The laws under which the planets move were discovered through the genius
of John Kepler, and are known as Kepler’s Laws of Planetary Motion.
Kepler derived these laws from observation only, but Newton first
explained them by showing that they were the necessary consequences of
the laws of motion and the law of universal gravitation.
KEPLER’S FIRST LAW states: “The earth and the other planets revolve
in ellipses with the sun in one focus.”
KEPLER’S SECOND LAW states: “The radius vector of each planet moves
over equal areas in equal times.”
KEPLER’S THIRD LAW states: “The squares of the periodic times of the
planets are in proportion to the cubes of their mean distances from
the sun.”
[Illustration: =DIAGRAMS ILLUSTRATING KEPLER’S FIRST TWO LAWS OF
PLANETARY MOTION=
The diagram on the top illustrates the ellipse, and explains the first
and second laws. The picture-diagram on the bottom illustrates the
second law, which is that, as the planet moves round the sun, its radius
vector describes equal areas in equal times. That is to say, a planet
moves from A to B in the same time as it takes to move from C to D.]
These laws cannot be fully understood without some acquaintance with
mathematics. They may, however, be briefly explained for the
comprehension of the non-mathematical reader. The figure in the
diagram is an ellipse--what is known in popular language as an
oval--which is symmetrical about the line AB, known as its major
axis. It has two foci, S and S₁. The fundamental law of the ellipse
is that if we take any point P on it, and join this point by a
straight line to the two foci, then the sum of these two lines SP
and S₁P is always the same--SP + S₁P = C.
The second law is rather less easy to understand. The _radius
vector_ is the line joining the sun to the planet at any moment; if
we suppose the sun to be at the focus S, and P to be the planet, the
radius vector at various positions of the planet will be represented
by the lines SP, SP₁, SP₂, and so on. If the positions P, P₁, P₂,
and so on, represent those which the planet occupies after equal
periods of time--say, once a month--then the sectors of the ellipse
bounded by each pair of lines, SP and SP₁, SP₁ and SP₂, will be
equal. If a planet were to move in a circle round the sun, it is
obvious that this law would imply that it moved with a uniform
speed; but since the curvature of the ellipse varies in every part
of its course, so must the speed of the planet, in order that its
radius vector may describe equal areas in equal times. The planet
will, in fact, be moving faster when it is near the sun, as at P,
than when it is far off from the sun, as at P₂.
The third law shows that there is a definite numerical relation
between the motions of all the planets, and that the time which each
of them takes to complete its orbit depends upon its distance from
the sun.
On his discovery of his third law Kepler had written: “The book is
written to be read either now or by posterity--I care not which; it may
well wait a century for a reader, as God has waited six thousand years
for an observer.” Twelve years after his death, on Christmas Day, 1642,
near Grantham, England, the predestined “reader” was born. The inner
meaning of Kepler’s three laws was brought to light by Isaac Newton.