The Path of Mercury
This is the path Mercury traces around the Earth, which sits at the centre, over thirteen years. About three times a year Mercury passes between us and the Sun, appears to run backwards for roughly three weeks, and draws a small loop on the inside of its path. Thirteen years hold 41 of those loops, and the lace they braid comes back within three days of where it began.
| Synodic period | 115.88 days |
|---|---|
| Loops in 13 years | 41 |
| Loops per year | about 3.15 |
| Distance from Earth | 0.55 to 1.45 AU |
What you are looking at
The Earth is the point in the middle and the ring around the edge is the zodiac, with 0 degrees Aries on the left, as on a birth chart. The faint dotted circle is the path the Sun seems to take around us in a year. Mercury never strays more than about 28 degrees from the Sun, so its path rides around that circle, swinging out to about 1.45 AU from the Earth when it is on the far side of the Sun and in to about 0.55 AU when it passes between us and the Sun.
Those close passes are the inferior conjunctions, marked with a small dot at the heart of each loop and a gold tick at its degree on the zodiac. Around each one Mercury appears to move backwards against the stars for about three weeks. Astrologers call that stretch Mercury retrograde, and each loop on the inside of the path is one of them.
The colour runs from deep blue to pale green over the years, so you can follow the order the loops were drawn in.
The math
Mercury goes round the Sun in 88 days, but because the Earth is moving too, it takes 115.88 days on average to lap us and come back to the same place between the Earth and the Sun. That is its synodic period. A year holds about 3.15 of them, which is why there are usually three Mercury retrogrades a year and now and then four.
For the whole picture to close, the span has to hold a near whole number of years and of synodic periods at the same time. Seven years hold 22 synodic periods and miss by about a week. Thirteen years hold 41 and miss by under three days, which is why the default picture looks complete. Forty-six years hold 145 and miss by about a day. One year and three years hold no whole number, so their loops are left open.
How it is computed
Positions come from astronomy-engine, an open-source library built on the VSOP87 planetary theory that agrees with the Swiss Ephemeris to well under an arcminute. The piece takes Mercury's position relative to the Earth for every day of the span (every two days for 46 years) in the fixed J2000 ecliptic frame, then turns the whole path once by the precession at the start date so its degrees line up with the tropical zodiac around it.
Inferior conjunctions are found by scanning for the moments Mercury and the Earth share a heliocentric longitude, then refined to the instant Mercury and the Sun share the same apparent degree, to within about a minute. The degree in the caption is that apparent tropical degree, the one an ephemeris prints.
Questions
Why does Mercury make loops?
It never really turns around. Mercury overtakes the Earth on its smaller, faster orbit, and while it swings past on the near side of the Sun its motion across our line of sight runs the other way, so for about three weeks it appears to slide backwards against the stars. That apparent backward stretch is the loop.
How is this related to Mercury retrograde?
Each loop on the inside of the path is one Mercury retrograde period. The piece Mercury Retrograde Triangles shows where in the zodiac every one of them falls, and how they move through the elements.
Why does the default span cover 13 years?
Thirteen years hold 41 synodic periods to within three days, so the path ends almost exactly where it began and the lace looks complete. The 46-year span closes even more tightly, within about a day, but its 145 loops crowd into a solid ring.