Introduction to the Maths and Physics of the Solar System

Planetary motion can seem like a collection of facts to memorize—until the mathematics shows how the pieces fit together. In Introduction to the Maths and Physics of the Solar System, Lucio Piccirillo builds from core mathematical ideas to the physics that explains orbits, tides, and other solar-system phenomena.

Shaped by an introductory undergraduate course, the book makes the reasoning behind scientific explanations part of the subject. It begins with the tools readers need, then uses them to investigate how the Sun, planets, and their motions can be described and understood.

Start with the mathematical foundations

The opening chapters revisit geometry, trigonometry, and calculus before assembling a practical math-and-physics toolkit. Vectors, coordinate systems, Newton’s laws, gravity, and mass provide the groundwork for the more specialized discussion that follows.

Follow the logic of celestial mechanics

The central chapter develops the ideas used to describe motion under gravity. Piccirillo explores conservation laws, Kepler’s laws, conic sections, energy and orbits, and the universal law of gravitation. Kepler’s problem receives particular attention, with approaches that include geometry, calculus, and geometric algebra.

That progression helps connect mathematical methods to physical questions: not just what an orbit looks like, but how its behavior can be derived and analyzed.

Bring the concepts back to the solar system

The final chapter applies the earlier material to a range of familiar and less familiar subjects, including geocentric and heliocentric models, motion and coordinates, the analemma, tides, the Roche limit, and measuring the speed of light within the solar system.

A companion for quantitative astronomy

This book is aimed especially at undergraduate astronomy students who want the mathematics and physics behind introductory solar-system topics explained alongside them. Its self-contained treatment also makes it relevant to interested readers who want to test astronomical explanations quantitatively and are prepared to engage with the underlying calculations.

For readers who want to understand how observation becomes a model—and how a model becomes a calculation—Piccirillo offers a structured route from basic tools to the mechanics of our planetary neighborhood.