# Introduction

1. Since the size of the Earth's shadow on the Moon during a lunar eclipse is approximately the same size as the Earth itself, the rays of the Sun must be essentially parallel when they hit the Earth.
2. This means that the angle intercepted by the Sun's rays by the Earth must be very small.
3. This in turn means that the distance from the Earth to the Sun must be very large compared to the distance from the Earth to the Moon.
4. Since the Sun appears larger than the Moon, it must be very much larger than either the Earth or the Moon.
His common sense told him that it is much more likely for a small object to rotate around a larger object than vice versa. Aristarchus was condemned by those who felt they should be at the center of the universe, and eighteen centuries passed before Nicholas Copernicus felt compelled to reexamine his theory.
1. A planet orbits the Sun in an ellipse; the Sun is at one of the foci.
2. Equal area sectors of the ellipse are swept out by the orbit of a planet in equal times.
3. The period of a planet's orbit is mathematically related to its distance from the Sun.
It is important to note that Kepler came to these conclusions in spite of the fact that his own and the prevailing religious beliefs of the time were in contradiction.
F = G myou mEarth / r2
We will study Newton's theory, which only ceases to be an accurate description of astronomical phenomena in the face of the developments and demands of technology in the last century. As Albert Einstein discovered in 1915, Newton's theory is a special case of the more comprehensive General Theory of Relativity.

Einstein's theory was developed without the benefit of observational data. He used the mathematical language of geometry and elegantly simple thought experiments about accelerating coordinate systems, and concluded that the presence of mass curves space and freely falling objects follow geodesics (the equivalent of straight lines) in the curved space:

Einstein's theory was subsequently verified by observations, and is the basis of all of the more speculative modern theories involving gravity. Its accuracy is required to explain the details of planetary orbits, to plan space missions and for the implementation of the Global Positioning Satellite system.

This short history of our understanding of the structure of our solar system and the reasons it behaves the way it does provides us with a model for describing the science of physics.

### Physics as a Science

In a somewhat recursive definition, we can say that physics is the study of physical phenomena. As such, its influence is far reaching; in many ways, it provides the fundamental basis for both chemistry and biology. The primary emphasis of this text is the application of physics to problems in those fields. We will see how physics explains the chemical structure of atoms and describes some of the characteristics of chemical reactions. We will also use physics to understand the mechanisms of the human body.

But the bulk of our example was intended to illustrate physics as a science. All science is based on observation: empirical data provides both the motivation for constructing theories and the evidence supporting them. A scientific theory has a domain of application: the theories used to describe subatomic processes are irrelevant when applied to planets. But within its domain of applicability, a scientific theory must not contradict relevant and consistent observational data.

Physics is unique in its use of mathematics as its fundamental language. Different scientists at different times and locations may perform the same experiment with seemingly different results, but if there is a consistent mathematical transformation from one set of results to the other, we find the data in agreement. Similarly, two theories which look very different may in fact be equivalent when a transformation is found which relates their mathematical formulations. Physical theories must be representable using mathematics; it is the basis of their legitimacy.

All science builds upon the work of previous scientists. A scientific theory is not merely a good idea; it is a good idea formulated by a person who is familiar with all of the work done by the scientists before them who thought about the same things. Scientific theories are rarely struck down, due to both the extensive training and immaculate honesty of the scientist. It is much more usual for a theory to be subsumed as a special case of a more general theory, or for a theory to be expanded to a larger domain of applicability.

And as demonstrated time and again in the history of science, a scientist does not allow emotional or political considerations to influence either the data or the theories which explain it. Science in general and physics in particular are concerned with the objective truth: just as an observation must not depend on the identity of the observer, a theory must not depend on beliefs, but upon careful mathematics and rigorous logic.