Foundations of Modern Cosmology

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Chapter 3: Newton's Machine

Chapter Summary Isaac Newton formulated the laws of mechanics that govern most motions in the universe. Newton's First Law is a definition of the conditions for inertial, or uniform, motion: a body at rest or in a state of uniform motion will remain at rest or in uniform motion unless acted upon by a net external force. Newton's Second Law defined mass as the connection between force and acceleration: the acceleration of an object is equal to the net force applied to it, divided by its mass. Mathematically, the Second Law can be expressed as F = ma. The First Law can be understood in terms of the Second: if the (net) applied force is zero, the acceleration is zero. (Newtonian phyics does not allow massless bodies.) Since acceleration is the rate of change of velocity with time, zero acceleration means that velocity does not change. Thus "uniform motion" can be seen to correspond to "constant velocity," where rest is a special case of constant velocity. Velocity, acceleration, force, and many other important physical quantities are vectors; that is, both their magnitude and their direction are important.

Newton's Third Law states: For every action there is an equal and opposite reaction. If a horse pulls a cart with a certain force, the cart pulls back upon the horse with the same magnitude of force, but in the opposite direction. How, then, can the cart move? In order to walk, the horse's hooves must push against the surface of the Earth. The Earth pushes back with a force that, at any instant, is equal in magnitude to the force exerted by the horse. The enormous mass of the Earth means that it acquires essentially no acceleration, whereas an equal magnitude of force results in a large acceleration for the horse. Newton's Third Law also explains how rockets work. Gas is forced by the engine through a nozzle, and the reaction force of the gas against the engine propels the rocket.

Once his laws of motion were in place, Newton could develop his Law of Universal Gravitation, which states that the gravitational force between two objects is proportional to the product of their masses divided by the square of the distance between them. The constant of proportionality is one of the fundamental constants of nature, the gravitational constant, symbolized by G. G was not first measured until nearly a century after Newton's death, and even today its value is known less precisely than the values of other important physical constants. Newton delayed publishing his results in part because he was forced to invent calculus in order to work out the results for the gravitational attraction of two extended bodies. Finally Edmund Halley persuaded Newton to publish his work. The book, Philosophiae Naturalis Principia Mathematica, appeared in 1687 and is one of the greatest scientific treatises ever written. In addition to revealing the laws of mechanics still used today, Newton was able to derive Kepler's laws, and to show that gravitational orbits must take the form of a family of figures called conic sections, of which the ellipse is one member. After the publication of the Principia, understanding of the universe increased dramatically; combined with breakthroughs in technology, the new science led to the era historians call the Enlightenment. One application of Newtonian physics was computed by Edmund Halley himself, who worked out an orbit for the famous comet that now bears his name.

The Newtonian cosmos was a majestic and deterministic clockwork. In principle, at least, a sufficiently powerful computer could compute the entire future of the universe from a knowledge of the initial positions and velocities. (Not until the twentieth century did scientists learn that gravitating systems of more than two bodies are chaotic, i.e. small differences in initial conditions lead to divergence of the solutions. Only for perfect knowledge can a prediction be made beyond some point in time; but perfect knowledge is unattainable in principle as well as in practice.) The clockwork universe and the new understanding of natural law influenced philosophy and theology. Many intellectuals of both Europe and North America embraced the ideas that natural laws governed human behavior in much the same way as they guided the motions of the planets, and that the universe was a majestic machine set in motion by a great Mechanic and left to evolve.

Nearly two hundred years passed before another major shift in thought occurred. As Newtonian physics had made possible an understanding of the true size of the solar system, geology and biology eventually led to a new appreciation of the age of the Sun and planets. Darwin and Wallace developed the theory of biological evolution late in the nineteenth century, before the age of the Earth had been determined. By the 1920's, radioactive decay had been employed to measure the age of the Earth to be very near to 4.5 billion years. This vast expanse of time not only forced humans to contemplate that most of the history of the Earth has taken place without our presence, but also allowed time over which biological evolution could occur.

Cosmology and Physics

The laws of physics provide the foundation for a particular cosmology. By the same token, discoveries about the nature of the universe must be consistent with the laws of physics. The heliocentric cosmology of Copernicus, as clarified by Kepler, led to the need for a new theory of motion. Newtonian mechanics, in turn, created a new vision for the cosmos, the Newtonian "clockwork" universe. Discoveries made toward the end of the 19th and the beginning of the 20th centuries led to the new physics of Einstein, and, in turn, to the modern Big Bang cosmology.

Points to Ponder

In thinking about the development of life on the Earth, as well as the implications of the Copernican principle, questions naturally arise about the likelihood of Life in the Universe.

Potential Pitfalls
Questions & Answers

Questions and Answers related to Chapter 3.

Web World

Go here for additional information about Isaac Newton.