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Periodicity of the transits of Venus

by Pierre Causeret last modified Jul 12, 2012 03:31 PM
Contributors: Dalida Halfaoui, Charles-Henri Eyraud

Venus revolves around the Sun in 224, 7 days and the Earth in 365, 26 days.
At steady intervals, Venus passes between the Earth and the sun which is called an inferior conjunction. But, seen from the Earth, Venus always passes below or above the sun as the plane of Venus’ orbit is inclined (of 3, 4°) to the plane of the Earth’s orbit (figure 1). This is the same phenomenon with the Moon; there is no solar eclipse at every new Moon.
The planes of the orbits of Venus and the earth cut themselves along a line called line of knots, in red in the figures below. We can observe a transit of Venus in front of the Sun if the inferior conjunction of Venus takes place on this line of knots or nearby.
As the earth passes at point A in early December and at point B in early June, these transits always occur in June or December.


1Transit_dessus.png 1Transit_transit.png
Fig. 1. we can see here from the Earth Fig. 2. here, we can observe a transit of Venus in front of the Sun


On June 8, 2004, the Earth, Venus and the Sun were lined up and we could observe Venus pass in front of the Sun (figure 3). Eight years later, on June 6, 2012, Venus will have revolved 13 times around the Sun and the Earth, 8 times. We have nearly the same positions and we will see again Venus pass in front of the Sun. In Europe, only the end of the transit will be visible at sunrise.

1Transit_8juin2004.jpg Fig. 3.The passage of Venus on June 8, 2044 photographed at 8.30 am.


But this interval of eight years is not steady. We can calculate that 8 revolutions of the Earth last 2 922 days whereas 13 revolutions last only 2 921 days. In 2020, after again 8 years, Venus will pass this time slightly to the north of the Sun because of this little gap.

On the other hand, a steadier period of 243 years exists which we can check by calculating the number of revolutions around the Sun made by Venus during this period.

By taking 365,256 days as a period of revolution for the Earth: 243 years 88 757 days.

With 224,701 days as period for Venus: 88 757 days 395 revolutions of Venus.

This period of 243 is made of 4 passages of Venus taking place every 8 years, 105,5 years or 121, 5 years as we can check thanks to the dates of passages between 1600 and 2120.


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