The groundwork for modern science was laid down by Greek “natural philosophers” beginning about 2500 years ago, when Pythagoras and his followers began using mathematics to describe natural phenomena. These Greek ideas, translated into Arabic, were rediscovered in the West in the seventeenth century. They led to the development of the scientific method of examining, understanding, and predicting how things work.

Science is actually two related things. First, it is a body of knowledge that we acquire through observations, experiments, and mathematical calculations. The fact the planets orbit the Sun, along with equations that describe and predict these motions, are examples of that knowledge.

Second, science is a process for gaining more knowledge and deeper understanding of nature in a way that ensures that the information can be tested and thereby accepted by everyone. Science as a process is also called the scientific method, which describes how scientists ideally go about observing, explaining, and predicting physical reality.

The scientific method (Figure 2-1) can begin in a variety of places, but most often it starts with people making observations or doing experiments. Observations of planetary orbits provided to Johannes Kepler enabled him to derive Kepler’s laws, which are presented later in this chapter. These equations then accurately predicted the paths of other bodies in the solar system, such as moons orbiting planets. Understanding why Kepler’s laws are correct required understanding the force of gravity. English physicists Robert Hooke and Isaac Newton proposed that the force of gravity decreases inversely with the square of the distance between any two objects, such as Earth and the Moon. (This means, for example, that if you double the distance, the force of gravity is four times weaker.) Newton went on to derive Kepler’s laws based on this assumption about the force of gravity. The force of gravity was thus added to the body of scientific knowledge and was then used to explain existing observations and to make predictions about previously unobserved motions.

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If a theory exists that purports to explain previous observations, new observations or experimental results are then compared with the predictions of the theory. If the new data and old theory are not consistent, then a hypothesis that modifies or replaces the existing explanation is proposed. (If no theory explains observations or experimental results, a new hypothesis is proposed to explain them.) Hypotheses on related topics that make accurate predictions are incorporated together as a scientific theory (often just called a theory). Scientific theories are presented in the form of mathematical equations and accompanying explanations.

An interesting example of beginning a scientific inquiry with equations, rather than observations or experiments, is the discovery of a particle called the Higgs boson. This particle is what causes matter to have mass, which in turn allows matter to interact gravitationally, among other things. In 1964, Scottish physicist Peter Higgs, along with other scientists, predicted the existence of this particle based on powerful equations that describe the properties of matter. Based on this prediction, experiments were run to discover the Higgs boson. Scientists believe that it was observed in July 2012, at the Large Hadron Collider in Switzerland.

In everyday conversation, a theory is an idea based on common sense, intuition, or deep-seated personal beliefs. Such theories neither originate in equations nor do they usually lead to rigorous predictions. The word theory in science has a very different meaning. A scientific theory is an explanation of observations or experimental results that can be described quantitatively (that is, in terms of equations) and tested formally. The mathematical description used in a scientific theory is considered a model of the real system. For example, Newton’s theory (or, in earlier usage, law) of gravitation is written as an equation that predicts how bodies attract each other. (The word gravity is often used as shorthand for gravitation, and both are used in this book.)

As just noted, to be considered scientific, a theory must make testable predictions that can be verified by making new observations or doing new experiments. Testing is a crucial aspect of the scientific method, which also requires that the theory accurately forecast the results of new observations in its realm of validity. Newton’s law of gravitation predicts that the Sun’s gravitational force makes the planets move in elliptical orbits, and it predicts how long it should take each planet to orbit the Sun. As we will see shortly, observations have confirmed most of these predictions.

For a theory to be considered scientific, it must also be potentially possible to disprove it. For example, Newton’s law of gravitation can be tested and potentially dis-proven by observations and thus qualifies as a scientific theory. The idea that Earth was created in 6 days cannot be tested, much less disproved. It is not a scientific theory but rather a matter of faith.

One important theme in science is to look for patterns that allow seemingly unrelated events or activities to be explained by one theory. For example, Newton observed that the Moon’s motion around Earth had the same behavior as the motion of a flying cannonball. Indeed, if you fired a cannonball fast enough, it would orbit Earth just as the Moon does. He hypothesized that they were both responding to Earth’s gravitational attraction, which led to his successfully applying the same equations to describe their motions. The motion of the planets around the Sun, he found, could also be described by the same equations. One theory. Three applications. Very satisfying! It is worth noting that Newton’s theory of gravity has since been applied successfully to myriad other situations.

Science strives to explain as many things as possible with as few theories as possible. As another example, we see billions upon billions of objects in the universe. It would be virtually impossible to study all of them separately so that we could come up with detailed descriptions of each one. Fortunately, individual theories explaining each object are not necessary. Scientists overcome this problem by noting that many of the bodies in space appear similar to each other. By categorizing them suitably and then applying the scientific method to these groups of objects, we form a few theories that describe many objects and how they have evolved. These few theories can then be tested and refined as necessary. Such groupings of objects have proven invaluable, and they give us insights into the structure and organization of billions of stars and galaxies that are, indeed, very similar to one another.

Often several competing theories describe the same concepts with the same accuracy. In such cases, scientists choose the simplest one—namely, the theory that contains the fewest unproven assumptions. That basic tenet, formally expressed by the philosopher and Franciscan friar William of Occam in the fourteenth century, is known as Occam’s razor. Indeed, the Sun-centered cosmology as refined by Johannes Kepler, which we are about to explore, was appealing because it made the same predictions within a simpler model than did the earlier Earth-centered cosmology. Remember Occam’s razor.

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If the predictions of a theory are inconsistent with observations, the theory is modified, applied in more limited circumstances, or discarded in favor of a more accurate explanation. For example, Newton’s law of gravitation is entirely adequate for describing the motion of an apple falling to Earth, the flight of a soccer ball, or the path of Earth orbiting the Sun; however, it is inaccurate in describing the orbit of Mercury around the Sun or the behavior of matter in the vicinity of very dense concentrations of matter, like black holes. In these cases, Newton’s law of gravitation is replaced by Einstein’s theory of general relativity, which describes gravitational behavior more accurately and over a much wider range of conditions than Newton’s law but at the cost of much greater mathematical complexity. (The Global Positioning System, or GPS, requires such accurate measurements that scientists must include general relativity in the equations used to determine the locations of GPS satellites orbiting Earth.)

The scientific method can be summarized in six words: observe, hypothesize, predict, test, modify, economize. I urge you to watch for applications of the scientific method throughout this book. Our first encounter with it is the discovery that Earth orbits the Sun.