Chapter 2 – Flat Earth or Round Earth?

In recent years, there has been a huge resurgence in the belief that the Earth is an enormous, flat plane, rather than a round globe. The number of YouTube videos on the subject is immense. Therefore, our journey will begin here. What, then, is the true shape of the Earth?

Many flat Earthers subscribe to the flat Earth model found in the book, Zetetic Astronomy: Earth Not a Globe by Samuel Birley Rowbotham (also known by the pen name of Parallax). This book was written in 1849, and was greatly expanded by the author in the years that followed. Zetetic Astronomy is a fascinating volume, and one which I highly recommend, even though I believe that it is quite mistaken in its view of the world. Its logic is impeccable, and it demonstrates that one can have excellent reasoning skills and still come to the totally wrong conclusion. I am sure that many will feel the same about the book that you are currently holding in your hands!

In his book, Rowbotham says that the Earth is a vast disk with a circumference of 52,800 miles. This is the flat Earth model that we will examine. The Sun orbits over this immense flatness at a distance of 700 miles. The orbital plane of the Sun is parallel to the Earth’s surface, but coincident with the Equator, orbiting directly over it, and always in line with it. Some flat Earthers believe that the Sun is 30 miles in diameter and 3,000 miles away. We will investigate both of these solar distances, as well as others, in an effort to determine whether or not the flat Earth model is viable.

At this point, we need to introduce a simple equation called the small angle equation. This equation finds wide use in astronomy, surveying, navigation, and orienteering. The equation is as follows:

For example, the Moon seems to have a visual angular size of 0.5 degrees. This means that an anglemeasuring instrument, such as a sextant, would record the Moon’s apparent width, from one side to the other, as seen from the Earth’s surface, as 0.5 degrees. Astronomically speaking, this is a very large angular size. The Moon is said to orbit the Earth at a distance of 240,000 miles, and is said to have diameter of 2,160 miles. Start with 2,160. Divide by 240,000. Multiply by 500. Divide by 9. The result is 0.5 degrees. So, if you know the diameter (or width or length) of something, and its angular size, then you can easily calculate its distance. In fact, if you know any two of the following parameters (angular size, diameter, distance), then you can algebraically rearrange the equation to calculate the missing third piece of data. Simple. This equation has been verified many times with terrestrial objects of known size and distance, and can be trusted completely. A sextant can be used to measure angular sizes. Distances, lengths, and widths of objects can be measured by any number of reliable techniques. A tall tree’s height could be measured using trigonometry, say, while its distance from the observer could be measured with an instrument as mundane as a carpenter’s tape measure. The point is that this equation is not subject to any uncertainty, since all parts of it can be experimentally measured. Then, the measured values can be plugged into the equation to see if the math corresponds to experiment. In all cases, the agreement is excellent.

Another fact not in dispute is the angular size of the Sun as seen from any point on the Earth’s surface: 0.5 degrees. Note that this is the same as the angular size of the Moon, which is, at the very least, most peculiar indeed. This close match in angular size between the two astronomical bodies is what allows solar eclipses to occur in the first place. We will come back to the subject of eclipses (both solar and lunar) in a later chapter.

It is important to realize that everyone on Earth, no matter the location, observes this same angular size for the Sun (0.5 degrees). We can use this simple fact to calculate the distance between the Sun and the Earth. As far as I am aware, this technique is completely new, and originates with me. At the same time, we can decide the veracity of the flat Earth model, since if our calculated distance to the Sun matches that of the flat Earth model for all observers, then we must conclude that the model has merit. On the other hand, a substantial difference in solar angular size for different observers would suggest the flat Earth model is refuted. Let us begin.

