a non-zero difference in the clock rate was found as a confirmation of the Sagnac effect. Subsequently, more precise satellite experiments have been carried out to measure the Sagnac effect within the Earth. The effect was also considered in general relativity and modified theories of gravity, where many works were carried out to study the influence of such parameters as angular momentum, cosmological constant, Ricci scalar, etc. on the Sagnac effect. An interesting task is to study the influence of a magnetic charge on the effect, since the solution with rotation described by a black hole with mass M and magnetic charge g is the Bardeen nonsingular black hole. The work will calculate the Sagnac effect in the space-time of the rotating Bardeen black hole for both geodesic and non-geodesic circular orbits of the light source / receiver (assuming that the light source and receiver are defined at the same point). Two types of circular orbits describe the opposing influence on the Sagnac effect: the Sagnac delay increases with an increase in the magnetic charge in the case of non-geodesic circular orbits and decreases in the case of geodesic circular orbits. However, the farther is the orbit of the light source / receiver, the less the magnetic charge affects the Sagnac delay. It is also assumed that the gravity of the Earth and the Sun near the surface is well described by the Bardeen metric.
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