Question 7.6: Sunrise in Boston. Find the time at which sunrise (geometric......
Sunrise in Boston. Find the time at which sunrise (geometric and conventional) will occur in Boston (latitude 42.3º) on July 1 (n = 182). Also find conventional sunset.
From (7.6), the solar declination is
\delta \ = \ 23.45 \ \sin \ \left[\frac{360}{365} \ \left(n \ − \ 81\right)\right] \ = \ 23.45 \ \sin \ \left[\frac{360}{365} \ \left(182 \ − \ 81\right)º\right] \ = \ 23.1ºFrom (7.17), the hour angle at sunrise is
H_{SR} \ = \ \cos^{−1} \left(−\tan \ L \ \tan \ \delta\right) \ = \ \cos^{−1} \left(−\tan \ 42.3º \ \tan \ 23.1º\right) \ = \ 112.86ºFrom (7.18) solar time of geometric sunrise is
Using (7.19) to adjust for refraction and the upper-limb definition of sunrise gives
\begin{matrix} Q & = \ \frac{3.467}{\cos \ L \ \cos \ \delta \ \sin \ H_{SR}} \left(\text{min}\right) \quad \quad \quad \quad \quad \\ & = \ \frac{3.467}{\cos \ 42.3 \ \cos \ 23.1º \ \sin \ 112.86º} \ = \ 5.5 \ \text{min} \end{matrix}The upper limb will appear 5.5 minutes sooner than our original geometric calculation indicated, so
\text{Sunrise} \ = \ 4:28.6 \ A.M. \ − \ 5.5 \ min \ = \ 4:23.1 \ A.M. \ \left(\text{solar time}\right)From Example 7.5, on this date in Boston, local clock time is 12.1 min earlier than solar time, so sunrise will be at
\text{Sunrise} \ \left(\text{upper limb}\right) \ = \ 4:23.1 \ − \ 12.1 \ = \ 4:11 \ A.M. \ \text{Eastern Standard Time}Similarly, geometric sunset is 7.524 h after solar noon, or 7:31.4 P.M. solar time. The upper limb will drop below the horizon 5.5 minutes later. Then adjusting for the 12.1 minutes difference between Boston time and solar time gives
\text{Sunrise} \ \left(\text{upper limb}\right) \ = \ 7:31.4 \ + \ \left(5.5 \ − \ 12.1\right) \ \text{min} \ = \ 7:24.8 \ P.M. \ \text{EST}