When it comes to the Sun and Moon, our experiences of these bodies is visceral enough that the wax and wane of their power needs no explanation. Mercury and Venus, however, are simply two dots in the sky to the untrained eye. The moment when these two planets are closest to the Earth is known as the inferior conjunction. At this time, those planets “pass” the Earth and appear to move backwards in the sky.

Here we come to an important side note in our derivations. Retrogrades have been known for ages as times when the planets powers are turned around, and here we come to a personal choice. One the one hand, the inferior conjunction as the peak of power maintains the idea that proximity to earth is directly correlated to power of influence. It updates notions of planetary power past the rudimentary understanding Europe had in the 1500’s.

On the other hand, there is something to be said for the power of tradition, and astronomy has its own internal logic: that the appearance of things moving across the sky is what dictates their power.

For the foreseeable future, I will be using the idea that physical proximity directly correlates to power of influence. Following this, the inferior conjunction of Mercury and Venus, the retrogrades, are the peak of their powers.

Mercury is known to multiple cultures as “traveler” due to how fast it moves in the sky. Being the fastest, it also governs communication and commerce along with travel. For this reason, I have chose this to use for an incantation.

There are two sets of numbers significant to Mercury. First, there are 3 Mercury days for every 2 Mercury years. Here we find the ratio of 2:3 to be important. Then Mercury’s synodic period, the amount of time it takes Mercury to return to the same place in Earth’s sky, is 116 Earth days. The 2:3 ration gives us the fundamental rhythm of Mercury; the synodic period gives us the timing that connects Mercury to Earth. 116 factors into 2*2*29. Using this information, we derive the circle.

Venus’s magical associations are often tied to its brightness in the sky, particularly, to how it shines at sunrise and sunset. For that reason, I am using this as my incantation.

Following the pattern we set at Mercury, we are interested in Venus’ synodic period and the ratio between its days and years. Venus takes 243 earth days to rotate once on its own axis, and 225 earth days to go around the sun. This gives us a ratio that’s sufficiently close to 1 that I don’t see a need to include it in the derivation of the circle. The synodic period, which ties Venus to the magician on Earth, is 584 earth days. This factors to 2*2*2*73 and gives us a five pointed inner polygon.

You could also use the naturally occurring Pentagram of Venus.

I would like to make it clear that the circles can still be used on a traditional astronomical calendar. It is my personal choice not to do so. Also, as a small safety reminder, these have not been tested as much as they need to be. I am still in the early phases of making these, even though it has taken me years to even get this far.