Spherical Astronomy Problems And Solutions Here
For altitude: [ \sin h = \sin \phi \sin \delta + \cos \phi \cos \delta \cos H ] (This is the most common formula.)
Altitude (h = 0°) (center of body).
Then determine (A) uniquely: If (\sin A > 0), (A) in (0°–180°); if (\sin A < 0), (A) in (180°–360°). Or use atan2. spherical astronomy problems and solutions
Compute both (\sin A) and (\cos A) from: [ \sin A = -\frac\cos \delta \sin H\cos h ] (sign depends on convention; careful: some texts use azimuth from south) and [ \cos A = \frac\sin \delta - \sin \phi \sin h\cos \phi \cos h ] Then (A = \textatan2(\sin A, \cos A)) in radians. Part 4: Comprehensive Worked Example Problem: On 2024-10-15 at 4h UT, an observer at (\phi = 35^\circ N), longitude (= 75^\circ W) observes a star with (\alpha = 6h 45m 12s), (\delta = +16^\circ 20'). Find the star’s altitude and azimuth at that moment. For altitude: [ \sin h = \sin \phi
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. Compute both (\sin A) and (\cos A) from:
