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Ludi Saeculares: the Transit of Venus

Vinay

On June 5 (or June 6, depending on which time zone you are in) of 2012, Venus will be seen from the Earth passing over the disk of the Sun. This is not only a rare event, but also one which has been of great historical importance in figuring out how big the Solar System is. A number of people all over the world, both amateurs and professionals, are making preparations to observe this event. Go to www.transitofvenus.org for a summary of what is cooking. You can even download an app on your smartphone to participate in a worldwide effort to time the transits.

The transit of Venus always occurs in a pair, separated by 8 years. The next pair then repeats a century later. This year’s transit happens to be the second of this cycle’s pair. The previous one occured in June 2004. The next pair will occur in December 11 2117 and December 8 2125.

The reason for this odd periodicity lies in the geometry and dynamics of the Solar System. First, note that the orbital period of Venus (i.e., a Venusian year) is 224.65 days, and for the Earth of course it is 365.24 days. So in the time that it takes the Earth to go around the Sun once, Venus would have done so 1.6 times. This ratio is approximately 13/8. That is, after the Earth has done 8 full orbits, Venus would have done 13, and both planets would be back where they started relative to the Sun.

Of course, during these eight years, Venus would have crossed the Sun-Earth line 13 times, so we should have seen 13 transits, right? No, because the orbit of Venus is tilted by 3.4 degrees relative to that of the Earth’s. It’s orbital plane cuts across Earth’s along a line (called the line of nodes) which the Earth happens to cross in June and December. Now, the diameter of the Sun as seen from the Earth is only half a degree, so for Venus to get in between the line of sight from the Earth to the Sun, it can be at most a quarter of a degree away from the orbital plane of the Earth. So transits of Venus can only occur when Venus is close to the line of nodes. As we have seen, if it happens once, we will have to wait 8 years for the next one.

But then why does it not keep happening every 8 years? Why is this the last transit of our lifetimes? Well, first of all, the 8 year period is not exact, and Venus shows up at slightly different locations every cycle. Second, there is a slight drift in the line of nodes as the orbit of the Earth circularizes. So the Sun-Venus-Earth line will not have quite reached the exact same configuration as the previous conjunction, and will have lagged a little bit, and Venus will not be at the same position for transit as before. After another 8 years, it will have drifted sufficiently far away that it no longer transits the disk of the Sun. But as it continues to drift, by approximately half a degree every 8 years, it drifts up its inclined orbit for 3.4 degrees and back down again to the other node, in about 14 8-year cycles, and so in slightly more than a century, we can expect the pair pattern to repeat.

Here is a nice 2-minute explanation, with paper plates, of how it works (from transitofvenus.org/):

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