Introduction to Understandable Physics
Volume I - Mechanics
by
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CHAPTER 11. ASTRONOMY AND THE FORCE OF GRAVITATION
11-1. Introduction
Early History of Astronomy
Observations of the Sun, Moon, planets, and stars have been a curiosity since ancient times. Greek philosophers in the fourth century B.C. are credited with the first recorded attempts for developing scientific theories to explain these observations. Most of these early theories assumed that the Earth was stationary at the center of the universe and that heavenly bodies were attached to various transparent concentric spheres that rotated about the Earth as center. Such theories that assume a stationary Earth at the center of the universe are referred to as geocentric theories.
In contrast to the early popularity of the geocentric theories, the Greek astronomer Aristarchus (c270 B.C.) proposed a heliocentric theory in which the Sun was at the center of the universe. Although we now know that the Sun is merely the center of our solar system, which moves with an arm of our galaxy, the Milky Way or Home Galaxy, Aristarchus offered a theory that would ultimately direct later astronomers in the right direction. Unfortunately, the consensus of astronomers during his time and almost the next two thousand years discarded the heliocentric theory and favored the geocentric theory.
The geocentric theory experienced some problems soon after the time of Aristarchus, where it was noticed that some planets varied in brightness, suggesting that the distance between these planets and the Earth also varied. Also the motions of these planets were not uniform. This behavior indicated that the planets could not be attached to spheres that rotated about the Earth as center. To address this problem, it was theorized that the planets moved in epicycles relative to these spheres, whereby the planet moved in a circular path relative to a point on the sphere. To give an analogy based on our present knowledge, we could consider the Earth as being the point on a sphere that rotates about the Sun, and the Moon as revolving around this point in an epicycle; viewed from the Sun, the distance and motion of the Moon would vary. Hipparchus (c130 B.C.), a Greek astronomer, mathematician, and geographer is credited with formalizing the mathematics of epicycles, and Ptolemy (c140 A.D.), another Greek astronomer, mathematician, and geographer is known for preserving this work in his writing of the Almagest.
Ptolemy's Almagest served as the bible of astronomy and preserved the geocentric epicycle theory until the time of the Enlightenment, which is considered to have begun around 1600. The groundwork for challenging the geocentric theory began somewhat earlier. In particular, Nicholas Copernicus (1473-1543), a Polish astronomer, published his theory of a heliocentric universe in the year of his death. Copernicus showed that a much simpler mathematical model of the motions resulted with this theory. The idea of seeking the most simple and basic description of science with the fewest assumptions had been emphasized and popularized by William of Ockham (c1340 A.D.), a medieval English philosopher; this idea is often referred to as “Ockham's razor”, which is used to cut away the nonessential parts and leave only the basics.
The heliocentric theory of Copernicus was quite controversial initially, as often is the case for a different way of thinking. Opposition arose both from the scientific and religious communities. Tycho Brahe (1546-1601), a Danish astronomer, realized there was a need for more accurate observations, whereby he developed a state-of-the art observatory that yielded copious data on the positions of stars and planets; the resulting angular positions were measured to within 1-2 min of arc. Johann Kepler (1571- 1630), a German astronomer, began to work with Brahe near the end of his life, and subsequently Kepler became the heir and steward of the extensive data Brahe had accumulated over the years. Kepler began to use these data to analyze planetary motion using a heliocentric model, which culminated in two laws that were announced in 1609 and a third one in 1619. During this time, Galileo Galilei (1564-1642), the pioneer Itailian physicist and astronomer, used his telescope invention to discover four moons that orbit Jupiter and to observe that the planet Venus has a crescent phase like the Moon; both observations contradict geocentric theories but are consistent with the heliocentric theory. [Unfortunately, the Inquisition forced Galileo, a sincere Catholic himself, to renounce his heliocentric belief, because it asserted that the Earth was not stationary]. Subsequently, Kepler's Laws gained increasing credibility and later provided Isaac Newton (1642-1727), the noted British physicist, with guidelines for deducing his Law of Universal Gravitation.
Chapter Overview
In this Chapter we will begin with a detailed look at Kepler's Laws of planetary motion, and then see how they lead to Newton's Law of Universal Gravitation. Next, we will examine various space and astronomical aspects that result from gravitation, including satellites, Earth gravity, tides, escape velocities, and black holes. Finally, an optional section explores the physical bases of Kepler's Laws in more detail.
11-2. Kepler's Laws
Johann Kepler developed three laws to describe the motion of planets, based on the time and position measurements accumulated by Tyco Brahe. The three laws are summarized as:
Kepler's Laws
1. Planets travel in elliptical paths with the Sun at one focus.
2. The line between planet and Sun sweeps out area at a constant rate.
3. The planet periods (T) and average distances (r) to Sun are related as T2 ~ r3.
It should be understood that the three laws were strictly empirical originally, meaning that they described the motion but were not based on a physical theory. We will now explore the physical basis of the laws.
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About the Book
Will Winn has written Introduction to Understandable Physics with the goal of presenting physics concepts in a building-block fashion. In the first chapter he develops mathematical tools for understanding the subsequent physics. Then successive chapters develop the physics tools that apply in later chapters. For example, the relations for acceleration, velocity, and distance subsequently couple with Newton's three force laws to develop concepts of force, energy, and momentum. Then these concepts apply to the special case of circular motion to develop concepts of torque, rotational energy, and angular momentum. While examining circular motion, the back-and-forth motion of a simple pendulum is shown to be a single component of a similar pendulum moving in a circular path, and its mathematical description matches that for an oscillating spring. The final chapter of this volume, Mechanics, examines Newton's Law of Universal Gravitation and its impact on astronomy. Using information of the preceding chapters, Newton could explain Kepler's observational laws of planetary motion, provided he introduced a gravitational force between objects. Applications of this force include satellite motion, gravity inside the Earth, tides, escape velocities, black holes, and dark matter.
Near the end of each chapter a Simple Projects section suggests experiments and/or field trips that may serve to reinforce the physics covered. Some of the experiments are simple enough for students to explore alone, while others benefit from equipment available to physics instructors. When opportune, the text develops relations that are revisited much later in the text. For example, Chapter 7 applies momentum concepts to deduce the speed of waves on a string, which are discussed further in Volume II. Also optionaltext sections provide students with a deeper appreciation of the subject matter; however they are not required for continuity. Some of these optional topics can be candidates for term projects.
About the Author
Will Winn has enjoyed a 50-yr physics career, which includes various experiences in teaching , pure research, and industrial applications. Early in his career he taught physics at both secondary institutions and universities, namely Cornell and Virginia Commonwealth, and in later years he taught again at University of South Carolina Aiken. Upon receiving his Ph.D. in nuclear physics at Cornell in 1968, he had commenced a post-doctoral appointment at the Washington University Cyclotron facility to conduct research on nuclear energy levels, and he continued this work with another post-doctoral appointment at the MP Van de Graaff accelerator at the University of Rochester. Seeking to apply his background to practical applications, he completed a masters degree program in Nuclear Engineering at University of Virginia in 1974. Then he began his research at the Savannah River Site, which included reactor experiments, nuclear chemistry, non-destructive testing, environmental monitoring, and non-proliferation studies. In 2000 he retired from SRS to teach math and physics at USCA, after which he commenced writing this text. Here, he refined physics notes he prepared for his USCA students, as well as drawing from his career writing experience, which includes over 60 published papers.
Dr. Winn has encountered a wide range of activities related to physics over the years. He has conducted research with university professors, chemists, biologists, geologists, engineers, and other physicists. As a former premed student who switched to physics, he also has had a continuing interest in the physics involved in medical applications. Accordingly, he has a good appreciation for the role of physics in a considerable number of fields, and this has influenced his teaching of students who require an introductory physics course. Furthermore, he has applied this experience to writing Introduction to Understandable Physics.