Cosmos by Carl Sagan Page A

Book: Cosmos by Carl Sagan Read Free Book Online
Authors: Carl Sagan
sense, the “harmony of the spheres.” Unlike the orbits of Mercury and Mars, the orbits of the other planets depart so little from circularity that we cannot make out their true shapes even in an extremely accurate diagram. The Earth is our moving platform from which we observethe motion of the other planets against the backdrop of distant constellations. The inner planets move rapidly in their orbits—that is why Mercury has the name it does: Mercury was the messenger of the gods. Venus, Earth and Mars move progressively less rapidly about the Sun. The outer planets, such as Jupiter and Saturn, move stately and slow, as befits the kings of the gods.

    Kepler’s second law: A planet sweeps out equal areas in equal times. It takes as long to travel from B to A as from F to E as from D to C; and the shaded areas BSA, FSE and DSC are all equal.
    Kepler’s third or harmonic law states that the squares of the periods of the planets (the times for them to complete one orbit) are proportional to the cubes of their average distance from the Sun; the more distant the planet, the more slowly it moves, but according to a precise mathematical law:
2 =
3 , where
represents the period of revolution of the planet about the Sun, measured in years, and
the distance of the planet from the Sun measured in “astronomical units.” An astronomical unit is the distance of the Earth from the Sun. Jupiter, for example, is five astronomical units from the Sun, and
3 = 5 × 5 × 5 = 125. What number times itself equals 125? Why, 11, close enough. And 11 years
the period for Jupiter to go once around the Sun. A similar argument applies for every planet and asteroid and comet.
    Not content merely to have extracted from Nature the laws of planetary motion, Kepler endeavored to find some still more fundamental underlying cause, some influence of the Sun on the kinematics of worlds. The planets sped up on approaching the Sun and slowed down on retreating from it. Somehow the distant planets sensed the Sun’s presence. Magnetism also was an influence felt at a distance, and in a stunning anticipation of the idea of universal gravitation, Kepler suggested that the underlying cause was akin to magnetism:
    My aim in this is to show that the celestial machine is to be likened not to a divine organism but rather to a clockwork …, insofar as nearly all the manifold movements are carried out by means of a single, quite simple magnetic force, as in the case of a clockwork [where] all motions [are caused] by a simple weight.

    Kepler’s third or harmonic law, a precise connection between the size of a planet’s orbit and the period for it to go once around the Sun. It clearly applies to Uranus, Neptune and Pluto, planets discovered long after Kepler’s death.
    Magnetism is, of course, not the same as gravity, but Kepler’s fundamental innovation here is nothing short of breathtaking: he proposed that quantitative physical laws that apply to the Earth are also the underpinnings of quantitative physical laws that govern the heavens. It was the first nonmystical explanation of motion in the heavens; it made the Earth a province of the Cosmos. “Astronomy,” he said, “is part of physics.” Kepler stood at a cusp in history; the last scientific astrologer was the first astrophysicist.
    Not given to quiet understatement, Kepler assessed his discoveries in these words:
    With this symphony of voices man can play through the eternity of time in less than an hour, and can taste in small measure the delight of God, the Supreme Artist … I yield freely to the sacred frenzy … the die is cast, and I am writing the book—to be read either now or by posterity, it matters not. It can wait a century for a reader, as God Himself has waited 6,000 years for a witness.
    Within the “symphony of voices,” Kepler believed that the speed of each planet corresponds to certain notes in the Latinate musical scale popular in his day—do, re, mi, fa,

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