Gravitation and Relativity

Gravitation and Relativity (Spring 2026) will tour the history of both the observational and the mathematical developments that led to our present understanding of gravity. This is a fascinating history, covering Tycho Brahe’s meticulous observations of the night sky, Kepler’s Laws of Planetary Motion, Newton’s Law of Universal Gravitation, the Lorentz Transformation, Einstein’s Theory of Special Relativity, and an introduction to Einstein’s Theory of General Relativity, including its prediction of gravitational waves and the announcement of the experimental observation of these waves one century later.

Briefly, we will start by learning about the painstaking years of observational data recorded by Tycho Brahe in the late 1500s, which Johannes Kepler later used to develop his empirical Laws of Planetary Motion, fully publishing them by 1619. Importantly, these laws correctly described Brahe’s data, but they did not provide any underlying understanding for why planetary motion resulted in Brahe’s data. For example, Kepler’s First Law states that the planetary orbits are ellipses with the Sun at one of the foci of the ellipse. Why is the orbit an ellipse, though, and why is the Sun at one of the foci? These are questions Kepler’s Laws couldn’t answer; we would have to wait for Sir Isaac Newton’s Law of Universal Gravitation, published in 1687, for our first answers to such questions.

For about 170 years, Newton’s Law of Universal Gravitation reigned supreme, successfully predicting, for example, the existence of Neptune based on aspects of Uranus’ motion unaccounted for by the other known planets. However, the limitations of the theory began to show by the mid-1800s, during which the orbit of Mercury, in particular, was measured precisely enough to discount Newton’s theory as a complete explanation for its motion. Eventually, Einstein’s Theory of General Relativity, first presented in 1915, updated our understanding of gravitation and led to a century-long effort to experimentally verify the existence of the gravitational waves it predicted to exist.

(You’ll notice in this mini-history that the Lorentz Transformation and Einstein’s Theory of Special Relativity are conspicuously absent. While they are not directly about gravitation, they are important stepping stones for fully understanding it and are thus included as topics in the course.)

Knowledge of calculus is required for this class, and problem sets will include computational questions that will range in difficulty so that all students, no matter their programming experience, will be challenged by the assignments. Python will be the preferred programming language for the course.

Once the Spring 2026 term is set, this description will be updated to include class meeting times and the application deadline.