Spherical Astronomy Problems And Solutions ((full)) May 2026

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.

Then obtain (H) using: [ \cos H = \frac\sin h - \sin \phi \sin \delta\cos \phi \cos \delta ] And control quadrant with: [ \sin H = \frac\cos h \sin A\cos \delta ] spherical astronomy problems and solutions

Apply the spherical law of cosines to the triangle formed by the two bodies and the pole. This is how ancient navigators determined latitude using

Then (\sin A = (\cos20 \sin30) / \cos57.4°) = ((0.9397 \times 0.5) / 0.537) = 0.46985/0.537 ≈ 0.875 → (A \approx 61.0^\circ) (since both sin and cos A are positive → NE quadrant). Azimuth = 61° east of north. Given: (\phi), (h), (A). Find: (H) and (\delta). Then obtain (H) using: [ \cos H =