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Periodicity Domains and the Transit of Venus

Andrew J. Simoson
The American Mathematical Monthly
Vol. 121, No. 4 (April 2014), pp. 283-298
DOI: 10.4169/amer.math.monthly.121.04.283
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Page Count: 16
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Periodicity Domains and the Transit of Venus
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Abstract A transit of Venus occurs when it passes directly between the Earth and the Sun. A straightforward linear algebraic model for the orbits of Earth and Venus—essentially using one parameter, namely, the relative angular velocity σ of Venus—is powerful enough to generate respectable transit year predictions. We generalize, allowing σ to vary; uncover an algebraic analog for predicting transits; and show that time cycles for transits are what they are because each σ is sufficiently close to a suitably simple rational number, which for Venus is 13/8 , and which in turn induces a modulo 8 shuffling of successive transit years by a factor of 3.

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