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The stars move from east to west across the sky each night. The ancient Greeks realized that the apparent movement of the stars would make sense if the stars were stuck on the inner surface of a giant celestial sphere that rotated around the Earth once every sidereal day. The Sun also moves from east to west across the sky, but not quite in the same way as the stars. The Sun’s motion can be tracked using shadows, and it appears to move eastward relative to the sphere of the stars along a path that is tilted relative to the celestial equator. The Sun completes its motion around the celestial sphere in one year, traveling through the constellations of the zodiac along a path called the ecliptic. As an observer moves around on Earth the apparent motions of the stars and Sun change in a way that shows the Earth to be spherical. The stars also display a very slow motion known as the precession of the equinoxes with a period of about 26,000 years.
This chapter introduces the fundamental mystery of the night sky: the wandering planets and their unusual retrograde motion. The story of the Copernican Revolution is the story of how this puzzle was solved, and then solved again. There are many reasons to learn about the Copernican Revolution: it is one of the great human intellectual accomplishments, it has had a tremendous effect on our understanding of the universe and the place of humanity within it, and it is a story that is often misunderstood. Furthermore, the Copernican Revolution is an excellent example of how science progresses. Science is a bit like puzzle solving, like making and using a map, like cooking, or even like doing art. New scientific theories provide us with new ways of perceiving the world that may be radically different from our previous perceptions. Learning the scientific story of the Copernican Revolution will help readers to better understand the nature of science.
Johannes Kepler was working as a mathematics teacher in Austria when he had a vision of how the universe must be constructed. Using the Copernican system as his model, Kepler thought that between each planetary orbital sphere was nested a regular polyhedron. There are only five regular polyhedra, so there could be only six planets. The relative sizes of the planetary orbits were set by the shapes that lay between them. Kepler’s idea caught the attention of Tycho Brahe and eventually he became Tycho’s assistant. When Tycho died, Kepler inherited Tycho’s accurate planetary data and he used these data to propose a new theory of planetary motion. Kepler found that the planets move in elliptical orbits with the Sun at one focus of the ellipse. Furthermore, Kepler believed the motion of the planets was powered by a force from the Sun that caused the planets to speed up when closer to the Sun and slow down when farther away. Kepler also discovered a curious mathematical relationship between the orbital periods of the planets and the size of the planetary orbits.
In 1671 Robert Hooke thought he had detected an annual parallax for the star Gamma Draconis, thus proving that the Earth orbits the Sun. Setting aside the uncertainty of Hooke’s meagre measurements, there remained the problem of how the Earth could orbit the Sun. Hooke thought he knew: the planets orbited the Sun because of a combination of straight line inertial motion and an attraction toward the Sun. But it was left to Hooke’s rival, Isaac Newton, to work out the mathematical details. While working out these details Newton established an entirely new physics based on three fundamental laws of motion and a universal gravitational attraction between all massive objects. Newton’s physics explained not only the orbits of planets, but also the motion of projectiles, the orbits of the Moon and comets, the precession of the equinoxes, and the tides. Newton’s physics was hailed in England but many European natural philosophers initially dismissed universal gravitational attraction as an “occult quality.”
While the Copernican theory was endorsed by some writers such as Thomas Digges and Giordano Bruno, most astronomers remained skeptical of a moving Earth. One such skeptic was Tycho Brahe, who set out to reform astronomy through improved observational methods. His careful observations of a new star (or “nova”) and a comet indicated that change could occur in the heavens, in contrast to the teachings of Aristotle. However, his observations of the angular size of stars seemed to contradict Copernicus’ theory. Tycho proposed a new geoheliocentric model in which the Earth sits at rest at the center of the cosmos and the Sun orbits around the Earth, but the planets orbit around the Sun. This model retained the stationary Earth but included some of the best features of the Copernican model. In an attempt to find evidence for his model, Tycho made extraordinarily extensive and accurate measurements of planetary positions, particular of the planet Mars.
In 1543, Nicolaus Copernicus published a radical new theory of the heavens. He proposed that the Earth rotates on its axis while the celestial sphere remains stationary. He also placed the Sun at rest near the center of the celestial sphere, while the Earth and other planets orbited around the Sun. Copernicus’ heliocentric theory could account for the motions of the stars, Sun, and planets about as well as Ptolemy’s theory did. It also helped to explain certain features of planetary motion that were mysterious in Ptolemy’s model. However, the idea that the Earth moved was too revolutionary for most of Copernicus’ contemporaries. While Copernicus believed that his model represented the real motions of the universe, most of his readers denied the Earth’s motion and accepted Copernicus' theory as nothing more than a useful mathematical device.
In 1609 Galileo Galilei heard about a new instrument that is now known as the telescope. He set out to make his own, and when he turned it to the sky he made a series of unexpected discoveries. He found many new stars that were invisible to the eye, mountains on the Moon, and four moons in orbit around Jupiter. Later he found that the Sun's surface was spotted and seemed to rotate, and that Venus went through a series of phases like the Moon. These discoveries cast doubt on the traditional Aristotelian-Ptolemaic model of the universe, but it was Galileo’s investigation of motion that helped to finally bring down the traditional views. Galileo’s experimental work and mathematical insight led him to conclude that all bodies fall to the Earth with the same constant acceleration, and that bodies moving horizontally will continue in their motion unless impeded. This new understanding of motion made the idea of a moving Earth more plausible. Although Galileo’s work led to conflict with authorities in the Catholic Church, his work helped many future astronomers to embrace the heliocentric models of Copernicus and Kepler.
This textbook offers a modern approach to the physics of stars, assuming only undergraduate-level preparation in mathematics and physics, and minimal prior knowledge of astronomy. It starts with a concise review of introductory concepts in astronomy, before covering the nuclear processes and energy transport in stellar interiors, and stellar evolution from star formation to the common stellar endpoints as white dwarfs and neutron stars. In addition to the standard material, the author also discusses more contemporary topics that students will find engaging, such as neutrino oscillations and the MSW resonance, supernovae, gamma-ray bursts, advanced nucleosynthesis, neutron stars, black holes, cosmology, and gravitational waves. With hundreds of worked examples, explanatory boxes, and problems with solutions, this textbook provides a solid foundation for learning either in a classroom setting or through self-study.
Finding our Place in the Solar System gives a detailed account of how the Earth was displaced from its traditional position at the center of the universe to be recognized as one of several planets orbiting the Sun under the influence of a universal gravitational force. The transition from the ancient geocentric worldview to a modern understanding of planetary motion, often called the Copernican Revolution, is one of the great intellectual achievements of humankind. This book provides a deep yet accessible explanation of the scientific disputes over our place in the solar system and the work of the great scientists who helped settle them. Readers will come away knowing not just that the Earth orbits the Sun, but why we believe that it does so. The Copernican Revolution also provides an excellent case study of what science is and how it works.