  We have studied long period, 206 and 412 day, variations in tidal sea level
corresponding to various moon phases collected from five observatories in the
Northern and Southern hemispheres. Variations in sea level in the Bay of Fundy,
on the eastern Canadian seaboard, with periods of variation 206 days, and 412
days, have been discovered and carefully studied by C. Desplanque and D. J.
Mossman (2001, 2004). The current manuscript focuses on analyzing a larger
volume of observational sea level tide data as well as on rigorous mathematical
analysis of tidal force variations in the Sun-Earth-Moon system. We have
developed a twofold model, both conceptual and mathematical, of astronomical
cycles in the Sun-Earth-Moon system to explain the observed periodicity. Based
on an analytical solution of the tidal force variation in the Sun-Earth-Moon
system, it is shown that the tidal force can be decomposed into two components:
the Keplerian component and the Perturbed component. The Perturbed component of
the tidal force variation was calculated, and it was shown that the observed
periodicity, 206 and 412 days, of atmospheric and hydrosphere tides results
from variations of the Perturbed component of tidal force. The amplitude of the
Perturbed component of tidal force is . It is the same order of magnitude as
the amplitude of the Keplerian component of tidal force: . It follows that the
Perturbed component of the variation of a tidal force must always be taken into
consideration along with the Keplerian component in geodynamical constructions
involving tides.
