Rotational Dynamics of the Inner Satellites of Jupiter

— The article considers the attitude stability of synchronous rotation and the most significant relativistic effects in the rotational dynamics of the inner satellites of Jupiter: Metis (J16), Adrastea (J15), Amalthea (J5), and Thebe (J14). It is established that the plane synchronous rotation of all inner satellites of Jupiter for the most probable values of the parameters of their shapes is stable with respect to tilting the axis of rotation. For the first time, the most significant secular, periodic, and mixed terms of the geodetic rotation of the inner satellites of Jupiter in the Euler angles relative to their own coordinate systems and in the angles of their rotation with respect to the fixed equator of the Earth and the vernal equinox (for the J2000.0 epoch) are determined. It is shown that there are objects in the Solar System with significant geodetic rotation caused primarily by their proximity to the perturbing central body rather than its mass. In particular, the value of the geodetic precession of the inner satellites of Jupiter (for which Jupiter is a less massive perturbing central body than the Sun) is 10 5 times greater than that of Jupiter rotating around its more massive central body (the Sun) and comparable with their precession in Newton approximation.