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Coastal tide prediction for any location on Earth is an empirical process, but it is based on very precise astronomical cycles of the Moon and the Sun. The primary cyclic changes are depicted in Fig. 1 below. Because I'm a southern hemispheric, rotations are as seen from far above Earth's South Pole, so it's clock-wise.
First, there is Earth's rotation period of 23h56m against the 'fixed' stars. Then the Moon's orbital period of 27.32 days, with the corresponding change in distance from perigee to apogee. Finally, there is Earth's orbital period around the Sun of 365.25 days, with the corresponding cycles of the seasons due to Earth's inclination to the ecliptic. The orbit is also elliptical and this of course also changes Earth's distance from the Sun based on this one year cycle.
Figure 1 
A much less known periodic cycle is the advance of the Moon's perigee with a period of 8.8 years. Shown in Fig. 2 is the change of the orientation of the ellipsoid of the orbit against the distant stars after just 2.2 years. This is an ordinary perigee advance caused by mainly by the Sun's gravity and is not a relativistic effect, which is utterly negligible in the case of the Moon-Earth system.
Figure 2
Probably the least understood, yet pretty important tidal cycle, is the precession of the Moon's orbital plane around Earth. As indicated in Fig. 3 below, the Moon's orbital plane is inclined by 5° to the ecliptic.
Figure 3
Due to the fact that the Moon's orbit is quite elliptical, the Sun's gravity causes this plane to precess like a top relative to the fixed stars. The period is 18.6 years, as shown in 90° steps in Figures 4 to 7 below (the perigee advance of Fig. 2 is ignored here for simplicity).
Figure 4
Figure 5
Figure 6
Figure 7
The 25.8°S has no more relevance than that it was the latitude of the venue where I gave a presentation (to amateur astronomers) using these slides. Some of them were pretty surprised that the Moon sometimes actually passes south of them! It only happens every 18 years or so.
There are even longer cycles, like Earth's spin axis that precesses around a full circle in about 25 thousand years, but they are normally not used in tidal prediction. The result of the primary cycles are that one needs data for at least 18.6 years for every region in order to make good tidal predictions.
In Part 2 of this mini-series I will show some other effects on the tides and then plot a few curves...
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Re: Tidal Prediction Part 1
