This short e-book is written for someone who knows a little math, and wants to understand how our Sun moves across the horizon throughout the year. It shows how to calculate the times of the sunrise, sunset and solar noon. It also explains the mathematics underlying the construction of sundials, and shows how to use a sundial to calculate the correct time as you see it on your watch. Starting with Kepler's first two laws of planetary motion, the e-book guides the reader step by step through the calculations described above. It assumes that the reader is comfortable with trigonometry, polar coordinates and introductory calculus.

The authors have presented and interpreted Johannes Kepler's Latin text to English readers by putting it into the kind of clear but earnest language they suppose Kepler would have used if he had been writing today.

The brilliant German mathematician Johannes Kepler (1571-1630), one of the founders of modern astronomy, revolutionized the Copernican heliocentric theory of the universe with his three laws of motion: that the planets move not in circular but elliptical orbits, that their speed is greatest when nearest the sun, and that the sun and planets form an integrated system. This volume contains two of his most important works: The Epitome of Copernican Astronomy (books 4 and 5 of which are translated here) is a textbook of Copernican science, remarkable for the prominence given to physical astronomy and for the extension to the Jovian system of the laws recently discovered to regulate the motions of the Planets. Harmonies of the World (book 5 of which is translated here) expounds an elaborate system of celestial harmonies depending on the varying velocities of the planets.

In Measuring Shadows, Raz Chen-Morris demonstrates that a close study of Kepler’s Optics is essential to understanding his astronomical work and his scientific epistemology. He explores Kepler’s radical break from scientific and epistemological traditions and shows how the seventeenth-century astronomer posited new ways to view scientific truth and knowledge. Chen-Morris reveals how Kepler’s ideas about the formation of images on the retina and the geometrics of the camera obscura, as well as his astronomical observations, advanced the argument that physical reality could only be described through artificially produced shadows, reflections, and refractions. Breaking from medieval and Renaissance traditions that insisted upon direct sensory perception, Kepler advocated for instruments as mediators between the eye and physical reality, and for mathematical language to describe motion. It was only through this kind of knowledge, he argued, that observation could produce certainty about the heavens. Not only was this conception of visibility crucial to advancing the early modern understanding of vision and the retina, but it affected how people during that period approached and understood the world around them.

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Johannes Kepler (1571-1630) is remembered, along with Copernicus and Galileo, as one of the greatest Renaissance astronomers. A gifted analytical thinker, he made major contributions to physics, astronomy, and mathematics. Kepler was trained as a theologian, yet did not hesitate to challenge church doctrine and prevailing scientific beliefs by supporting the theory of a Sun-centered solar system. As Imperial Mathematician to the Holy Roman Emperor, he analyzed the precise observations of the heavens that his predecessor, the great astronomer Tycho Brahe, had recorded. The book follows the ingenious scientist along the difficult pathway from raw data to his monumental discovery--the three Laws of Planetary Motion. Kepler also made fundamental contributions to optical theory, including a correct description of the function of the eye and a new and improved telescope design. His unique Rudolfine Tables, universal calculations of planetary motion, were unprecedented in their accuracy. James Voelkel vividly describes these scientific achievements, providing enough background in astronomy and geometry so even beginners can follow Kepler's thinking and enjoy this book. Equally captivating is his account of Kepler's tumultuous life, plagued by misery, disease, war, and fervent religious persecution.Oxford Portraits in Science is an ongoing series of scientific biographies for young adults. Written by top scholars and writers, each biography examines the personality of its subject as well as the thought process leading to his or her discoveries. These illustrated biographies combine accessible technical information with compelling personal stories to portray the scientists whose work has shaped our understanding of the natural world.

Controversial at the time, Copernicus's discoveries led to the scientific revolution, and a greater understanding of our place in the universe. An accessible, abridged edition with a new introduction. Renaissance Natural philosopher Nicolaus Copernicus's pioneering discovery of the heliocentric nature of the solar system is one of the few identifiable moments in history that define the understanding of the nature of all things. His great work was the consequence of long observation and resulted in the first stage of the Scientific Revolution by correctly positing that the earth and other planets of the solar system revolved around the sun. Not only did this promote further study to understand the place of humanity in the world and the universe, it questioned the authority of the organised Christian Church in the West to be the keeper of fundamental truths. Ultimately this would lead to the Enlightenment, and the separation of religion, government and science. The FLAME TREE Foundations series features core publications which together have shaped the cultural landscape of the modern world, with cutting-edge research distilled into pocket guides designed to be both accessible and informative.