distance from the Sun, I came to the conclusion that this force must be something substantial.”

Thus, what ultimately changed Kepler’s opinions on these matters was the realization that planetary motion could be explained through simple mathematical rules. This revelation came through a systematic study of the orbital behavior of the planet Mars and generalizing these results to other bodies in the solar system. Kepler discovered that each planet travels along an elliptical path around the Sun, sweeping out equal areas (of the region inside the ellipse) in equal times. He also found relationships between each planet’s orbital period and its average distance from the Sun. These discoveries, known as Kepler’s laws, led him to conclude that rock-solid mathematical principles, not ethereal spiritual influences, govern celestial mechanics.

Picking up where Kepler left off, Isaac Newton brilliantly revealed the mainspring of this clockwork cosmos. He discovered that the same force that guides acorns down from oak trees and cannonballs down to their targets similarly steers the Moon around Earth and the planets around the Sun. Calling this force gravitation, from the Latin gravitas or heavy, he showed that it exerts an attractive pull between any pair of massive objects in the universe. The Moon, for instance, is pulled toward Earth just like a ripe fruit from its branch. Earth is similarly drawn toward the Moon—which explains the movements of the tides.

Newton further demonstrated that the strength of gravity varies in inverse proportion to the square of the distance between any two masses. That is, if two objects are flung twice as far away from each other, their gravitational attraction drops by a factor of 4. This reduction in strength with distance explains why the Moon, rather than any of the stars (as massive as they are by comparison), lifts and lowers Earth’s ocean waters.

Some contemporary believers in astrology have asserted that the marching parade of constellations exerts a changing gravitational influence on the temperaments of children born under these signs.

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