The Principal Terrestrial Latitude Circles

According to Eq. (40), the sun's declination varies between $-\epsilon$ and $+\epsilon$ during the course of a year. It follows from Eq. (59) that it is only possible for the sun to have an upper transit at the zenith in a region of the earth whose latitude lies between $-\epsilon$ and $\epsilon$. The circles of latitude bounding this region are known as the tropics. Thus, the tropic of Capricorn--so-called because the sun is at the winter solstice, and, therefore, in the first degree of Capricorn, when it culminates at the zenith at this latitude--lies at latitude $-23^\circ 26'$. Moreover, the tropic of Cancer--so-called because the sun is at the summer solstice, and, therefore, in the first degree of Cancer, when it culminates at the zenith at this latitude--lies at latitude $+23^\circ 26'$.

Equations (59) and (60) imply that the sun does not rise for part of the year, and does not set for part of the year, in two regions of the earth whose terrestrial latitudes satisfy $\vert L\vert> 90^\circ - \epsilon$. These two regions are bounded by the poles and two circles of latitude known as the arctic circles. The south arctic circle lies at latitude $-66^\circ 34'$. Likewise, the north arctic circle lies at latitude $+66^\circ 34'$.

The equator, the two tropics, and the two arctic circles constitute the five principal latitude circles of the earth, and are shown in Fig. 12.

Figure 12: The principal latitude circles of the earth.