# Explanation for the mathematics behind Venus' retrograde motion

I've always been interested by the pattern within Venus' orbit around the sun. I found this image and formula of its retrograde motion in the upper right hand corner which confused me. What does it mean? can someone break this down in layman's terms?

Thank you

• @Omen This question is about Venus' revolution around the Sun, not its rotation about its own axis, so not a duplicate, methinks. OP, are you confused that Venus has retrograde motion (like the outer planets) or that it forms such an interesting pattern long term?
– user21
Commented Nov 4, 2014 at 20:46
• That's the formula for the Golden Ratio en.wikipedia.org/wiki/Golden_ratio Commented Nov 5, 2014 at 9:30
• @barrycarter Well not sure what is surprising about retrograde motion. Didn't know that was particularly odd for outer planets. This was more out of curiosity of mainly about mathematics involved within it's patterns. Commented Nov 8, 2014 at 2:11
• I was taught that only the outer planets exhibited retrograde motion. Recently (but before this question was asked), I learned that the inner planets also exhibit retrograde motion, but we can't normally see it because it occurs near their inferior conjunction.
– user21
Commented Nov 8, 2014 at 15:59

The really simple explanation is that Venus' orbital period is 225 days. Earth's is 365 days.

That ratio is 13:8 (well, more accurately 12.9777777777..:8) so you can see that your complete cycle is 13 orbits of Venus to 8 of Earth, but within that cycle our view of Venus travelling round the sun gives the pretty pattern as shown in your image.

This YouTube video is quite a nice visualisation - should make it easy to understand.