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Ptolemy's "Equant"

Astronomers in Kepler's day could observe that the planets moved fastest when they were closest or "in conjunction" to the Sun (measured in terms of degrees of arc in the sky) and slowest when farthest away or "at opposition" from it, on the opposite side of the Zodiac.

Planet orbiting the sun

Ptolemy explained the observed changes in a planet’s speed using a geometrical device he called the “equant.”

Planet orbinting with 'equant' shown

This “equant," according to Ptolemy, controls the speed of the planet--although neither he nor his followers were particularly clear about how this "worked." The "equant" is an imaginary mathematical point that "sees" the planet move at a uniform angular speed. 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.

What physical cause did Ptolemy's equant device approximate?

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