The pentagram of Venus

The pentagram of Venus

Venus, our sister planet, orbits closer to the sun than Earth. Specifically, while the average Earth-Sun distance is 1 AU (approximately 150 million Km), the average Venus-Sun distance is 0.723 AU. This difference causes Venus to orbit the sun faster than Earth: while a terran year lasts approximately 365.2 terran days, the venerian year lasts approximately 224.7 terran days—interestingly this is only 0.924 venerian (sidereal) days! Now, the fraction 365.2 / 224.6 is very close to 13 / 8, which means that every 8 terran years the orbits of Venus and Earth complete one cycle, in which Earth orbits the sun 8 times and Venus 13 times. Additionally, Venus approaches Earth 5 times forming a beautiful 5 petal pattern known as the Pentagram of Venus. Here, we see a simulation of the 8 (terran) year cycle from two viewpoints: one with a fixed Earth in the center and another one with the sun at the center. When the Earth is fixed, Venus draws its trajectory from Earth's viewpoint, when the sun is fixed, a trajectory is drawn from the midpoint of the line connecting the two planets.