# Basic Calculus of Planetary Orbits and Interplanetary Flight

Intended for a one- or two-semester course, this text appliesbasic, one-variable calculus to analyze the motion both of planetsin their orbits as well as interplanetary spacecraft in theirtrajectories. The remarkable spacecraft missions to the inner andoutermost reaches of our solar system have been one of the greatestsuccess stories of modern human history. Much of the underlyingmathematical story is presented alongside the astonishing imagesand extensive data that NASA’s Voyager, NEAR-Shoemaker, Cassini,and Juno missions have sent back to us.First and second year college students in mathematics,engineering, or science, and those seeking an enriching independentstudy, will experience the mathematical language and methods ofsingle variable calculus within their application to relevantconceptual and strategic aspects of the navigation of a spacecraft.The reader is expected to have taken one or two semesters of thebasic calculus of derivatives, integrals, and the role that limitsplay. Additional prerequisites include knowledge of coordinateplane geometry, basic trigonometry, functions and graphs, includingtrig, inverse, exponential, and log functions.The discussions begin with the rich history of humanity’sefforts to understand the universe from the Greeks, to Newton andthe Scientific Revolution, to Hubble and galaxies, to NASA and thespace missions. The calculus of polar functions that plays acentral mathematical role is presented in a self-contained way incomplete detail. Each of the six chapters is followed by anextensive problem set that deals with and also expands on theconcerns of the chapter. The instructor has the flexibility toengage them with greater or lesser intensity.“I have been an aerospace engineer for 39 years and honestly, itwould be hard for me to overstate how valuable I believe this bookwill be to numerous scientific and engineering disciplines and inparticular to the future of aerospace engineering … This book isperfectly crafted to motivate, educate, and prepare the scientistsand engineers who wish to reach for the sky and beyond.” ―Dr. MarioZoccoli, Aerospace Engineer, NASA and Lockheed Martin