The right ascension and declination of the seven stars of the Big Dipper are given below.

Star Right Ascension Declination

Alkaid 13h48m +49◦190

Mizar 13h24m +54◦560

Alioth 12h54m +55◦580

Megrez 12h15m +57◦020

Phecda 11h54m +53◦420

Merak 11h02m +56◦230

Dubhe 11h04m +61◦450

(a) Find range of latitudes for which all of the stars of the Big Dipper are circumpolar.

(b) Find the southernmost latitude from which all of the stars of the Big Dipper can be seen.

(c) Find the range of latitudes for which none of the stars of the Big Dipper are ever seen above the horizon.

Hints: Use the results from problem 1.9(c) and (d). Be careful when subtracting angles given in degrees and arcmin.

For example, 58◦150 − 22◦230 = 57◦750−22◦230 = 35◦520 . Also, note that −37◦180 = −37◦−180 , not −37◦+180 . So, for example, 15◦200−31◦120 = 15◦+200−31◦−120 = −16◦+80 = −15◦520 .