orbits of Earth and Moon around the Sun. The response of the sea to this force cannot be 

 determined solely from first principles. Good predictions, however, can generally be 

 obtained from equations of the form 



h(t) = ho + 2 A„ cos (a„t - 0„) 



(1) 



where 



h(t) 



On 



X„ 



On 



ho 



= tidal height at time, t 



= frequencies determined from theory 



= ampUtudes 



= phases determined partly from theory and partly from measurements 



= height of the local MSL datum above the datum of reference 



The rotation of tlie Earth about the Sun and the Moon about the Earth gives rise to 

 primary variations in the tide-generating force with periods near 1 day and near 12 hours. 

 The amplitude of these oscillations is modulated by the variation in direction and distance 

 of the selected point on the Earth's surface from the center of the Moon and the center of 

 the Sun. The most prominent periods in the modulating terms are near 1 lunar month and 1 

 solar year. Interaction between these oscillations leads to other prominent periods near 2 

 weeks and near 19 years. Several of the more prominent astronomical periods, important for 

 tide prediction, are Usted in Table 1. 



Table 1. Astronomical periods affecting the tides (Schureman, 1941; 

 Doodson and Warburg, 1941). 



Phenomenon 



Astronomical 



period 



(d) 



(yr) 



Sidereal day (with respect to fixed stars) 

 Lunar day (with respect to the Moon) 



0.997270 

 1.035050 





Nodical month (north-south cycle) 

 Tropical month (vernal equinox) 



27.212220 

 27.321582 





Anomalistic month (perigee to perigee, distance) 

 Synodical month (phases of the Moon) 



27.554550 

 29.530588 





Eclipse year (with respect to the lunar orbit) 

 Tropical year (vernal equinox) 

 Anomalistic year (distance) 



346.620 

 365.242 

 365.259 





Revolution of lunar perigee 

 Revolution of Moon's node (ecliptic) 

 Saros cycle (recurrence of eclipses) 

 Metonic cycle (recurrence of lunar phases) 





8.85 

 18.61 

 18.03 

 19.00 



Revolution of solar perigee 



209 centu 



ries 



25 



