The Heliocentric Model

In the night sky, stars rise and set due to the rotation of Earth. However, the pattern of stars that is seen in the sky, how far apart a pair of stars are seen from each other, stays the same over time scales of thousands of years. However, planets move in the sky relative to the pattern of background stars. They change their position in the sky from night to night. The term “planet” originates from the Greek word for “wanderer.” This phenomenon can’t be really be seen on any given night. But if you note the location of a planet relative to the background stars, and note its location again several nights later, you will see that it has moved. This could be seen if you took a series of photos every night for a month with a chosen star highest in the sky and laid them over the top of each other. Planets typically move eastward, the direction of increasing right ascension, which we know today is due to their revolution around the sun. Note that a planet still rises in the east and sets in the west on any given night due to the rotation of Earth. This video will focus on a variation of that motion known as retrograde motion. This apparent motion concerns the planet slowing in its eastward motion, stopping, moving westward for a while, and stopping again before continuing on its eastward journey. For superior planets, those that orbit the sun further out than Earth, and the only planets that will be discussed in this video, this effectively creates a loop in the sky.

Two thousand years ago, the Greek astronomer Ptolemy explained retrograde motion with a geocentric system of wheels within wheels, kind of like the kids’ drawing game Spirograph. It was believed that Earth was at the center of everything and that a planet moved on a circular path called an epicycle, the center of which moved on a larger circle called the deferent. This allowed the existence of retrograde loops to be explained, although in a complicated way. We know today that this explanation was completely wrong.

In the 1500s, Copernicus explained retrograde motion with a far more simple, heliocentric theory that was largely correct. Retrograde motion was simply a perspective effect caused when Earth passes a slower moving outer planet that makes the planet appear to be moving backwards relative to the background stars. Thus, retrograde motion occurs over the time when the sun, Earth, and planet are aligned, and the planet is described as being at opposition – opposite the sun in the sky. This is why retrograde motion is referred to as “apparent retrograde motion” by many. Nothing is changing in the planet’s motion, and retrograde motion occurs as a natural perspective effect. Let’s look at a demonstration for teaching retrograde motion. It consists of the sun at the center, in red. Earth and a superior planet in a circular orbit around it. Here, a white rod connects Earth and a superior planet similar to Mars and represents the perspective, pointing to the location where Mars would be seen in the sky from Earth. East is counter-clockwise around this circle. A system of circular gears controls the positions of Earth and Mars and their rates of motion.

A hand crank allows the demonstrator to advance Earth and Mars, while the gears ensure appropriate relative rates. Note that an arrow illustrates the direction of apparent motion in the sky. And we have placed background stars around the edge where we will see the apparent position of Mars. We start our demonstration several months before Mars reaches opposition. Remember that Earth is moving faster than Mars and will shortly overtake it. The rod connecting Earth to Mars points to Mars’ apparent position in the sky.
As we turn the crank slowly to advance time, Mars is initially moving eastwards. We have now reached the point where Mars’ eastward motion appears to stop, the beginning of retrograde motion. Note that Mars is now moving westward. Mars reaches opposition at the middle of retrograde motion. We have now reached the point where Mars’ westward motion appears to cease. The end of retrograde motion. As we continue to advance time, Mars resumes its normal eastward motion relative to the stars. Note that this effect is entirely due to perspective. Nothing changed in the motions of Mars or Earth.

This diagram illustrates the perspective effect that underlies retrograde motion.

At which (lettered) location in the sky does a superior planet appear to be located for the planet and earth locations indicated? Please record your vote on a piece of paper and explain your method for determining your answer.

To determine the apparent location of the planet in the sky, one would simulate a line of sight by drawing a line from earth through the planet into the surrounding sky.
Let’s finish up by discussing the general characteristics of retrograde motion.

The table below shows several values describing the retrograde motion of superior planets. The table provides the synodic period. This is how often Earth passes a superior planet, the time from one opposition to another, so it is also the time interval between retrograde motions. Note that as one considers planets in larger orbits, the synodic period gets closer and closer to one year. In fact, for the planet “Far Out,” which is in a very large orbit, the synodic period would be exactly one year, as it would orbit so slowly that it would effectively not move. Correspondently, the retrograde interval, the time spent moving westwards is smallest for Mars, and grows to half a year for our “Far Out” planet. Note that the size of the retrograde loop, the angular extent of the backwards moving tract in the sky, is largest for Mars and decreases to zero for the “Far Out” planet. This can be understood in terms of our change in perspective. Mars is the closest planet to Earth and thus moves the most during the time that it takes Earth to pass it. Thus, it can appear to be in the largest range of positions. The perspective effect is largest.

More teaching materials can be found on the web at astro.unl.edu