Astronomical reference systems have been continually developed for thousands of years. Ancient astronomers considered objects in the night sky to be fixed on a spherical "shell" around the Earth. Amazingly, this geocentric reference system is still used today -- after all, we make most observations from the Earth. This handout teaches celestial coordinate systems as well as providing a math-heavy lesson into spherical trigonometry.

In this handout, we will learn the ways in which our measurements for observations are altered by atmospheric and positional phenomena and how to correct for them. Warning: this handout applies a heavy amount of physics and calculus.