IA 2 : IBDP HL Math AA

Modeling the Sun’s Elevation Using Trigonometry

For my IBDP Math HL - Internal Assessment, I wanted to explore something that connects both astronomy and mathematics, so I chose to model how the Sun’s maximum elevation angle changes throughout the year. This variation is caused by the Earth’s axial tilt and its elliptical orbit. I used real-world solar elevation data from the U.S Naval Observatory and derived a cosine function that could accurately predict the Sun’s peak elevation on any given day of the year.

What made the challenge more interesting was adapting the function to account for latitude. I extended the model beyond the equator and developed a formula that could calculate solar elevation at any location on Earth. I even addressed limitations, such as elevation values exceeding 90° by introducing reflection logic into the function.

To ensure accuracy, I compared the model’s output with actual solar elevation data at different latitudes and the error margin was within ±2.1°. This project helped me understand periodic behavior in trigonometric functions and their application in the real world. It also showed me how mathematical modeling can be used in climate science, solar panel optimization and space research, all areas that I am deeply passionate about.