The flat Earth model espoused by Rowbotham has, as we stated above, a circumference of 52,800 miles. For simplicity, we will round this off to 53,000 miles. The use of the word “circumference” implies a flat, circular Earth. Since the circumference of a circle equals pi times twice the radius, C = 2 * pi * r, we can easily rearrange the equation to calculate the radius of the flat Earth. It’s 8,435 miles. This, then, is the distance between the exact center of the flat Earth, which is designated as the North Pole in the model, and the edge of the planet, which is regarded as the South Pole. Note that the South Pole in the flat Earth model, unlike the North Pole, stretches all the way around the circumference of the Earth, and is located at its outermost edge. The Sun orbits above the Earth, and its orbital plane is parallel to the ground, yet always in line with, and directly above, the equator. The equator is located halfway between the North Pole and the South Polar edge, which would put the equator at 4,218 miles (8,435 divided by 2) from either pole. In the same way, latitude 45 degrees north would be located halfway between the equator and the North Pole, at 2,109 miles (4,218 miles divided by 2) from either. You can draw a simple diagram of the situation to make all of this much clearer.

At this point, we are not passing judgment on the flat Earth model. Rather, we are using details provided by one of its adherents in order to determine whether or not the model has any internal consistency. In other words, does the model “give back” the phenomena that we actually observe from the surface of the Earth? We will have occasion to engage in this type of exercise many times in this book as we search for the truth about the world in which we live.

So, we have, in effect, three observers – one at the North Pole, one at 45 degrees north latitude, and one at the equator (zero degrees latitude). The corresponding distances, as measured from the Equator, would be 4,218 miles, 2,109 miles, and 0 miles, respectively.

I set up a simple spreadsheet using one of the many free spreadsheet programs available today. One column of the spreadsheet listed the distance to the Sun at the flat Earth Equator. To cover a variety of possibilities, I chose distances of 100, 1000, 10,000, 100,000, 1,000,000, 10,000,000, and 100,000,000 miles between the Earth and the Sun. Earlier, we saw that many flat Earthers believe that Sun is 30 miles across and 3,000 miles distant – a factor of 100 between the two measurements. The small angle equation confirms that this “factor of 100 phenomenon” is a real feature of the world we live in. For example, if a small asteroid with a diameter of one mile came within 100 miles of the Earth’s surface, how big would it look in the sky? 0.56 degrees across, of course, nearly the same angular size as the Sun or the Moon. Therefore, I maintained this same factor of 100 for all hypothetical Solar distances, making the Sun’s diameter in each case to be, 1, 10, 100, 1,000, 10,000, 100,000, and 1,000,000 miles, respectively. Plugging these diameters and distances into the small angle equation gives 0.56 degrees – very nearly the 0.5 degrees that is actually observed for the apparent angular size of the Sun. So, at this point, we see that a Sun 30 miles across at a distance of 3,000 miles from the Earth’s surface would give a solar angular size that agrees with observation. But would all observers measure the same angular size at different locations?

To find out, we can use the Pythagorean Theorem (A^2 + B^2 = C^2, where side C is the length of the hypotenuse of a right triangle, and side A and side B are the lengths of the other two sides, respectively). The spreadsheet makes these calculations easy. Note that, for our observer at the equator, the Sun is directly overhead (perhaps he or she is making observations at noon on the first day of spring or autumn), so no calculations are needed; the distance to the Sun is simply a given. For our mid-latitude and polar observers, we have right triangles, where the vertical side of the triangle (side A) is the distance to the Sun at the equator, the horizontal side of the triangle (side B) is the distance between the observer and the equator, and the hypotenuse (side C, the slanted side of the triangle) is the distance between the observer and the Sun. Taking the square root of C^2, and applying the small angle equation, gives the apparent angular size of the Sun for each observer. At what diameter and distance will the Sun appear to have the same angular size for everyone concerned? The various columns and rows of the spreadsheet reveal the answer at once.

