Mechanics, Planetary Motion and the Modern Science Revolution 53
orbits using different geometrical forms. After many unsuccessful
attempts he finally discovered that the actual orbits of the planets are
ellipses with the Sun sitting at one of the two foci of the ellipse as is
shown in Fig. 6.2. This constitutes Kepler’s first law of planetary motion.
The eccentricities of the ellipses are very small so that they are almost
circular.
(^) ∆ 1
Fig. 6.2
He discovered that the same area is swept out by the planet in its
orbit in equal the orbits time intervals as is shown in Fig. 6.2. This is
Kepler’s second law of planetary motion. He also showed that the
orderly relation between the distance of planets from the Sun and the
period, T, of their orbit (the time to make one revolution) can be given a
precise mathematical statement namely the square of the period is
proportional to the cube of the distance, R, from the Sun to the planet
(T^2 = kR^3 ). (R is actually the length of the semi-major axis, which is
approximately the same as the distance between the Sun and the planet
because the ellipsisity of the orbit is not very great.) This is Kepler’s
third law of planetary motion. His three laws using a more technical
language may be summarized as follows:
(^) ∆ 1