28 | Berichte des BSH Nr. 57 
The period P.,n between two equal moon phases (e. g. from full moon to full 
moon) is called a synodic month. The period PHy of the semi-monthly inequality 
corresponds to half a synodic month 
Pau 
L 
7 
p 
syn 
Referring to Figure 2, and based on the relationship 
distance = velocity * time, the following angles can 
be identified for the moon and sun, which are swept 
during a synodic month: 
(Moon) 360° +a= $- Poyn (1) 
(Sun) a = RA Poyn (2) 
with the angular velocities of the mean ecliptic 
jongitudes of the Moon ($ = 0,5490165197°/h) 
and Sun (h = 0,0410686399°/h) (International 
Earth Rotation and Reference Systems Service. 
2010). If we solve equations 1 and 2 for & and 
equate them, we get 
I_C)S 
© 
% 
HM 
She 
\ 
* 
Figure 2: The angles 
of the sun (S) and 
moon (M) passing 
through during a 
synodic month as seen 
from the earth (E). 
Ba 360° _ 360° 
m sh Gay 
Here, On IS the angular velocity associated with the synodic month. 
Thus, we get the period of the semi-monthly inequality: 
Pau = ln = 1 360° = 354,3671h = 14.7653 d 
HU 72» mM 20 ’ — , 
The duration of a tide and thus the time interval between successive high 
waters (or low waters) is not constant. As the time of high or low water is also 
subject to periodic variations, which is to be evaluated when analysing the 
semi-monthly inequality, this cannot be used as an independent time variable 
(see also Section 3). This role is taken over by the transit time of the Moon. In 
the case of semi-diurnal tides, a preceding upper or lower lunar transit can be 
assigned to each high and low water. The Moon is said to be in transit when it 
crosses the meridian (the line connecting north and south at the observer's 
(location).