Chapter 3 – Models of the Solar System – The Ptolemaic System
In the next three chapters, we will look at the three models of the Solar System that have competed for dominance in the marketplace of ideas over the many centuries of human history. These are the Ptolemaic system, the Copernican system, and the Tychonic or Tychonian system. We will not be delving into the history of these models; much has already been written about that online and elsewhere. Instead, we will be looking for correspondence between each model and reality. In other words, if a given model reproduces the structure and motion of the Solar System that we actually observe, then that model deserves our attention, while the others should be discarded. We will also be incorporating into each model the discoveries that we have made in the previous chapters: the Earth is a spherical body, 8,000 miles in diameter, located 93,000,000 miles from the Sun, while the Sun is a vastly larger body, with a diameter of 865,000 miles. Any model that can’t accommodate these facts will be summarily rejected. We will follow this pattern in subsequent chapters, always building our model of reality on the foundation of the facts that have come before. In this way, we will eventually arrive at the truth about the world in which we find ourselves.
The Ptolemaic system carries the last name of Claudius Ptolemy, the great Greco-Roman astronomer who developed the model in about 150 A.D. The Ptolemaic system was accepted as truth for over 1,500 years, by far the longest period of acceptance by mainstream science (MSS) of any of the three major Solar System models. The Ptolemaic system is a geocentric model of the Solar System in which all of the planets orbit the Earth, which is located, motionless (in the sense of orbital motion), at the center of the Solar System. The order of the planets (and the Sun) in the Solar System under the Ptolemaic model, moving outward from the Earth, is as follows:
Moon
Mercury
Venus
Sun
Mars
Vesta
Ceres
Jupiter
Saturn
Uranus
Neptune
Pluto
Eris
Sedna
I have included several additional asteroidal (Ceres, Vesta), planetary (Uranus, Neptune), and dwarf planetary (Pluto, Sedna, Eris) bodies that were unknown to MSS when the Ptolemaic system held sway. Some versions of the Ptolemaic system reverse the order of Mercury and Venus, with Venus being closer to Earth. The Earth spins on its rotational axis in 24 hours, creating the day-night cycle. The Sun orbits the Earth in one year’s time. The planets closest to the Earth orbit more quickly than those farther out. The stars are more distant than any of the planets, since occultations of stars by planets occasionally occur.
The orbits of the planets were considered to be circular when the Ptolemaic system was in vogue. This works well for the Sun and the Moon, neither of which changes much in angular size as they orbit the Earth. However, due to the application of the telescope to astronomical problems by Galileo in 1610, it is now known that all of the planets change their angular widths over time in repeating cycles unique to each planet. This would ordinarily cause a huge problem for the Ptolemaic model, since if the distance between each planet and the Earth is a constant (the radius of the planet’s circular orbit), then the angular size cannot possibly change. We can easily accommodate this behavior by simply saying that all of the planets, Mercury, Venus, and Mars in particular, have elliptical orbits that carry them far from Earth at certain times, and close to it at others. In this way, a constantly changing apparent size is produced, matching what we see in real life.
Even the phases of the Moon, Mercury, and Venus could, in principal, be reproduced in the Ptolemaic model simply by properly timing the appearance of certain orbital phenomena, such as inferior and superior conjunctions in the case of Venus and Mercury. This simply means that when these two planets are closest to Earth, their angular diameters are maximal, and they display crescent phases (the usual case) or black disks (in the case of transits, which happen on those rare occasions when a planet crosses in front of the Sun’s brilliant disk). At these times, we say that a planet is in inferior conjunction. Similarly, when Mercury and Venus are far from Earth, their telescopic disks are small and full (superior conjunction). All of these situations could be accommodated by “starting” the Ptolemaic Solar System model at a particular time of our choosing such that the required effects are produced as needed, with the planets already in the necessary positions in their orbits to bring about the desired outcomes.
This all sounds promising, but note that thus far we have described the Ptolemaic system only in the broadest of terms. No attempt has been made to quantify the model to see if at actually conforms to reality in a mathematical sense. When we applied this approach to the flat Earth model, the result was that the model had to be discarded. Let us now see what happens to the Ptolemaic system when we apply that same level of scrutiny.
We will start with the planet Venus, the brightest of all of the planets and, therefore, the easiest to observe with the naked eye, usually after sunset in the west or before dawn in the east. In 2012, however, I had the opportunity to observe a transit of Venus from my own backyard. As stated above, transits occur when a planet passes in front of the Sun, allowing us to observe the planet’s disk in silhouette against the Sun’s bright background. Using my little 4-inch Newtonian reflector-style telescope, I was able to project a fairly enormous image of the Sun onto a white screen. I could measure the Sun’s diameter with an ordinary ruler. I equated this distance to the Sun’s apparent angular size, which we have already established to be 0.5 degrees. Sure enough, the jet black disk of Venus’ night side was thirty times smaller than the Sun’s, placing it at 60 seconds of arc in diameter (0.5 degrees/30 = 0.0167 degrees, and 0.0167 degrees * 3,600 seconds of arc/degree = very nearly 60 arc seconds), which matches the angular size found by many other transit observers over the past four centuries. Note that this is the largest angular width that Venus ever presents to Earthbound observers. This is an experimental fact; there is no disputing it. It is a simple, straightforward measurement of length. The large size of Venus’ shadow floating in front of the Sun also suggests that Venus is the planet closest to Earth in the direction of the Sun, not Mercury.
