Kepler begins the chapter by saying:
The testimony of the ages confirms that the motions of the planets are orbicular. Reason, having borrowed from experience, immediately presumes this: That their gyrations are perfect circles.
The of course refers to all various hypotheses prior to Kepler’s work. This likely originated with the Greek astronomers who, thanks to Plato and Pythagoras, held geometric perfection to be divine and thus filled the heavens with circles and assumed the underlying geometry of nature to be comprised of other Platonic solids. (This will be discussed more in another post.)
This tradition was carried down through the centuries and even infected Copernicus who, although he moved the Sun to the center of the system, still maintained the “perfection” of perfect circles.
Brahe did away with the notion of the planets being carried on crystalline spheres when he observed a comet that would have smashed through them thanks to its trajectory, but while this prompted him to have new ideas about the workings of the solar system, he too assumed perfect circles.
However, Kepler quickly dismisses this, saying:
[W]hen experience seems seems to teach something different to those who pay careful attention, namely, that the planets deviate from a simple circular path, it gives rise to a powerful sense of wonder, which at length drives people to look into causes.
Thus, Kepler sets out to investigate these causes by first engaging in a more careful examination of the motion of the heavens.
He defines two sorts of motion.
The first is the daily passage of the stars; rising in the east, peaking along the meridian, and setting westerly. This is referred to as the “common motion.”
Contrary to that motion is the motion of the wanderers. The sun, moon, and planets drift slowly west to east. The exception to this is when planets move in retrograde but Kepler does not venture into that at this point. Regardless, motion amidst the background stars is referred to as “proper motion.” (These two motions follow directly from Book I of Ptolemy’s Almagest.)
The complexity of predicting the motion of the planets rises in part due to the combining of these motions. But, he notes, by separating out the motion of the stars we can begin to see the motion of the planets as they are. However, there are yet further complications.
Kepler notes
it was apparent that the three superior planets, Saturn, Jupiter, and Mars, attune their motions to their proximity to the sun. For if the sun would approach them they moved forward and were swifter than usual; where the sun would come to the signs opposite the planets they retraced with crablike steps the road they had just covered; between these two times they became stationary.
This is an interesting observation that demands further explanation as it is not immediately obvious as to what it means. The latter part, in which “they retraced their crablike steps the road they had just covered” is obvious: It refers to the retrograde motion of the planets.
The difficulty in interpretation comes from the phrase “proximity to the sun” during which time the planet moves faster. With our modern understanding, we may think it means physically closer to the sun in space, which stands to reason since planets do move faster as they approach the sun in their elliptical orbits (as described by Kepler’s 2nd law).
However, the format of Astronomia Nova is following Kepler’s development of his ideas so he had obviously not yet come to that conclusion and that interpretation cannot be correct.
Rather, the implication is that the planets move faster when closer to the sun in apparent position, meaning when they look closer to the sun in angular distance.
This is a somewhat difficult thing to visualize. I initially tried drawing out the orbit of Earth and Mars and sketching in lines of sight as they orbited, but this quickly became too complex to visualize so I turned to a more thorough solution. Namely, I opened Stellarium, a free planetarium software, to examine the position of Mars relative to the Sun.
Watching the day to day change visually was next to impossible to judge. So went through the course of an entire year (2018) transcribing the positions of both the Sun and Mars into a table every day at noon. From there, I could calculate the angular separation between the two as well as the angular change of Mars day to day. (This was done in Google sheets, so you’re free to peruse the source data here.)
Here’s what the graph looked like:
(Minor note: There’s a few data points that are obviously a tiny bit off in the hump. I’m certain these were transcription errors as I caught several others. However, due to the density of the points, I wasn’t able to figure out exactly which these were and they’re so close I didn’t worry about it. The trend is clear anyway.)
This graph is a bit hard to interpret as the x-axis scale is a bit odd. It starts with Mars about Mars about 57º away from the sun. At that time, it’s changing it’s position by a little over 0.60º/day. As the motion of the sun and Mars separate them further and further, you can see that Mars’ daily speed drops quickly. However, once Mars reaches opposition (which should happen at 180º, but since the orbits aren’t entirely coplanar, the maximum angular separation is reduced along the perpendicular axis), the angular separation again starts dropping as Mars approaches the sun from the other side.
