Best Books on Spherical Astronomy

I am preparing for an astronomy olympiad and a good amount of questions in the olympiad come from Spherical astronomy, some of the books ive tried reading were too hard to understand as this topic requires a good amount of visual representation. Does anyone have any good courses or books on this topic for beginners which like deals with spherical trignometry then goes on to the celestial sphere, I would be greatly appreciate it if anyone can help me.

• To what extend do you want to learn? Just for example law of cosines, sines, solid angles, surface area and transformations? (These are the only topics related to astronomy in spherical trigonometry as far as I can tell.) Jun 15, 2021 at 15:29
• I want to learn all the above topics you mentioned and I want to learn about right ascention declination zenith hour angle , circumpolar stars etc Jun 15, 2021 at 17:04

There's also Smart's Textbook on Spherical Astronomy

you can preview it here: http://aprsa.villanova.edu/files/Smart-SphericalAstronomy.pdf

I am not sure if it suits your purpose, it really is a textbook and is pretty slow and thorough. But if something is bugging you and other sources are inadequate, this might you clear up some of the finer points.

• Thanks a lot this book is exactly what I was looking for Jun 16, 2021 at 4:35

If you just need some astronomy related spherical stuff, I can recommend the same book I started with: Fundamental Astronomy. It includes exercises as well and is designed for your purpose.

Spherical astronomy is from page 11 to 46. At the beginning, it starts with some basic spherical trigonometry theorems and then with additional astronomy related concepts (like declination, hour angle, transformation between coordinate systems ...). I find the mathematical part (11–14) very short and concise, for example:

1. The part about the area of spherical triangle is very concise, so I needed to find the proof with longer explanation on the internet.
2. The part about the law of cosines for spherical triangles is very concise as well, and one can't easily imagine that. I just went on Wikipedia page and found a proof with vectors which I find easy.

But of course you don't need to know how to derive, for example, law of cosines for spherical triangles. It just helps you with the intuition, so the concise mathematical part is not so important with all its derivations. You just need to know area, surface angle, basic properties of sphere and its triangles, law of cosines and sines, special Pythagorean theorem, the area of lune, and so on.

The next part is longer (14–41) and is directly related with astronomy. I found it much easier because it is more intuitive.

At last, the exercises (41–46). You have to also know that the exercises are included at the end of each subchapter, too.

There’s the classic (1966) Spherical Astronomy (Amazon).