The Harmonies of the World

The Harmonies of the World

Johannes Kepler understood many things by the word harmony: the order and beauty of planetary motion – an idea that goes back to Pythagoras – and even harmony in the musical 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 observe the motion of the other planets against the backdrop of distant constellations. The inner planets move rapidly in their orbits – that is why 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 third and 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: P2 – a3, where P represents the period of revolution of the planet about the Sun, measured in years, and a the distance of the planet from the Sun measured in “astronomical units”.

An astronomical unit is the distance of the Earth from the Sun, and a3= 5x5x5=125. What number times itself equals 125? Why, 11, close enough. And 11 years is the period for Jupiter to go once around the Sun. A similar argument applies for every planet and asteroid and comet.

Astronomy is part of physics, astrology is part of metaphysics. Image: Zesty Gorgeous Pretty Beautiful Stunning Breathtaking by © Meg Jorgensen (Elena)

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.

Kepler’s first law: A planet moves in an ellipse with the Sun at one of the two foci.

Kepler’s second law: A planet sweeps our 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 areas are all equal.

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.