Tracking Venus and Earth over 8 years

I came about this tweet:

It reminded me strongly of the waning moon and linear mod art projects that I’ve been playing with.

For instance, here’s a screenshot from the waning moon (specifically y = 56x)
A quick intro: the picture above was made by taking 360 points around a circle, and shifting them by the function (y = 56x), and then graphing a line between the input and output. If the output is greater than 360, then take the remainder after dividing by 360.
pent drift
From lunar planner.

And from John Carlos Baez’s blog:

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

224.701 / 365.256 ≈ 0.615187

Earth years. And here’s the cool coincidence:

8/13 ≈ 0.615385

That’s pretty close! So in 8 Earth years, Venus goes around the Sun almost 13 times. Actually, it goes around 13.004 times.

2015-05-19 13h39_41
Hey do you recognize what that ratio is close to?

Anyway, there’s a lot to investigate here. How is the function y = 56x related to these planetary orbits?

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