The «resonance-spectra» of the revolution frequencies of massive satellites are computed in order to determine the rotation periods of gravitating masses of the giant planets. Based upon the tidal theory, it is supposed that the best common multiple of the satellite sidereal frequencies should be close to the rotation frequency of the central planet. A new «dynamical» period of Uranus, 16.14±0.20 h (95 % C.L.), coincides well, within the error limits, with the period 16.16±0.33 h determined earlier by spectroscopic technique. The most probable Neptune's period, 13.43±0.16 h (99 %), agrees with its dynamical oblateness. It is shown that the frequencies of all six fast-rotating planets and major asteroids occur to be in near-resonance with the frequency V₀ = 103±2 μHz. The nature of the mysterious V₀-resonance in the solar system is unknown.