Only a solar diameter of 1,000,000 miles viewed from a distance 100,000,000 miles gives the exact same angular size of the Sun for all earthbound observers – a bit over half a degree, out to eight decimal places – with the spreadsheet that I used. Lesser distances and diameters did not agree in this incredibly exact way. This is a very interesting result. First, it refutes the flat Earth model completely, since a fundamental feature of that model is a small and close Sun. As a result, we will not consider the flat Earth model further in this book. Second, this is a minimum size and distance for the Sun. The Sun could be even larger and even more distant, but that has serious implications for the length of the year, which is fixed amount of time, requiring faster and faster orbital motion to maintain the year at its present length. Also, the brightness of the Sun becomes a problem with ever increasing distance from it. What power source could maintain daytime illumination at the observed level for thousands of years of recorded history if the Sun were many light-years away? Therefore, for the above reasons, it is very unlikely that the Sun is much farther away than 100,000,000 miles. Third, we gave the flat Earth model every opportunity to prove itself right, but ended up proving the round Earth model, instead, with its large and distant Sun. Fourth, the diameter and distance of the Sun given above are very close to the values found by today’s astronomers using professional-grade equipment: 865,000 miles for the diameter, 93,000,000 miles for the distance. The distance has a special name: the Astronomical Unit (abbreviation AU). We will use these accepted values throughout the remainder of this book.

Is there any other evidence for a round Earth besides some obtuse calculations? The roundness of the Earth’s shadow on the partially eclipsed Moon has always seemed rather convincing to me. After all, what shape looks like a circle, regardless of viewing angle? A sphere, of course. Our inability to see very far across the surface of the Earth also suggests that we live on a relatively small and significantly curved round ball. The way that the North Star (Polaris) seems to fall towards the northern horizon as we travel south is another observation readily explained by the globe Earth model. Distant thunderstorms over the ocean are “cut off” by the horizon, while closer storm clouds are visible from bottom to top. Even the rising or setting Sun is halved by a flat horizon. All of these observations are easily explained by a round Earth blocking our vision as its opaque bulk curves away beneath us.

The Luxor Las Vegas hotel/resort/casino is just 5.36 miles from my backyard. A giant pyramid 350 feet high, the Luxor can’t been from my location, but its brilliant searchlight beam, shooting straight up from the apex of the pyramid, can. Again, this is more proof of the curvature of the Earth. The intense beam of xenon light extends upward for miles, even though the view of the pyramid itself is blocked by the bulk of the globe Earth. I’ve even tried – without success, I might add – to see the Luxor from the highest point on the roof of my home. Simple observations such as these are very difficult to explain using the flat Earth model, but follow easily if we are all actually living on the surface of a great rocky ball – the Earth!

The temperature difference between the Earth’s equatorial tropical regions and its two poles also suggests a round Earth. Light rays from the distant Sun arrive at Earth parallel to each other. At the Equator, sunlight from the overhead Sun strikes the ground or ocean head-on at right angles to the surface, heating it furiously, while at the poles, the same light rays skim right across the surface, barely touching it at all before heading back out into space. Freezing cold temperatures are the result.

How big is the Earth? Eratosthenes cleverly figured this out in 240 B.C., using shadows of objects cast by the noonday Sun at different locations on the surface of the Earth. We will not go into the minute details of his method here (you can look it up online), but I find no flaws in his reasoning, and accept his values for radius (4,000 miles), diameter (8,000 miles), and circumference (about 25,000 miles).

So, where does this leave us?

1. The Earth is a solid, relatively small spherical body (although much of its surface is covered by oceans of liquid water that are shallow compared to the overall size of the Earth).
2. We live on the exterior of its strongly curved surface, which merely appears flat due to the large difference in scale between planetary bodies and human bodies.
3. The flat Earth model does not hold up to close scrutiny.
4. The Bible confirms these views:

Isaiah 40:22 King James Version (KJV)

It is He that sitteth upon the circle of the Earth, and the inhabitants thereof are as grasshoppers; that stretcheth out the Heavens as a curtain, and spreadeth them out as a tent to dwell in: