Spherical Astronomy Problems And Solutions May 2026

Spherical Astronomy: Problems and Solutions

• Provide full derivations for any formula above,
• Produce code (Python) that computes conversions, rise/set times, parallactic angle, and separations,
• Generate worked examples for specific stars, dates, and observer locations (I’ll need a date and location).

• $\sin(40) \approx 0.643$
• $\sin(30) = 0.500$
• $\cos(40) \approx 0.766$
• $\cos(30) \approx 0.866$
• $\cos(60) = 0.500$

Spherical Astronomy Problems, with Solutions (Villanova University) spherical astronomy problems and solutions

• $\tan(40) \approx 0.839$
• $\tan(-10) \approx -0.176$

The Problem: Over 20 years, a star’s position can shift by nearly 17 arcminutes. Spherical Astronomy: Problems and Solutions

• If the star is setting, $h=0$.
• If the star is at culmination (highest point), $H=0$.
• If the star is circumpolar, check if $\delta$ is within the "circumpolar cap."

Interpretation: The star sets at Hour Angle $H = 81.5^\circ$. Since $15^\circ = 1$ hour, the star sets $81.5 / 15 \approx 5.43$ hours after it crosses the meridian (Upper Culmination). Provide full derivations for any formula above, Produce

For more advanced exercises, you can find digitized classic textbooks like Smart's Textbook on Spherical Astronomy or practice sheets from the Villanova Astronomy Archive.