Post by Centaur on Mar 9, 2009 2:36:58 GMT -6
Connecting the positions of Venus in its orbit at each successive inferior conjunction produces a pentagram. A pentagram is a five pointed star shape drawn with five strokes.
Draw a circle to represent the orbit of Venus with the Sun at the center. Mark a point on the circle as the position of Venus at its next inferior conjunction. Then mark Venus’ position at the following inferior conjunction, which will be clockwise with a mean value of about 144°. Connect those two positions with a straight line. Continue this five times and you will have drawn a pentagram. In reality, the result is not exact but close. After 8 years Venus has orbited the Sun 13 times and lapped the Earth 5 times. That lapping occurs about every 1.6 years and is the synodic period of Venus.
Over longer periods of time the pattern gets out of sync, causing the pentagram to slowly rotate. After 243 years the pentagram rotates by about 72° and appears near its original orientation. That’s also the period of time for the repeat of pairs of transits of Venus across the Sun during the same month of the year. Another pair of transits occurs approximately in the middle of that period at the opposite time of the year.
Below is a diagram I created to demonstrate the pentagram of Venus. The orbits are drawn with their true eccentricities. It begins with the transit of 2004 and connects Venus at each inferior conjunction until the transit of 2012. Inferior conjunctions occur each 1.6 years during which time the Earth has circled the Sun 1.6 times and Venus has done so 2.6 times.
Draw a circle to represent the orbit of Venus with the Sun at the center. Mark a point on the circle as the position of Venus at its next inferior conjunction. Then mark Venus’ position at the following inferior conjunction, which will be clockwise with a mean value of about 144°. Connect those two positions with a straight line. Continue this five times and you will have drawn a pentagram. In reality, the result is not exact but close. After 8 years Venus has orbited the Sun 13 times and lapped the Earth 5 times. That lapping occurs about every 1.6 years and is the synodic period of Venus.
Over longer periods of time the pattern gets out of sync, causing the pentagram to slowly rotate. After 243 years the pentagram rotates by about 72° and appears near its original orientation. That’s also the period of time for the repeat of pairs of transits of Venus across the Sun during the same month of the year. Another pair of transits occurs approximately in the middle of that period at the opposite time of the year.
Below is a diagram I created to demonstrate the pentagram of Venus. The orbits are drawn with their true eccentricities. It begins with the transit of 2004 and connects Venus at each inferior conjunction until the transit of 2012. Inferior conjunctions occur each 1.6 years during which time the Earth has circled the Sun 1.6 times and Venus has done so 2.6 times.