Intended for a one-semester course, this text provides the reader with a detailed illustration of basic calculus in action as it explains the orbits of the planets and the maneuvers of interplanetary spacecraft.  The remarkable exploratory spacecraft missions to the inner and outermost reaches of our solar system have been some of the greatest success stories of modern human history. The mathematical story is presented alongside a full album of the fascinating images and by incorporating the extensive data that the Voyagers, NEAR Shoemaker, Cassini, MESSENGER, Juno, and other missions have sent back to NASA and the Jet Propulsion Laboratory. Extensive problem sets accompany all the discussions. An instructor has the flexibility to engage them with greater or lesser intensity.

First and second year college students in mathematics, engineering, or science, as well as those seeking an enriching independent study, will gain an understanding of single variable calculus of polar functions and a deep sense of the capacity of its language and its methods to explain the complex natural phenomena and technological challenges that arise in the exploration of space. Even though a detailed exposition of the essential mathematical tools is provided, the reader would profit from the mathematical maturity gained from one or two semesters of basic calculus with its agenda of derivatives, integrals, and the fundamental theorem. Prerequisites include a working knowledge of coordinate geometry in the plane, functions and graphs, basic trigonometry, and the elementary functions (including trig, inverse, exponential, log functions).

The book begins with a broad history of the efforts of the Greeks, the geniuses of the Scientific Revolution, and those of more recent astronomers to understand the solar system and the universe beyond it. This is followed by an overview of the space missions and the data about the solar system that they have returned. The basics of polar calculus and a modern version of Newton’s theory of centripetal force are developed next. The applications to elliptical orbits and their precession and to the mathematics of interplanetary flight conclude the book.