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The retrograde motion of planets

Looking at the sky, night after night, man no doubt noticed very early that most of the brilliant dots he could see there retained their relative position. A triangle in that corner looked pretty much the same next night, and the night after that; and the same could be said of most of the figures he saw. But there were a few dots that moved against the fixed background of stars. These no doubt provoked great curiosity, and were the subject of very careful scrutiny. The ancient greeks dubbed them wanderers for their relative rambling behavior, and it is from this greek term that their modern name comes: Planets.

The simplest model to explain the motion of the planets has them, along with the Moon and the Sun (the other two wandering objects in the sky), moving in circles, centered around a fixed Earth. This model explains why these celestial objects move against the background of the stars, but there were some oddities in their movements that were not well explained by it.

One of the most notable of these behaviors has to be the retrograde motion of the planets. Planets, as we noted, move relative to the stars, and they do so, generally, moving from west to east in the sky. If we look at the sky, at the same time of the night on two different nights, we will generally notice that the planets have moved a little to the east. But every once in a while, a planet will do something funny: it will slow down its motion, will appear to "stop" for a short while, and will then start moving in the opposite direction, to the west. Eventually, it will stop again, and resume its movement towards the east.

A typical planetary orbit (Ptolemy) It was unacceptable that a planet would stop in its track and reverse its motion along its circular paths for a short while, to reverse them once again a while later. So, clearly, a better model was needed. Ptolemy devised the most sophisticated of these models that still kept the Earth as the center (so called geocentric models, although to account for other, subtler, irregularities, in his model the Earth was no longer at the exact center). One of its basic ideas was that planets were carried on a small circle (called the epicycle, whose center moves along another, larger, circle around the Earth, called the deferent.

This model worked well as far as retrograde motion was concerned, since when the planet is in the lower part of the epicycle it is moving in the opposite direction as viewed from the earth. But, as mentioned above, there were subtler oddities that needed to be taken into account, too, and Ptolemy was forced to introduce more and more complications into his model to attempt to explain them. The model grew rather complicated and cumbersome to use, but still reproduced the actual motions well enough that it remained in use for over 1400 years. Ptolemy's geocentric model

Around the year 1540, Copernicus offered a different kind of model, a heliocentric one, where the center was occupied no longer by the Earth, but by the Sun.
Copernicus heliocentric model
In Copernicus' model, planets still moved in circles, so he still needed to use some epicycles; but these, now, were only to explain the subtler irregularities. Retrograde motions arise from the combined motions of the planets and the Earth. Copernicus reasoned that planets further away from the sun would move more slowly than closer ones. As a faster planet overtakes the Earth in their rotations, its motion against the stars, as seen from the Earth, reverses. Look, for example, at the next figure:
Animation of retrograde motion of Venus

As we view the moving Venus from the more slowly moving Earth, the line of sight (i.e., where in the sky, relative to the stars, we will see Venus) reverses its motion: it is first rotating counterclockwise, then (near the fourth and fifth position) starts rotating clockwise. This corresponds to the first reversal of apparent motion. A while later (around the ninth position) it starts rotating again in a counterclockwise direction, resulting in the second reversal. The same explanation works for the outer planets, too, only now it is the Earth that overtakes the other planet.



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