Venus Pentagram

Look down on the plane of the Solar System from above the Earth. Track the Earth so it always appears directly below you, but don't turn along with it. With the passage of each year, you will see the Sun go around the Earth. As the Sun goes around the Earth 8 times, Venus goes around the Sun 13 times, and traces out the pretty curve shown here. It's called the pentagram of Venus, because it has 5 'lobes' where Venus makes its closest approach to Earth. At each closest approach, Venus move backwards compared to its usual motion across the sky: this is called retrograde motion. Actually, what I just said is only approximately true. The Earth orbits the Sun once every days. Venus orbits the Sun once every days. So, Venus orbits the Sun in / ≈ Earth years. And here's the cool coincidence: 8/13 ≈ That's pretty close! So in 8 Earth years, Venus goes around the Sun almost 13 times. Actually, it goes around times. During this 8-year cycle, Venus gets as close as possible to the Earth about 13 -- 8 = 5 times. And each time it does, Venus moves to a new lobe of the pentagram of Venus! This new lobe is 8 -- 5 = 3