Unlock the secrets of the cosmos through captivating observations.

Spherical Trigonometry & Celestial Coordinates

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'll learn about the different ways in which units of time are measured, then we'll learn about the effects that affect our observation and how to correct for it. This handout heavily applies the knowledge you learn from spherical trigonometry and celestial coordinates.

Observational Effects

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.


Telescopes have been mankind's windows to the cosmos, enabling us to peer into the depths of space and time and uncover breathtaking celestial phenomena. Whether you're an aspiring astronomer or simply curious about the wonders of the universe, this handout will introduce you to the fundamentals of telescopes and how they work.