## Transits of Venus

Venus's orbit is inclined slightly with respect to Earth's, by 3.394 degrees. But there are two points in the orbit where Venus will cross the ecliptic traveling north (ascending node) or south (descending node). If Venus reaches inferior conjunction within about forty hours of crossing a node, its orbital path will carry it across the face of the Sun creating what is called a transit. Transits of Venus are exquisitely rare events. They can only occur if Venus passes inferior conjunction and crosses the node of its orbit within about two days of each other. So if inferior conjunction occurs within a four-day wide window in early June or early December, then a transit will occur. Since the time of inferior conjunction backs up by about two days with each eight-year cycle of apparitions, transits usually occur in pairs spaced eight years apart. A transit occurred with Venus just past the descending node of its orbit on June 8,2004 and another will occur just prior to Venus reaching the descending node on June 6, 2012. These transit pairs are spaced by 122 years. The last transits prior to 2004 were in 1874 and 1882, respectively. Transit pairs take place on opposing sides of the Sun at each cycle. The 1874 and 1882 events were at the ascending node and took place in December. The next pair on December 11, 2117 and December 6, 2125 will also be ascending node events. If however a transit occurs right on the node, the rate at which inferior conjunction will regress on the calendar is greater than the radius of the transit window of opportunity can contain and in such a case there will only be a single transit in the cycle. The time between the first ascending node transit of one cycle and the first ascending node transit of the next such pair is called the Venus Cycle and lasts 243 years. The two pairs of transits are not precisely spaced. The time between the first ascending node transit of one pair and first descending node transit of the next pair is always 129.5 years while the time from the first descending node transit to the first ascending node transit of the following pair is always 113.5 years.

The same resonant motion of the two planets that we have been discussing is what causes transits to occur in such a regular cycle. Since the planet repeats the same five apparitions basically over and over again, there are five points along the orbits of both planets where inferior conjunction occurs. These five points form a pentagon shape in space. The fourteen-to-eight resonance of the two planets is not quite that precise. The time between the June 2004 and 2012 inferior conjunctions is actually 7.997 years, not eight years. As a result of this, the point of each inferior conjunction on the pentagon slowly drifts westward around the Sun with each cycle. Each 243 years, one of the pentagon points will drift past each one of Venus' nodes enabling two transit sets to occur. One pair will be at the descending node in June and the next pair at the ascending node in December. Over the course of thousands of years, the passages drift away from the previous locations. For example each 243 years, the path followed by the 2004 and 2012 transits will slowly drift northward until the 2012 path drifts off the Sun entirely and the 2004 path will be nearly at the center of the Sun's disk. When this occurs, the pentagonal point for the next passage will drift too far away from the node after the eight-year cycle and no second transit can occur. This last occurred in the year AD 60 and will next occur in 3956.

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