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We can observe Venus traveling in front of the Sun during a Venus transit. These transits occurs when The Sun, Venus and the Earth will be on an straight line in space (see below figure). |
Source : Solar System Simulator of NASA
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Venus transits occur in pairs, 8 years separated, alternately in June and December. After two June transits it will take 105½ years until the next pair of transits, in December, will occur. Then again it takes 121½ years before the June transits occurs etc. (see below figure). |
Source : Transit of Venus Bibliography
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The period between two corresponding transits is therefore 243 years (105½+8+121½+8=243). How can we explain this periodicity? A Venus transit only occurs when Venus moves between the Sun and the Earth, this is called an "inferior conjunction". The time period between two inferior conjunctions is called the "synodic period" and this is the key to the solution. Calculation of the synodic period of Venus The Earth completes one orbit (360°) around the Sun in 365,256 days and Venus does the same in 224,701 days. This means that the Earth moves 0,986° per day and Venus moves 1,602° per day. Each day Venus will move 1,602°-0,986°=0,617° away from the Earth. In order to go from one inferior conjunction to the next inferior conjunction Venus needs 360/0,617=583,923 days. Therefore the synodic period of Venus is 583,923 days. Not every inferior conjunction results in a Venus transit because of the difference in inclination (3,39°) between the orbits of the Earth and Venus (see figure). |
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If we look to the figure above we can see that a transit only can occur when the inferior conjunction will take place at the moment Venus crosses the plane of the Earths orbit because only then the Earth, the Sun and Venus are on one straight line. In all other cases Venus will be just above or under the solar disk during an inferior conjunction.
The points where the orbit of Venus crosses the plane of the orbit of the Earth are more or less fixed in space and occur on December 9 and June 7. Therefore the transits always occur at the beginning of June and the beginning of December. To complete we need to explain why it takes 8, 105½ and 121½ years between transits. |
Inferior Conjunction during 5 synodic periods
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In above picture we can see that after 5 synodic periods (8 years) the inferior conjunction occurs not exactly on the same place. 5 synodic periods are 2919,61 days 8 years are 2922,05 days The 5th synodic period ends 2,44 days before the 8 years, after the first synodic period, are completed. Therefore the next inferior conjunction moves 2,4° to the east and so on. Due to the distance between Venus and the Earth during inferior conjunction and the inclination (3,39°) of the orbit of Venus the path of Venus moves approximately 21' to the north regarding to the previous one. If we look to the 2004 event we see that the path of Venus over the Sun lies 11' below the center of the solar disk. For the 2012 event this means that the path of Venus will be 21'-11'=10' above the center of the solar disk. Due to the diameter of the solar disk (31') also then we can observe a Venus transit. The difference between the 105½ and 121½ years period occurs due to the elliptical shape of the orbits of Venus and the Earth. Due to the second law of Kepler a planet moves faster if it's closer to the Sun and therefore the period between the June transits and the December transits is 105½ years and the period between the December and June transits is 121½ years. |