Part II

Pages: Opposition | 8 | 9 | 11 | 13 | 13-2 | 15 | 16-20 | 21


An article written on Part II, The Fallacy of the Equant, was published in the March 2007 issue of DUNAMIS.


Here, Kepler tries to determine a hypothesis for understanding the first inequality, using the same basic techniques as "the ancients." Hopefully, Part I made clear the difference between the first and second inequality. To review: the motions of planets against the background of the fixed stars consists of two inseparable motions. One, the first inequality, is the motion of the planet across the zodiac. The second inequality is the impact of the sun on the motion of the planet. That's how it appears to the eyes. In the Copernican system, the first inequality is simply the proper motion of the planet, while the second inequality is the motion of our earth, which changes where we see the moving planets. The term inequality seems strange: but so do other words. For example, undertakers used to be people who undertook to do things, but now undertake a very particular task. Similarly, the very movements themselves that moved nonuniformly, became, themselves, known as "inequalities."

To eliminate the effect that our motion on earth has on our observations of the planets, a technique was developed of using observations at "opposition." This is the time when the sun, earth, and planet lie in a straight line, meaning that we see the planet in the same direction as the sun sees it. We are able to take observations from the sun. This technique was used by Ptolemy, Copernicus, Brahe, and, now, Kepler as well. For Ptolemy, the purpose was not to see the planet from the sun, but rather to line up the epicycle so that the planet appeared to be in the same direction as the center of its epicycle.

A difficulty in determining oppositions is that the sun, earth, and planet rarely lie on the same line -- they do not all travel in the same flat plane, but, rather, the planet moves in a plane inclined to the plane of the earth. So, how to we determine when we should consider observations to be at opposition? This is taken up in chapter 9.

We also have to determine the measure of the inclination of the angle between the planes of the earth and the planet. This will come up in chapters 12 and 13, but first, in chapter 11, Kepler discusses the question of parallax. Close one eye and look around the room while twisting your head. Your eye's changing position changes the relationships of objects in your field of view. The earth rotates every day, and we have to determine how far away we are in space in the morning and the evening, since we are on opposite sides of earth's orb. Kepler concludes that this parallax is far too small to take into account or make corrections for.

Kepler now constructs a table of oppositions, using the true, apparent sun (rather than the false, mean sun used by all other astronomers). We review his determination of mean longitudes in chapter 15.

He is now ready to take up the motion of the planet Mars, following the methods (and false assumptions) of the ancients. In working through the failure of the vicarious hypothesis (chs. 16-21), Kepler proves the non-existence of uniform motion in God's creative universe. Chapter 21 demonstrates how a false hypothesis may appear true. If geometry fails us, what will succeed? The solution is in Part III.