The Flat Earth model, part 1: A bit of history

The earth is an oblate sphere with a radius of about 4,000 miles. It revolves around the sun in an elliptical orbit at a mean distance of about 93 million miles. And it rotates on an axis that is inclined at about 23 degrees to the plane of its orbit around the sun. I do not take these claims as articles of faith but as observable facts. But I will readily admit that these facts are not trivially obvious, and that their discovery was hard won over a very long time.

The notion that the earth is flat originated in ancient times. More recent propagandists– Samuel Rowbotham and Charles K. Johnson among them– claimed to have proved that the earth is flat. But with the death of Mr. Johnson in 2001 his International Flat Earth Society died along with him and for a time the flat earth model was not widely publicized. But recently there has been a resurgence of interest in the flat earth model. Today there are many web sites that promulgate the flat earth model; here is one:

Mr. Johnson would not have recognized the model espoused by the contemporary Flat Earth Society. Mr. Johnson was a Christian fundamentalist who believed that the bible states that the earth is flat and unmovable. The link above describes a very different model of the earth– one that is not just moving through space, but that is actually accelerating at the rate of 1 g. And whereas Charles Johnson believed that the sun revolves around the earth the Flat Earth Society’s model shows the sun moving in a circular orbit ABOVE the earth. The Flat Earth Society’s model further asserts that the sun is like a flashlight in that the light it casts on the earth is confined to a narrow cone. I will call the Flat Earth Society’s model the “solar flashlight” model of the flat earth. Charles Johnson’s model, which involves a sun that revolves around the earth, I will call the “traditional” flat earth model.

The arguments one hears from flat earth propagandists betray a wealth of ignorance about the history of this debate. So let’s begin with a brief recounting of the history of the various models of the earth’s shape.

We should mention at the outset that the debate about the shape of the earth has always been entangled with the question of whether the earth moves. That’s because the evidence that the earth is spherical and that the earth moves is not readily apparent. If we look out over a wide expanse do we see a curved horizon or a flat horizon? No, we see only flat horizons, not curved. Residents of our planet do not sense that the earth is moving. If it were moving would we not experience a wind blowing against the direction of the earth’s travels? We experience no such wind. Wouldn’t we get dizzy if the earth were spinning at the rate of 1,000 miles per hour? We experience no such dizziness. These direct observations were sufficient to convince early observers that the earth is flat and that it does not move.

To perceive the curvature of the earth with the naked eye would require vision sensitive enough to detect a difference of 1.6 inches over a length of 100 feet. Human vision just isn’t that sensitive. It’s no wonder that people of the ancient world found it so difficult to believe in a spherical earth.

The model of a flat immobile earth was commonly accepted in the ancient world. We might call it a naive model, but doing so disparages a view that did in fact appear to be supported by physical evidence. I shall call it the “natural” model in recognition of the fact that it is hard to observe evidence of either the curvature or the movement of the earth.

The old and new testaments of the bible include a number of passages that either explicitly or implicitly state that the earth does not move, one of which is the following:

Yea, the world is established; it shall never be moved;

Psalm 93:1, Revised Standard Version

Pope Urban VIII cited a number of such passages as proof that the earth cannot move when he turned Galileo over to the Papal Inquisition for the investigation of heresy.

There are no passages in the bible that explicitly state that the earth is not a sphere, but there are passages that clearly indicate that the authors of the bible believed in a flat earth.

The visions of my head as I lay in bed were these: I saw, and behold, a tree in the midst of the earth; and its height was great. The tree grew and became strong, and its top reached to heaven, and it was visible to the end of the earth.

Daniel 4:10-11, Revised Standard Version

It would not be possible to see a tree, however tall it might be, from all points on a spherical earth, so the above quotation only makes sense in the context of a flat earth model. But although the flat earth model was widely accepted and had the imprimatur of scriptural authority there were clear signs to some thinkers of the ancient world that the earth could not be flat. For example, when a sailing ship heads out to sea the hull disappears below the horizon, then the deck, then the masts. This simple observation could not be explained by a flat earth model.

