ASTRO 801
Planets, Stars, Galaxies, and the Universe

The Heliocentric Model

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Additional reading at www.astronomynotes.com


The geocentric model of the Solar System remained dominant for centuries. However, because even in its most complex form it still produced errors in its predictions of the positions of the planets in the sky, some astronomers continued to search for a better model.

The astronomer given the credit for presenting the first version of our modern view of the Solar System is Nicolaus Copernicus, who was an advocate for the heliocentric, or Sun-centered model of the solar system. Copernicus proposed that the Sun was the center of the Solar System, with all of the planets known at that time orbiting the Sun, not the Earth. Although this solved many longstanding problems in the Ptolemaic model, Copernicus still believed that the orbits of planets must be circular, and so his model was not much more successful than Ptolemy’s in predicting the position of the planets. His model was very successful, however, in solving the problem of retrograde motion in a very elegant manner. This is illustrated in the animation below. Click on the "start" button to see the retrograde motion.

Animation Caption:

This animation created with Starry Night begins with a top-down view of the Solar System with the orbital paths of the inner planets shown. It zooms out to show only the Earth and Mars. Lines are drawn from Earth to Mars to show where on the sky someone on Earth looking at Mars would see Mars with respect to the background stars. Each arrow is labeled with the date on Earth, and as both planets orbit the Sun, we see that the position of Mars with respect to the stars appears to move as time goes forward. In May of 2016, the Earth overtakes Mars, so the arrow for this date appears to move in the opposite direction compared to the previous dates. This continues for June and July before Mars appears to move in the original direction again beginning in August.

The solution to the problem of retrograde motion is to realize that the Earth is moving more quickly around the Sun than Mars. Along its orbit, Earth will at some times lag behind Mars from an angular point of view. That is, if Earth is at the 3 o’clock position along its orbit, Mars may be at 1 o’clock. Since Earth moves faster along its path, Earth will overtake Mars as they both hit the 12 o’clock position at the same time. After passing Mars, Earth will reach the 9 o’clock position on its orbit while Mars only makes it to 11 o’clock. From our point of view on Earth, Mars will appear to move prograde on the sky when we are approaching it; however, as we overtake Mars (which you can see in the animation if you replay it and watch the relative positions of the two planets closely), it will appear to come to a stop and then begin to move retrograde. A good analogy to help clarify this concept is to visualize runners on a track. Imagine two runners, one moving quickly in an inside lane (Earth) and another moving more slowly on the outside lane (Mars). When both are on the straightaways, the Earth runner will see the Mars runner moving forward but slowing down as the Earth runner catches up. However, when both hit the turn, the Earth runner will pass Mars, who will seem to be moving backwards (or retrograde!) from Earth's point of view.

Test this with Starry Night!

Note also that you can reproduce the animation (but without the arrows) with Starry Night! This is a bit more tricky, but here are the steps:

  1. Instead of choosing a location on Earth or on Mars, you can choose a stationary location. In this case, you want to be floating above the Sun, so you can set the location to X = 0, Y = 0, and Z = 1 billion miles (or in Astronomical Units, 10 AU).
  2. Choose to label planets and moons from the labels menu
  3. If you do not see the Sun and planets, search for the Sun in the find menu and double click on the word "Sun" when it comes up
  4. Right click on Earth and Mars and choose "orbit"
  5. Set the time step to days; press play

You can now watch the orbits of Earth and Mars on a given set of dates to choose when Earth is overtaking Mars, and then you can reset things so you are watching the sky from Earth on that same date and watch Mars go through a retrograde loop! I have not created a Starry Night file for this example, but please let me know if you would like one.

Starry Night does have some built in "Favorites".  They do have a similar one for the inner Solar System. In the Favorites menu, choose Solar System, then Inner Planets, and then Inner Solar System, and it will show you a view of the Inner Solar System slightly different from the one you will see if you follow the instructions above. You can also get to this Favorite by clicking on the "hamburger menu" (the three horizontal lines) on the right side of the top status bar.

Although Copernicus’ model solved some problems, its lack of accuracy in predicting planetary positions kept it from becoming widely accepted as better than the Ptolemaic model. The advocates for the Geocentric model also proposed another test for the heliocentric model: if the Earth is orbiting the Sun, then the distant stars should appear to shift from our point of view, an effect known as parallax. We will study parallax in more detail in a later lesson on stars. However, for now I will note that this caused a problem for advocates of the heliocentric model. If they were right, we should observe parallax, but not even the most accurate observers of the day were able to detect a measurable amount of parallax for even a single star.

Forgetting parallax for a moment, the advances necessary to increase the acceptance of the heliocentric model came from Tycho Brahe and Johannes Kepler. Brahe is credited with being one of the best observers of his time. At his observatory, and over approximately 15 years, using instruments he designed and built, Brahe compiled a continuous list of accurate positions for the planets on the sky. Johannes Kepler came to work with Brahe shortly before Brahe died. Kepler used his mathematical skill to study the accurate observations of Brahe and then proposed three laws that accurately describe the motions of the planets in the solar system.