The (Almost) Venus-Earth Pentagram

Steven Dutch, Natural and Applied Sciences,University of Wisconsin - Green Bay
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In The Da Vinci Code, Dan Brown makes a big deal of the perfect five pointed star that Venus makes in the sky. What actually happens is 13 Venus revolutions equals eight earth years equals five synodic periods, or alignments of the Earth, Venus and the Sun. It's remarkable, but not perfect. On June 8, 2004, for example, Venus passed in front of the Sun, a transit. The next one will occur June 5-6, 2012, not quite eight years later. But the next time the cycle repeats (June 3, 2020) Venus and the Sun will once again be aligned as seen from the Earth, but Venus will miss the Sun. There will not be another transit until 2117.

In this animation, the region where Venus is above the earth's orbit (the ecliptic) is green and the region below is orange. The line of intersection is called the nodes. Only a very narrow window either side of the nodes permits transits, less than two days either side of Venus' passing its node. The windows of opportunity are colored yellow. After each conjunction, a red arrow moves to earth's location at the next conjunction, and a blue radius shows the alignment of Earth, Venus, and the Sun. Previous alignments are shown in light colors. You can speed up the animation using the Speed box. Start is self explanatory. Pause halts the animation so you can study it or change the speed. Stop resets it to zero.

Note: the orbits are approximated as circles, so this animation cannot be used for accurate preditions. The earth moves faster in December than June, so conjunctions don't occur with quite the regular spacings shown here.

If Venus inscribed a perfect five-pointed star, there would be a transit every five synodic periods. More than likely, there would never be a transit because none of the points of the star would ever line up with a node. But because there's a slight mismatch, the points of the star "walk" around the ecliptic. Right now we have pairs of transits eight years apart, then it takes over a hundred years for a point of the star to migrate to a node. Note that the nodes alternate. The 2004-2012 transits are in June, but the 2117 and 2125 transits are in December.

Transits don't repeat exactly, meaning points eventually migrate out of the transit window. When that happens, only a single lineup will occur in each window and there will be single transits. The last single transit was in 1396 and the next will be in 3089. But because the orbits of Earth and Venus are not perfectly circular, there are occasional double transits near the start and end of a single-transit epoch.

Also, because the points of the star migrate across the transit window, the interval between transits changes. Right now, transits occur 105.5 and 121.5 years apart. But after the next period of single transits ends, the long intervals will be different.

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Created 14 February 2012, Last Update 09 March 2012

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