Eratosthenes of Cyrene was a Greek mathematician who lived from 276 BCE to 194 BCE. He was the first person known to have calculated the circumference of the earth. The experiment he conducted and the method he used were models of elegance. Eratosthenes knew that at noon on the day of the summer solstice the bottom of a well in Syene (near modern day Aswan Egypt) was fully illuminated by the sun. But that was NOT true of wells in Alexandria on the same day. By measuring the deviation of the sun’s rays on the day of the summer solstice from the vertical in Alexandria he was able to calculate the circumference of the earth using nothing more than plane geometry. The value he obtained is in close agreement with modern values. As far as I am aware no advocate of the flat earth model has ever found significant fault in either his reasoning or his method.

Aristarchus of Samos was a Greek astronomer who lived from 310 BCE to 230 BCE. He proposed a heliocentric model of planetary motion in which the earth revolved about the sun on a circular orbit. His ideas were not widely accepted, but at the very least his proposal shows that the geocentric model of planetary motion was not the only model considered by ancient thinkers.

One of the primary objections to the heliocentric model at the time concerned parallax. If the earth is orbiting around the sun, then one should be able to observe nearer stars shifting side-to-side throughout the year relative to more distant stars. This phenomenon was not observed in ancient times. Aristarchus is said to have rebutted this argument with the claim that the stars are so distant from earth that parallax could not be observed. But as this was an explanation of a lack of evidence his heliocentric model lost out to the geocentric model.

Today it is possible to observe parallax with ground based telescopes. Aristarchus was correct, but with the technologies available at the time there was no way for him to prove it. Parallax is another phenomenon that cannot be explained by an immobile earth.

Claudius Ptolemy was an Alexandrian astronomer and mathematician who lived from roughly 100 CE to 170 CE. He was the author of a book known by the title given it by Islamic scholars: the Almagest, or “Great Book”. It was certainly one of the most influential books ever written. It codified a system in which the model of an immovable earth was merged with Greek astrology to explain the movements of the planets. Astrology depended on the precise calculation of where a planet could be seen in the night sky relative to the constellations, whether in the past or in the future. Ptolemy’s system provided a method for making such calculations with great precision.

One of the key difficulties that astronomers sought to explain is that of retrograde motion. Roughly every two years it is possible to observe Mars advancing from west to east in the night sky only to reverse direction later, loop backwards through the sky, then reverse course again to return to its usual west-to-east motion. These observations require patience as the retrograde motion of Mars is only apparent over several weeks.

All of the outer planets exhibit retrograde motion, but that of Mars is the most obvious.

To account for this Ptolemy used what are known as epicycles. The planets, according to Ptolemy, rotated about the earth in circular orbits with circular epicycles. The resulting path would have looked roughly like a spiral looped around a circle.

The system worked in that it could provide accurate calculations for the motions of the planets and therefore accurate horoscopes for those wealthy enough to pay for them.

Ptolemy’s theory– and it was a scientific theory– was enormously successful. It was adopted throughout Rome, the Moslem empire, and Europe. And because it made astrology possible it became indispensable to civilization.

In 1543 Nikolas Copernicus, a Danish astronomer, published a book in the last year of his life in which he advanced a heliocentric model of planetary movement. The earth, Copernicus said, circles the sun, as do all of the other planets.

Copernicus simply did not have enough hard physical evidence to prove his case. But Johannes Kepler learned of the Copernican model and made it his life’s mission to prove that Copernicus was right. For years Kepler labored to develop what we now know as his three laws:

(1) The planets do not move in circular orbits with circular epicycles; rather they move in elliptical paths with no epicycles and the sun is at one of the two focii of each planet’s elliptical path

(2) The line connecting the sun and a planet sweeps out equal areas in equal times

(3) The square of the planet’s orbital period is proportional to the cube of the semi-major axis of a planet’s path

These laws represent the most dramatic shift in thinking about the planets and their orbits since the time of Eratosthenes. They were based on the direct observations of the motions of the planets of Tycho Brahe, which were the most accurate available. And they were verifiable in that one could use his laws to predict the location of any planet in the night sky just as one could with the Ptolemaic theory. The main difference is that Kepler’s theory ascribed a cause for the motions of the planets– the “magnetic” force of the sun.

