2026-10-30

Mercury's "analemma" over $79$ and $46$ years

Mercury stays close to the Sun, moves fast relative to its own idealized mean version, and takes $79$ years to make an approximately closed "analemma"; the next best being $46$ years but with $3\times$ more error. Refer to this table for the source of these numbers.

This basically means that the "analemma" curve is going to be so densely packed as to almost make it look like a sheet.

Mercury's "analemma" over $79$ years

Mercury's "analemma" over $46$ years

Even over $46$ years, the trace is quite dense.

Similar to my Mars "analemma", due to the number of tracking shots involved, I decided to forgo saving the screenshots (and thus gave up the option of making a movie). Instead, only Mercury's position was captured every $3$ solar days starting $2026$-Jul-$13$ $11$:$59$:$44$ UTC. Only one screenshot (of the starting position) was captured to serve as the base image to overlay the "analemma" trace on. The line width of the trace was reduced from $3$ (used earlier for other planets) to $1$.

Mars' "analemma" over $79$ years

After previous posts on "analemmas" for Jupiter ,  Venus ,  Saturn , and Jupiter (again) this is the "analemma" for Mars tracked over $79$ years. Refer to this table that motivates the chosen duration.

I captured data every $7$ mean meridian transit periods (i.e., $6.99103561122795$ days). As $79$ years is a rather long interval, I decided to forgo saving the screenshots (and thus gave up the option of making a movie). Instead, I contented myself with only capturing the $(x,y)$ pixel coordinates in Stellarium. I captured one screenshot of the starting position to serve as the base image to overlay the "analemma" track on.

Mars' "analemma" over $79$ years

2026-10-26

Jupiter's "analemma" over $83$ years

I previously made a post on Jupiter's "analemma" over $12$ years.

Jupiter's orbital period being $11.86$ years, it does not align nicely with the $12$ year duration chosen in that post. That makes the "analemma" only very approximate. For a more perfect "analemma", a duration of $83$ years is needed (see the table in this post). $83$ years equals $7$ Jovian orbits with an error of only $13.027483$ days or $0.301\%$ of the Jovian year.

Tracing Jupiter's "analemma" over $83$ years yields the following path which is definitely more Lissajous and has a better symmetry.

Jupiter's "analemma" over $83$ years