related to gods. It seemed obvious that a perfect body must move in a perfect figure. Moreover,
since the heavenly bodies move freely, without being pushed or pulled, their motion must be
"natural." Now it was easy to suppose that there is something "natural" about a circle, but not
about an ellipse. Thus many deep-seated prejudices had to be discarded before Kepler's first law
could be accepted. No ancient, not even Aristarchus of Samos, had anticipated such an hypothesis.
The second law deals with the varying velocity of the planet at different points of its orbit. If S is
the sun, and P 1 , P 2 , P 3 , P 4 , P 5 are successive positions of the planet at equal intervals of
time-say at intervals of a month--then Kepler's law states that the areas P 1 SP 2 , P 2 SP 3 , P 3
SP 4 , P 4 SP 5 are all equal. The planet therefore moves fastest when it is nearest to the sun, and
slowest when it is farthest from it. This, again, was shocking; a planet ought to be too stately to
hurry at one time and dawdle at another.
The third law was important because it compared the movements of different planets, whereas the
first two laws dealt with the several planets singly. The third law says: If r is the average distance
of a planet from the sun, and T is the length of its year, then r^3 divided by T^2 is the same for all
the different planets. This law afforded the proof (as far as the solar system is concerned) of
Newton's law of the inverse square for gravitation. But of this we shall speak later.
Galileo ( 1564-1642) is the greatest of the founders of modern science, with the possible
exception of Newton. He was born on about the day on which Michelangelo died, and he died in
the year in which Newton was born. I commend these facts to those (if any) who still believe in
metempsychosis. He is important as an astronomer, but perhaps even more as the founder of
dynamics.
Galileo first discovered the importance of acceleration in dynamics. "Acceleration" means change
of velocity, whether in magnitude or direction; thus a body moving uniformly in a circle has at all
times an acceleration towards the centre of the circle. In the language that had been customary
before his time, we might say that he treated uniform motion in a straight line as alone "natural,"
whether on earth or in the heavens. It had been thought "natural" for heavenly bodies to move in
circles, and for terrestrial bodies to move in straight lines; but moving terrestrial bodies, it was
thought, would gradually cease to move if they were let alone. Galileo held, as against this view,
that