Kepler’s approach was fundamentally different from that of Ptolemy in that he began from first principles. His objective was to derive the laws of motion of the planets from Brahe’s raw data. To accomplish that he threw out all of the assumptions that were key to both the Ptolemaic and the Copernican theories. Ptolemy was content to define a deferent, an epicycle, an eccentric, and an equant for each planet. Kepler used nothing more than the planet’s distance from the sun and it’s angular momentum.

Isaac Newton developed a theory of what we now call gravitation that was based on an attractive force obeying an inverse square law. It is a standard exercise of mathematical physics to show that Kepler’s laws can be derived from the simple assumption of a centrally directed force that obeys an inverse square law. This confirms that Kepler was right to throw out all of the preconceived notions that were central to the Ptolemaic theory and to attempt to derive the principles of planetary motion from the fewest possible assumptions.

Another standard derivation shows that the possible paths of a satellite under the influence of the gravitational field of a larger mass can only be one of the conic sections: a circle, an ellipse, a parabola, or a hyperbola.

The greatest success of Newton’s theory of gravitation was the discovery of the planet Neptune. In 1781 William Herschel discovered the planet Uranus with the 20 inch reflector telescope he owned. Followers of Newton’s theory were most interested in confirming that the new planet conformed to Kepler’s laws and that its path was indeed an ellipse. But the practiced observers of the time noticed that Uranus’s path had a wobble. Perhaps, it was suggested, there is something amiss in the edifice that Kepler and Newton had erected.

Independently a British mathematician named John Couch Adams and a French mathematician name Jean Joseph Le Verrier conjectured that the path of Uranus was being influenced by another planet in a more remote orbit. And they were both able to calculate an estimated path for it. A German astronomer by the name of Johann Gall saw Le Verrier’s result and used it to discover the planet that we now call Neptune. He found the planet on the first night he looked for it.

The Ptolemaic theory could never have predicted the existence of another planet. It was an ad hoc theory in the respect that deferents, epicycles, eccentrics, and equants were all fitted to the observed motion of each planet, one at a time. Not only was the model developed by Kepler and Newtonian far simpler, it was also far more powerful. Newton’s was a universal theory of gravitation– one that applied to all bodies of matter in the universe. It provided a natural explanation for the cause of each planet’s movement– the gravitational field of the sun. And it was predictive in the respect that it could be used to infer the existence of heavenly objects that had not previously been observed.

The hypothesis of an immobile earth has been exhaustively tested and has failed. The earth does move– it revolves around the sun as do all the other planets– and we now have a profound and powerful explanation for its movement.

What about the shape of the earth? Once it was understood that Newtonian mechanics accurately describes the motions of the planets it was realized that the same principles could be used to launch vehicles into space. Albert Einstein’s General Theory of Relativity adds some additional nuance, but for the most part these differences are not significant to the problem of launching a human occupied vehicle into orbit around the earth.

The launch trajectories of all artificial satellites and manned vehicles that have been vaulted into space have been based on the assumption that the earth is spherical, not disc shaped. A disc of the same surface area as the spherical earth would have twice the radius. If a rocket were launched into orbit around a disc shaped earth on the basis of a spherical earth’s dimensions the rocket would crash before completing even one orbit. When such missions have failed it has not been because of our understanding of the shape of the earth. The spherical earth model has in fact been resoundingly confirmed again and again. All of the photos returned from space vehicles have shown the earth to be spherical, not disc shaped. And these photographs number in the tens of thousands. NASA maintains an archive of photos from the entire history of space missions here:

The story of the debate about the shape of the earth and the motion of the earth is one of the great triumphs of science. Kepler’s laws in particular represent the emergence of a new way of understanding the world around us.

This is not the history of the flat earth debate that flat earth apologists want you to know about. In the following blogs I will discuss at length what they don’t want to talk about, and some of the issues that their completely lame model cannot explain.

Written 2019-01-24.

Copyright (c) 2019 David S. Moore. All rights reserved.

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