Ptolemy's "Equant"
Although astronomers in Kepler's day could observe how the speed of a planet changed as it approached the position of the Sun on the celestial sphere. |
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They noted that the planets moved fastest when they were closest or "in conjunction" to the Sun and slowest when farthest away or "at opposition" from it, on the opposite side of the Zodiac.
While declining to state a physical cause, Ptolemy explained the observed changes in a planet’s speed using a geometrical device he called the “equant.”
This “equant” controls the speed of the planet. According to Ptolemy's formula, the "equant" is an imaginary mathematical point that "sees" the planet move at a uniform angular speed. However, because it is not located in the center of the orbit it "causes" the planet's actual speed on the orbit to change.
Kepler questioned how a planet could “know” to move at a constant rate around an empty point.
Yet as a computational tool, Ptolemy's "equant" worked surprisingly well.
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