Page 5 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 1
Kepler, and the Italian, Galileo Galilei – started publicly to support the Copernican theory, despite the fact that
the orbits it predicted did not quite match the ones observed. The death blow to the Aristotelian/Ptolemaic
theory came in 1609. In that year, Galileo started observing the night sky with a telescope, which had just been
invented. When he looked at the planet Jupiter, Galileo found that it was accompanied by several small
satellites or moons that orbited around it. This implied that everything did not have to orbit directly around the
earth, as Aristotle and Ptolemy had thought. (It was, of course, still possible to believe that the earth was
stationary at the center of the universe and that the moons of Jupiter moved on extremely complicated paths
around the earth, giving the appearance that they orbited Jupiter. However, Copernicus’s theory was much
simpler.) At the same time, Johannes Kepler had modified Copernicus’s theory, suggesting that the planets
moved not in circles but in ellipses (an ellipse is an elongated circle). The predictions now finally matched the
observations.

As far as Kepler was concerned, elliptical orbits were merely an ad hoc hypothesis, and a rather repugnant one
at that, because ellipses were clearly less perfect than circles. Having discovered almost by accident that
elliptical orbits fit the observations well, he could not reconcile them with his idea that the planets were made to
orbit the sun by magnetic forces. An explanation was provided only much later, in 1687, when Sir Isaac Newton
published his Philosophiae Naturalis Principia Mathematica, probably the most important single work ever
published in the physical sciences. In it Newton not only put forward a theory of how bodies move in space and
time, but he also developed the complicated mathematics needed to analyze those motions. In addition,
Newton postulated a law of universal gravitation according to which each body in the universe was attracted
toward every other body by a force that was stronger the more massive the bodies and the closer they were to
each other. It was this same force that caused objects to fall to the ground. (The story that Newton was inspired
by an apple hitting his head is almost certainly apocryphal. All Newton himself ever said was that the idea of
gravity came to him as he sat “in a contemplative mood” and “was occasioned by the fall of an apple.”) Newton
went on to show that, according to his law, gravity causes the moon to move in an elliptical orbit around the
earth and causes the earth and the planets to follow elliptical paths around the sun.

The Copernican model got rid of Ptolemy’s celestial spheres, and with them, the idea that the universe had a
natural boundary. Since “fixed stars” did not appear to change their positions apart from a rotation across the
sky caused by the earth spinning on its axis, it became natural to suppose that the fixed stars were objects like
our sun but very much farther away.

Newton realized that, according to his theory of gravity, the stars should attract each other, so it seemed they
could not remain essentially motionless. Would they not all fall together at some point? In a letter in 1691 to
Richard Bentley, another leading thinker of his day, Newton argued that this would indeed happen if there were
only a finite number of stars distributed over a finite region of space. But he reasoned that if, on the other hand,
there were an infinite number of stars, distributed more or less uniformly over infinite space, this would not
happen, because there would not be any central point for them to fall to.

This argument is an instance of the pitfalls that you can encounter in talking about infinity. In an infinite
universe, every point can be regarded as the center, because every point has an infinite number of stars on
each side of it. The correct approach, it was realized only much later, is to consider the finite situation, in which
the stars all fall in on each other, and then to ask how things change if one adds more stars roughly uniformly
distributed outside this region. According to Newton’s law, the extra stars would make no difference at all to the
original ones on average, so the stars would fall in just as fast. We can add as many stars as we like, but they
will still always collapse in on themselves. We now know it is impossible to have an infinite static model of the
universe in which gravity is always attractive.

It is an interesting reflection on the general climate of thought before the twentieth century that no one had
suggested that the universe was expanding or contracting. It was generally accepted that either the universe
had existed forever in an unchanging state, or that it had been created at a finite time in the past more or less
as we observe it today. In part this may have been due to people’s tendency to believe in eternal truths, as well
as the comfort they found in the thought that even though they may grow old and die, the universe is eternal
and unchanging.

Even those who realized that Newton’s theory of gravity showed that the universe could not be static did not
think to suggest that it might be expanding. Instead, they attempted to modify the theory by making the

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