As the earth rotates on its axis, a point on the earth's 

 surface experiences two high tides and two low tides each 

 lunar day (note that the moon is also rotating around the 

 earth in a period of about a month). The tidal constituent 

 described here, with a period of about 12.42 hours, is 

 called Mp, the M for the moon and the subscript for the 

 cycles per day. 



The moon does not really have a circular orbit around 

 the earth, but rather an elliptical orbit that is closest to 

 the earth as a point called perigee and farthest at apogee. 

 Therefore the attractive force will vary, being greatest at 

 perigee and smallest at apogee. Tidal scientists cop-^ with 

 this by concocting a second moon and placing it also in a 

 circular orbit around the earth. They select a period about 

 12.66 hours, so that the resulting force, named constituent 

 N2, will be exactly in phase with M^ at perigee and exactly 

 in opposite phase with it at apogee, thus modulating the 

 Mp force over the period of a lunar month. 



A similar treatment is designed for the solar forces, 

 with the principal solar constituent (period 12 hours) 

 labeled as Sp- Thus when Mp and S2 are in phase at new and 

 full moon, we have spring tides (larger than average) and, 

 since Mp and Sy are exactly opposed at quadrature, there 

 are neap tides (smaller than average) at these times. If 

 spring tides and perigean tides coincide, the range is even 



26-5 



