What is Retrograde Motion?

Via Wikipedia (see "References"): "Schematic animation of Mars retrograde. As Earth (E) passes a superior planet such as Mars (M), the superior planet (M') will temporarily appear to reverse its motion across the sky."

When the great Greek astronomer Claudius Ptolemy looked into the night, the odd movements of the stars and the “wandering stars” (planets)* forced him into thought; this thought led him to the Ptolemaic Model of the Universe, otherwise known as the geocentric model, which postulates that earth is the center of the universe, and is surrounded by rotating heavens known as the celestial sphere. Everything in his model – the distant stars and planets, the sun, the other planets in the solar system, and everything else – orbits around planet Earth. The orbits of the heavenly bodies around Earth were perfect circles in his model, but he quickly found that observations of some “stars” did not agree with his model. Ptolemy soon saw that the sun, the moon and the planets – at least from Earth – didn’t appear to be traveling in perfect circles. Observations he made particularly perplexed him: a few planets reversed their course on some nights, only to resume their course later on. Revising his model, he described that the imperfect movements result from epicycles, a small intermediate orbit whose center moves around the circumference of a larger orbit. With the heliocentric model, however, epicycles were revealed not to exist; we now know that the apparent reverse motion of some celestial bodies is the result of retrograde motion.

An Anomaly in the Night Sky

Let us follow the moon cycle: we will go outside at 8 P.M. every night, beginning at the full moon on November 30th. We quickly notice that, every night, the moon rises later; if the moon were to rise at 8:04 P.M. on November 30th, it may rise at 8:51 on December 1st. We would also see that the moon is now east of the stars it had been covering the night before. This particular movement puzzled many ancient astronomers. Why do the moon and the planets move differently than the stars?

When Earth rotates, it does so significantly faster – twenty-seven times faster – than the moon orbits Earth. Therefore, each night the moon appears to rise later than it had previously. This lasts throughout the synodic period, the time it takes the moon to go through all its phases – it takes about 29 ½ days for the moon to go through all its phases. 

What is the Motion?

The eastward motion of the moon relative to the sky is known as retrograde motion. Retrograde motion is the “apparent motion of a planet in a direction opposite to that of other bodies within its system, as observed from a particular vantage point.” 

Ptolemy was very frustrated by retrograde motion. In the Ptolemaic model, he worked out, after a lot of tireless work, the epicycles and deferents in a complicated orbital cycle in order to keep his geocentric model “accurate.” Although he obviously was wrong, he was not the only astronomer who had trouble working around retrograde motion.

The ancient Greeks also had to try and explain retrograde motion. The Greeks named the starlike objects in the night sky “planets.” Planets, to us, are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune; but to the Greeks, they were much different. Planetes – from which the word “planet” is derived – is the Greek word for wanderer. 

The geocentric model, unfortunately, was not corrected until Nicolaus Copernicus and Johannes Kepler both realized that, instead, earth and the planets orbited the sun. Once Kepler examined the distances and orbital periods of the planets in our solar system and proposed his laws of planetary motion, he discovered that retrograde motion was simply an apparent shift in the location of a planet in the sky relative to Earth. 

Retrograde motion has perplexed me since I first tried to understand it; for over a month, any research I did left me just as confused as I had been. It made sense as to why they reversed, but it did not make sense as to why they reverted back in the opposite direction. 

The mistake I made, as dumb as it is, was that I was imagining the planets orbiting the sun in a straight line. I imagined that Earth was moving faster than Mars, so Mars’s motion throughout the sky should appear to slow, halt, and then reverse. I realized later, however, that the odd circular motion results from the elliptical shape of each planet’s orbit, rather than some tenebrous phenomenon that my brain would be unable to process.

Let us consider Mars. As Earth reaches opposition with Mars – when Earth is nearest to Mars during Mars’s orbital period – because it orbits the sun much closer than does Mars, and because it orbits faster than Mars does, Mars’s motion relative to the stars in the night sky will change. For a few months, it will continually slow down to a point in which it is not moving at all relative to the stars, and then it will eventually reverse. Imagine a 2D surface of Mars and Earth at the height of the orbit (imagine two ellipticals surrounding the sun with both Mars and Earth on the tops of their ellipticals), and imagine planet Earth moving faster than Mars. You will see that as it moves through its orbit, the apparent region in the night sky relative to Earth will shift. Mars will appear to reverse its motion throughout the sky, every night for around a month, and then this motion will slow, and Mars will reverse again, moving in similar motion to what it had been in previously. Retrograde motion occurs because of the angle of Earth relative to Mars during their orbits.

Imagine Earth has moved from the top of the circle to the left side of the circle – assume a counterclockwise orbit. Mars, because its orbit is much longer than Earth’s, is much closer to the top of the circle. Imagine now what may be happening to the direction Mars is from Earth as Earth passes Mars at the top of the circle and continues down the middle-left side of the circle while Mars remains near the top of the circle. Imagine a line pointing directly from Earth to Mars throughout this entire period, and watch how it changes (at the top of this entry is the gif of this conjecture).

Over the course of many nights, you will see that same circular pattern with the planets. The animation and my description of the animation does justice to what is happening, but not to what it actually looks like if you take a composite image of the planet each night for many nights. Retrograde motion, just like almost every topic in astronomy, is odd and requires some straining to understand, but it is nevertheless so odd that it is inspiring. As always, take care and stay curious, everyone.

Mars in retrograde motion (composite).

* Before Galileo discovered individual planets, all points of light in the sky were assumed to be stars. The word planet originates from the Greek word planetes, roughly translating to wanderer. The planets were wanderers, because they moved through the sky at different rates – faster – than the surrounding stars, resulting in them moving relative to the rest of the celestial sphere – growing closer to some stars and farther from others, and repeating the process throughout their orbital periods.

If you have any questions, comments, or corrections, please comment on this post or email learningbywilliam@gmail.com with your concerns. Thank you.

References

(n.d.). Retrieved from https://people.highline.edu/iglozman/classes/astronotes/retrograde.htm

Apparent retrograde motion. (2022, June 23). Retrieved from https://en.wikipedia.org/wiki/Apparent_retrograde_motion

How did Ptolemy's model account for retrograde motion?: Socratic. (2016, February 09). Retrieved from https://socratic.org/questions/how-did-ptolemy-s-model-account-for-retrograde-motion

Ptolemaic system. (n.d.). Retrieved from https://www.britannica.com/science/Ptolemaic-system

Retrograde motion can be real or illusory. (2022, May 11). Retrieved from https://earthsky.org/space/what-is-retrograde-motion