When at its most distant point from Earth, Venus shows a tiny, fully illuminated disk only 10 arc seconds in diameter. Again, this is an experimental fact with which one cannot argue. So, we see that Venus changes its distance from Earth by factor of six as it orbits the Earth in the Ptolemaic model. The idea that Venus could actually change its planetary dimensions while it orbits is rejected outright as a preposterous notion. This means that all of the apparent changes in Venus’ size are entirely due to its changing distance from Earth. Let us now see if there is enough “room” for Venus’ orbit between the Earth and the Sun.
First, we have already established that the Sun is 93,000,000 miles from Earth. Therefore, all of Venus’ orbit, from its closest point to Earth to its most distant, must fit within this relatively narrow band of space. We will now call upon our old friend, the small angle equation, to help us find a solution to this problem. First, we know that Venus presents a disk 60 arc seconds in diameter when closest to Earth. If the planet were as far away as the Sun is, then the small angle equation indicates that the diameter of Venus would have to be 27,900 miles. However, Venus would then have to be more distant than the Sun to produce a 10 arc second disk, which is clearly not allowed since we have already established that the entirety of Venus’ orbit around the Earth must fit within the space between the Earth and the Sun. Therefore, Venus must be smaller than 27,900 miles in diameter. But how much smaller?
To find out, we can plug different values into the small angle equation, and see what happens. If Venus were only 5,000 miles in diameter, then it would present a 60 arc second disk at just under 17,000,000 from Earth, and a 10 arc second disk at 100,000,000 from Earth. Again, this is not a suitable diameter for Venus, since the most distant point in its orbit would be farther away than the Sun. We need to keep trying.
If Venus were only 2,500 miles in diameter, then it would present a 60 arc second disk at just over 8,000,000 miles from Earth, and a 10 arc second disk at 50,000,000 miles from Earth. Here we have at last found a diameter and distance that would fit within the required boundaries, and still produce the apparent angular sizes that are actually observed with a telescope. But just how big can Venus actually be and still meet all of the requirements of the Ptolemaic system? The small angle equation provides the answer: 4,650 miles in diameter, with the caveat that the most distant point of Venus’ orbit around the Earth would intersect with the orbit of the Sun, raising the possibility of an eventual collision. Since such collisions have never been observed, Venus would have to be made even smaller to provide a “buffer zone” between itself and the Sun, all the while maintaining the angular sizes that are actually observed. But are these smaller-than-Earth diameter values physically reasonable?
In my opinion, the answer is no, and it is the telescope itself that casts doubt on the Ptolemaic system altogether. When the planet Venus is observed telescopically from Earth, no surface features are ever observed. The planet looks completely bright, white, and featureless, regardless of the phase that it is displaying at the time. Ever since the first telescopes were trained on Venus, people have suspected that what they are actually seeing is the top of an extensive layer of highly reflective clouds. Modern space probes have since confirmed this hypothesis. The clouds seem to be composed of myriad tiny floating droplets of concentrated sulfuric acid (H2SO4), and they never part. In all of the centuries that people have been observing Venus with optical aid, there has never been a single break in that monotonous, monotone cloud cover. Venus is like a New England valley, filled with morning fog. Earthbound observers are like hikers in the hills above the valley, looking down on it from afar. All that can be seen of the valley is the top of the mist layer, blindingly bright in the sunlight above the clouds. Venus’ fog, however, never gets burned off by the Sun!
We have already established that the Earth is some 8,000 miles in diameter. Eratosthenes’ famous experiment proved that long ago. The key question is simply this: Is it reasonable that a planet considerably smaller than Earth, which Venus must be, as we have seen, should have a much more substantial atmosphere than the Earth? In my opinion, no, this is not reasonable. No location on Earth is completely covered with clouds all of the time, and yet this is the norm on Venus. From the standpoint of proportions alone, Venus should have a thinner, less extensive atmosphere than Earth, since it must be the smaller of the two worlds in the Ptolemaic system. Venus’ closeness to the Sun also speaks to it having a thinner atmospheric envelope than Earth simply because greater solar heating, which the planet must experience by virtue of its distance from the Sun, has the well-known tendency to drive gaseous substances out of and away from solid bodies. Comets, for example, provide a well-known example of this behavior. Yet, on Venus, the opposite seems true, and solar heating instead causes both the production and accumulation of gases beyond all reasoning for a smallish planetary body. There are only two possibilities left to us. Either Venus can do the impossible, or there is something seriously wrong with the Ptolemaic system. Obviously, the latter is the more likely possibility. Therefore, the Ptolemaic system is considered refuted, and will not be considered a viable Solar System model throughout the remainder of this book.
Some may wonder about Saturn’s giant moon, Titan, whose surface atmospheric pressure is actually greater than that of Earth, despite being smaller than Earth. Couldn’t Venus be doing the same thing? No, and it is Titan’s location in the frigid darkness of the outer Solar System that works in its favor here. The deep, penetrating cold found far from the warming Sun makes Titan’s gaseous envelope sluggish, almost on the verge of liquefaction, helping it to cling to Titan’s globe despite that body’s small size and gravity. Such an effect fails to explain the atmospheric situation on Venus, which is even closer to the Sun than is the Earth.
One may also wonder why the Ptolemaic system lasted for as long as it did. The reason is simple. With the telescope and the small angle equation both absent from consideration, the model was essentially one of predicting planetary positions as a function of time. Without the need to account for the actual physical conditions found on the planets themselves, one has much more freedom to theorize. And the theory worked very well indeed, plotting planetary positions with sufficient accuracy for the technology of the day.