The Loops of Mars
This is the path Mars draws around the Earth, computed day by day from its real position. The red line is Mars moving forward through the zodiac. The bright gold hooks near the centre are its retrograde loops, the weeks when Mars seems to walk backwards, and the white dot in each one marks the night Mars stood opposite the Sun.
| Time between oppositions | About 780 days |
|---|---|
| A retrograde loop lasts | 60 to 81 days |
| Distance at opposition | 0.37 to 0.68 AU |
| Closest near repeat | 79 years, within 2° |
What you are looking at
The Earth sits at the centre and the zodiac wheel runs around the edge, with 0 degrees Aries on the left and the signs running counterclockwise, as on a birth chart. The line is where Mars was, seen from here, on every day of the span. When Mars is on the far side of the Sun it is between 2.4 and 2.7 times as far from us as the Sun is, so the path swings wide around the outside of the picture.
About every 780 days the Earth catches up with Mars on the inside track. For two or three months around that moment Mars appears to stop, run backwards, stop again and carry on. Drawn from the Earth, that backwards stretch is a loop, and it always happens when Mars is closest to us, so the loops cluster near the centre. Each one is drawn in gold, and the dot inside it is the opposition, when Mars rises at sunset and is up all night.
The gold ticks on the inside of the wheel mark the exact degree of each opposition. In astrological tradition a Mars retrograde is read as a time to revisit and review rather than push ahead. That is the tradition's reading; the picture shows only where Mars went.
The math
Mars goes round the Sun once every 687 days and the Earth once every 365, so the Earth laps Mars every 780 days on average. That is the synodic period, and it sets the rhythm of the loops: one loop, and one opposition, per lap. The gap between oppositions varies from 764 to 811 days because both orbits are ellipses, and the loops last between 60 and 81 days.
The ellipse also sets the size of each loop. Mars's orbit is noticeably stretched, so an opposition near Mars's closest point to the Sun brings it within 0.37 AU of the Earth, as in August 2003, the closest of the 20th and 21st centuries, while one on the far side of its orbit keeps it 0.68 AU away. That is why the ring of loops sits off centre: the close loops crowd one side of the Earth.
The pattern nearly repeats. In 15 years Mars goes round the Sun almost exactly 8 times, in 32 years 17 times, and in 79 years 42 times, so after those spans the Earth and Mars are back in almost the same arrangement on the same calendar date: within about 9 degrees after 15 years, 5 after 32, and 2 after 79. The span menu offers those, so a long picture closes on itself and the loops line up into a ring.
How it is computed
Positions come from the astronomy-engine library, which uses the VSOP87 planetary theory and agrees with the Swiss Ephemeris to well under an arcminute. Mars is sampled every day (every two days for 79 years) as a vector from the Earth in a fixed frame, so decades of loops are not smeared by the slow turning of the equinoxes, then rotated once to the tropical zodiac of the start date so the path and the sign wheel agree.
A stretch of the line counts as retrograde when the path's own longitude decreases from one day to the next, so the gold is exactly the backwards part of the line you see. Oppositions are found where Mars and the Earth share a heliocentric longitude, then refined to the minute when Mars's apparent position, light travel time included, is 180 degrees from the Sun. Those are the dates and degrees an ephemeris prints: the caption checks against 16 January 2025 at 26 degrees Cancer and 19 February 2027 at 0 degrees Virgo.
Questions
Does Mars really move backwards?
No. Mars always moves forward around the Sun. It only looks backwards from the Earth, because we are moving faster on the inside track and overtake it, the way a slower car seems to slide backwards when you pass it on the highway.
How often is Mars retrograde?
About every 26 months, once per lap of the Earth around the Sun relative to Mars (780 days on average). Each retrograde lasts between 60 and 81 days, and the opposition, when Mars is brightest, falls in the middle of it.
Why are some loops bigger than others?
Mars's orbit is an ellipse. When the Earth overtakes Mars near Mars's closest point to the Sun, Mars is only about 0.37 AU away and its loop is drawn close to the Earth; on the far side of its orbit it stays about 0.68 AU away. The closest oppositions come round every 15 or 17 years: 2003, 2018, 2035, 2050.
Why 79 years?
In 79 years Mars goes round the Sun 42 times, almost exactly, so on the same calendar date the Earth and Mars are back within about 2 degrees of where they were. Babylonian astronomers used this 79 year cycle, written in their Goal-Year texts, to predict where Mars would be.