So apparently I'm in a models-of-the-solar-system mood recently, so tonight I am going to tell you about Tycho Brahe's geocentric model, generally referred to as the Tychonic model of the solar system.
Tycho Brahe lived around the same time as Galileo. During this period, the Catholic Church was busy with the Counter Reformation, an attempt to strengthen its authority which was under assault from the Protestant Reformation throughout Europe. This involved an increased sensitivity to threats to Church authority, and among the perceived threats was heliocentrism, which implied that humans did not hold a special place at the center of creation and was in apparent contradiction with several Bible passages.
Geocentrism, on the other hand, placed Earth at the very center of creation but did not provide very accurate predictions of the planets' positions in the long term. By the fifteenth century, the Ptolemaic model (the geocentric model in use, developed by Claudius Ptolemy in the first or second century) had become incredibly complicated. In its original form, it had everything moving around the earth in perfectly circular orbits. However, this failed to account for some aspects of the planets' movement, especially retrograde motion--the phenomenon when a planet appears to stop moving, travel in the opposite direction for a bit, and then resume its course. People compensated by adding epicycles: circular deviations from the circular orbit, so that the planets would literally travel backward occasionally, but would do so because they were following a path determined by a system of circles. The end result looks something like this:
Over time, as the Ptolemaic system's predictions deviated from the observed paths of the planets, more and more epicycles were added on top of each other. Copernicus (known for developing what was essentially the heliocentric system we use today) was driven to look for alternatives because he felt that God would not have made his system so messy. The heliocentric system solved the problem of retrograde motion by showing that it was an illusion created by our own motion relative to the other planets. This video demonstrates how that works:
However, as I mentioned above, the Church was not ready to adopt a heliocentric model. Tycho Brahe developed his model as a compromise between the two systems. According to the Tychonic system, the Earth is at the center of the solar system, with the sun and moon orbiting it, while all the other planets orbit the sun. This still allows for retrograde motion without resorting to epicycles and provided more accurate predictions than the Ptolemaic system.
In fact, the Tychonic system is mathematically indistinguishable from the Copernican system Galileo was teaching (and in fact it is the system he was fighting, rather than the Ptolemaic system as is commonly believed), in which the moon orbited the Earth while the Earth and other planets orbited the sun. The difference is simply where you place your reference point.
To explain: We know today that nothing in our universe is truly stationary because everything is in motion relative to everything else. However, picking some stationary reference point simplifies our diagrams and calculations. Any point will do, provided we make the appropriate adjustments around it. When you are sitting in a car traveling at sixty miles per hour and tossing a baseball up and down, you don't need to throw it forward at sixty miles per hour to avoid breaking your own nose; as far as you are concerned, the car isn't moving, and those trees outside are simply whizzing by. It is the same idea here. If I wanted to, I could propose a model of the solar system with Titan at its center, Jupiter orbiting Titan, the sun and Jupiter's other moons orbiting Jupiter, and all other planets orbiting the sun. If you were in a high school physics class solving a word problem set on Titan, you might even find it convenient to do this.
The main scientific reason for using a heliocentric system today is that we conventionally say that lighter objects orbit heavier objects, as the heavier objects are less influenced by the mutual gravitational attraction. But if you know a fifth grader who likes to stump the teacher in class, you should tell him about Tycho Brahe's geocentric model of the solar system.
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