Spherical Astronomy Problems And Solutions High Quality

Plug (h=0) into the altitude formula: [ 0 = \sin \phi \sin \delta + \cos \phi \cos \delta \cos H ] [ \cos H = - \tan \phi \tan \delta ]

Better to say: The star is above horizon when (|H| < H_0) with (H_0 = \arccos(-\tan\phi\tan\delta)). For this example, (H_0=115.7°), so visible for (2\times115.7/15 \approx 15.4) hours. Problem: Observer measures a circumpolar star’s upper transit altitude (a_max) and lower transit altitude (a_min) (both north of zenith). spherical astronomy problems and solutions

[ \sin A = \frac\cos \delta \sin H\cos h ] Plug (h=0) into the altitude formula: [ 0

[ H = \arccos( - \tan \phi \tan \delta ) ] [ \sin A = \frac\cos \delta \sin H\cos

This is how ancient navigators determined latitude using Polaris (though Polaris is not exactly at the pole). Given: Equatorial coordinates ((\alpha_1, \delta_1)) and ((\alpha_2, \delta_2)). Find: Angular separation (\sigma) on the sky.