20 



Figure 11.— Moon's orbit and the 

 ecliptic. 



In figure 1 1 : 



U is the vernal equinox. 

 the moon's ascending node. 

 / the intersection of the moon's 

 orbit with the equator. 

 UO the echptic. 

 UI the celestial equator. 

 10 the moon's orbit on the celestial 

 sphere. 

 When the moon's ascending node coin- 

 cides with the vernal equinox the inchna- 

 tion of the moon's orbit to the equator has 

 its maximum value of 23°.452 + 5°.145 = 28°.597. When 9K years 

 later it coincides with the autumnal equinox the inclination of the orbit 

 has a minimum value of 23°.452-5°.145=18°.307. The maximum 

 monthly declinations of the moon, both positive and negative, range 

 between the same limits. 



36. Longitude oj the moon's node. — The angular distance on the 

 ecliptic from the vernal equinox U to the moon's ascending node 0, 

 figure 1 1 , is the longitude of the moon's node, and is designated by the 

 letter N. It determines the inclination, I, of the moon's orbit to the 

 equator. The value of / may be found from A^ by the solution of the 

 spherical triangle lUO, since in this triangle the angle lUO is the 

 known inclination of the ecliptic to the equator and 10 U is the known 

 inclination of the orbit to the ecliptic. The values of / in terms of N 

 are tabulated in manuals on tidal analysis. 



37. The lunar equilibrium tide in terms of the latitude of the tidal 

 station and the moons declination. — In figure 12, CN is the axis of the 

 earth, iVits north pole, 

 PiMi the equator, the 

 angle PxCP the lati- 

 tude, X (lambda), of a 

 tidal station P, NPPi 

 the meridian through 

 P, the angle M^OM 

 the declination, S 

 (delta), of the moon, 

 NM'Mi the hour cir- 

 cle through the fine CM joining the centers of the earth and 

 the moon, and the spherical angle PNMi the hour angle, H, of the 

 moon with respect to the meridian through P. The angle PCM' is 

 then 6, the zenith distance of the moon. 



From the spherical triangle PNM' : 



cos 0=cos (90°-X) cos (90°-5)+sin (90°-X) sin (90°-5) cos i? 

 =sin X sin 5+cos X cos 5 cos H (21) 



Figure 12. 



