TWICE IN A LIFETIME FREQUENCY OF VENUS TRANSIT Abhimanyu Chawla Department of Physics, Panjab University, Chandigarh Contents Frequency of Venus Transits Synodic Period Demonstration Activity Frequency of Venus Transits Come in pairs that are eight years apart Followed alternately by spans of 121 ½ years and 105 ½ years. Hence twice in a lifetime! But why is it so rare? Synodic Period Time required for a planet to move from a certain position, with respect to the Sun, back to that same position as seen from Earth. Synodic Period For Earth: 365 days 360 degrees Hence, in one day 360/365 = 0.986 degrees For Venus: 225 days 360 degrees Hence in one day 360/225 = 1.6 degrees Synodic Period Each day Venus gains (1.6-0.986) degrees on Earth (1.6-0.99) degrees in 1 day, So 360 degrees in 360/(1.6-0.986) = 586 days = 1.6 years This is the Synodic Period of Venus: After every 1.6 years, Venus comes in the same position w.r.t the Sun, as seen from the Earth. Activity Two factors Inclined Orbit The orbit of Venus is tilted about 3.394° with respect to the orbit of Earth Orbital Speed Time taken by Venus to complete a lap is not exactly 8/13th the time by Earth, rather 7.997/13 Inferior Conjunctions shift clockwise.