But what to make of the hump? This is Mars’ retrograde motion. It first slows down (and would stop if the graph had better resolution), then reverses course. Since this daily change only measures the absolute change in placement from night to night (in other words, not considering it negative when in retrograde), the speed picks up again, before slowing to reverse direction again.
Ultimately, as Mars heads back towards conjunction, it speed picks up again.
But looking at it in the modern view is really getting ahead of ourselves. Let us instead simply remember that when superior planets appear near the sun in the sky, their night-to-night position is changing the fastest. This is an observation that demands explanation in any model of the solar system.
So again, we have several components of motion being observed. This is strongly reminiscent of something Ptolemy noted in the Almagest. Specifically, he too noted these two types of what he referred to as anomalous motion. Specifically, the first was the retrograde motion of the planets against the stars. Second was that superior planets sped up at conjunction and retrogressed at opposition which he defined as his second anomalous motion. Clearly this problem had been plaguing astronomers for 1600 years!
A second observation Kepler introduces in this chapter is that the planets appear brighter when nearer the sun. In the context of the geocentric model, Kepler suggests that this must mean they are closer to the Earth. This is, in some respects, a reasonable supposition as it follows from the inverse square law of light. This is a notion that Kepler would certainly have been familiar with since he discussed it in his 1604 book, Ad Vitellionem Paralipomena, quibus astronomiae pars optica traditur. To my knowledge, he was the first person to state that light spreading spherically from a point source must diminish proportionally to the surface of the sphere (the surface area being given by 4πr2).
Kepler then mapped out what this motion towards and away from the stationary Earth would look like from 1580 to 1596.
Kepler states that this diagram is “the accurate description” [based on the geocentric model] of what Mars’ orbit must be like. What’s important is the scale. The main orbit would be somewhere in the middle of the spiral, but due to the epicycle, it moves inwards and outwards. Based on how long it takes to go side to side (and the distance around Mars must cover in that time), Kepler obviously inferred the distance in and out since the epicycle was assumed to be circular too.
He points out that this would imply that, should this be correct, that Mercury, Venus, and the Moon (whose orbits were all faster and thus believed to be closer to the Earth than Mars) would all have to have their own orbits stuffed within the tiny dotted circle at the center to avoid interference with one another.
Given that they too exhibit retrograde motion and have need of epicycles of their own, there simply isn’t room for everything!
Instead, he offers Copernicus’ heliocentric model, sweeping away the complicated spirals and giving each planet their own closed orbit which they repeat eternally.
As a minor note on language, this is a truly defining use of the word “orbit”. Prior to the establishment of the heliocentric model orbit simply meant “whatever path the planets take” as its original use came from the tracks left by wagon wheels. Here, Kepler truly redefined the word.
Kepler closes out the chapter by quickly discussing the motion of the sun noting that if you truly want to understand the motion of the superior planets (since it is somehow effected by the sun), you should probably have a good understanding of the sun’s position. However, the Sun itself has some irregular motion; its passage along the ecliptic is not uniform from day to day since our orbit is not perfectly round.
To simplify things Ptolemy, Copernicus, and Brahe all averaged this motion out using the “mean” (average) position. Kepler, however, promises to use the “apparent” sun, in other words, where the sun truly appears in the sky.
As we discussed at some length, the planets move faster when near conjunction. Conversely they move more slowly when at opposition. Thus, all astronomers trying to explain these anomalous motions were concerned with observations made at opposition since this was when the apparent effect of the Sun was minimized. This is the reason that Kepler was concerned about using the true position of the Sun: That was the only time Mars would truly be at opposition!
But beyond stating that he intended to do this, Kepler did not go into the differences between the mean and apparent sun. As such, I too shall forego that discussion here, especially since it is a complicated topic (one which I have not yet fully digested at this point in my journey) that each model tackles slightly differently and Kepler will return to it in chapter 5. But if you want to peek ahead, I recommend reading here.
For another take on this chapter see this site.