Eric David comments: “Now, my next project is going to be to print your two locus plots, Mars and Jupiter, on thin paper, then overlay them and trace the path of Jupiter onto the Mars plot, then scan the resulting plot on my scanner and view it on my computer to finally arrive at my long-envisioned diagram showing at what two regions of the ecliptic zone Mars and Jupiter could theoretically have very close mutual oppositions. I promise to leave this subject alone now so that you may move on to other topics in peace.”
That was two days ago (had to get on with some other things yesterday). Hoping to be in time to save Eric all that trouble, I’ve (fairly) quickly plotted the curves for the loci of Mars’ and Jupiter’s oppositions in one picture. From this it can be seen that they cross in the southwestern corner of Aries and the southeastern end of Virgo.
It has to be remembered that planets’ orbits change slowly over the aeons. But these locus curves are probably true enough for several centuries around our time.
Guy, thank you so much for plotting these two loci together! I also was caught up in other things over the last several days, including watching the Europa transit and its shadow transit across Jupiter the other night from start to finish, to work on this, so you have saved me the time. It is much appreciated! The rarity of coincident oppositions at either of the two points is easily appreciated when you consider how infrequently each planet comes to opposition within a few degrees of either point. One of those events at the Aries / Taurus border would be spectacular, since Mars is still pretty bright at that location!
This reminds me of when I was a child, playing with a hand-cranked orrery at a science museum. I wanted to make all the planets line up on the same side of the Sun. It didn’t happen, and after a quarter hour or so I gave up and wandered off to wait for the Foucault pendulum to knock over a little brass cylinder.