Periodicity of Mars-Venus Conjunctions

I wrote explicitly about Mars-Venus conjunctions in a post titled Mars-Venus on January 27th 2017. However, I've also referred to the topic in Synodic Periods on March 30th 2017 and Mars: A Close Approach and Retrograde Motion of Planets on August 4th 2018. Today (July 13th 2021), when Mars is once again conjunct Venus, I thought it was time to revisit the topic. In this conjunction, the latitudes of these two planets are very close, 1°39' versus 1°11' north latitude. Their longitudes become identical 19°48'57" at 8:33pm, Jakarta time. See Figure 1.

Figure 1

Adapted from Stellarium, Figure 2 shows the view from Jakarta looking to the West about 6:30pm on July 13th 2021. The star Regulus is quite near to the Moon, being at a latitude of 0°08' of Virgo.

Figure 2

This would be the first of three conjunctions of Venus and Mars. The next two conjunctions of Mars and Venus are slated to take place on February 12, 2022 and March 12, 2022. These three form what is called a triple conjunction defined as:

A triple conjunction is an astronomical event where two planets or a planet and a star meet each other three times in a short period, either in opposition or at the time of inferior conjunction, if an inferior planet is involved. The visible movement of the planet or the planets in the sky is therefore normally prograde at the first conjunction, retrograde at the second conjunction and again prograde at the third conjunction. Source.

Figure 3 shows another view of what the first conjunction might look like:

Figure 3

Venus-Mars repeated conjunctions occur every 32 years (plus 0.5 to 4.5 days). During that time, 15 to 17 different conjunctions occur with nearly each one repeating in turn. Some series last >1200 years (up to 40 events). Others are considerably shorter. At the beginning and end of these series, the interval can be one week longer than 32 years. The reason why this happens is because for nearly every 20 times Venus returns to its similar position in the sky, Mars completes almost 15 returns. If these cycles were exactly whole numbers, the repeated conjunctions would last much longer.

This can be confirmed by looking ahead to 2053 and seeing how Mars and Venus are positioned. We find that Mars and Venus are again conjunct in 23°26' of Leo at 7.42pm on July 14th 2053. This is less than 4° from the July 13th 2021 position in 19°49' of Leo. See Figure 4. Remarkable!

Figure 4: Mars-Venus conjunction 2053

Going back to 1989, we find the the two planets were conjunct in 16°17' of Leo at 12:21am on July 13th 1989. This  is about 3.5° behind the 2021 position. See Figure 5.

Figure 5: Mars-Venus conjunction 1989