The Flat Earth model, part 5: The Solar Flashlight model

The Flat Earth Society maintains a web site here:

https://www.tfes.org/

Their model of the flat earth has the sun and the moon traveling in circular orbits above the earth. In this model the sun is envisioned as a kind of flashlight, with the light from the sun falling on the earth in a bounded cone. I will call this the “solar flashlight” flat earth model.

The advocates of this model explain that it doesn’t suffer from the problems described in Part 2 of my discussions as the sun never dips below the horizon. And they further claim that gravity doesn’t work the way that Newton described it. Instead they claim that what we call the attractive force of gravity is really due to the fact that the planet is accelerating upwards at a rate of 1 g. They claim that there is scientific evidence for this idea based on the recent discovery that the rate of the expansion of the universe is increasing, rather than decreasing.

This model ignores several key facts about the earth and about the motions of physical objects in our universe.

First problem: It ignores the results of the Cavendish experiment, described in Part 3. That experiment shows that there is indeed an attractive force between all bodies of matter. The point of the Cavendish experiment is that all bodies of matter in the universe exert an attractive force on all other bodies of matter. Furthermore that experiment showed that the direction of attraction between two separated bodies is not just “up and down”, but is rather directed along the line that intersects the two centers of mass. The force of gravitation is therefore “universal” because it is exerted between all bodies of matter in the universe, and in all directions. So the notion that “gravity works differently on earth” contradicts long standing known experimental results.

Second problem: The orbits of the sun and the moon as described in the solar flashlight model cannot possibly be maintained. Newton’s three laws of motion prohibit it. These laws are as follows:

An object at rest will remain at rest, and an object in uniform motion will remain in uniform motion unless acted on by an external force.
The force acting on a body of mass is equal to the change in momentum per unit time.
For every action there is an equal and opposite reaction.

According to the solar flashlight model, the sun and moon are constrained to circular orbits. How? According to Newton’s first law bodies in uniform motion will remain in uniform motion unless acted on by an external force. The sun and moon in the solar flashlight model are not in uniform motion because they move in circles, not in a straight line. Therefore according to the first law they must be under the influence of an external force. But what force? There is nothing in the model that could possibly exert a force that would constrain both objects to circular orbits.

In the Copernican model of planetary motion the planets are constrained to elliptical paths by the gravitational force of the sun. Without something to pull the sun and the moon toward a central point they would go flying off into space. Those who support this model therefore must not believe in Newton’s first law of motion. And it’s pretty clear that they don’t believe in the other two of Newton’s three laws either.

Third problem: A flashlight focuses light within a cone because it has a parabolic mirror behind the light bulb. Are the advocates of the solar flashlight model claiming that there is a parabolic mirror behind the sun that focuses the light? If so that mirror should be visible to our telescopes. Oddly, no such mirror has ever been observed– except in the fevered imaginings of the advocates of the solar flashlight model.

NASA created two spacecraft that were designed to observe the sun simultaneously from two different positions– thereby providing us with a stereoscopic view of Coronal Mass Ejections. The spacecraft were launched in 2006. Here is a link to the NASA web site that describes the details of this mission: https://www.nasa.gov/mission_pages/stereo/mission/index.html

The STEREO spacecraft are currently on the other side of the sun and are therefore seeing the sun from behind. They have never observed a parabolic mirror focusing the light of the sun. Here is a link to a video that explains the mission’s current configuration: https://svs.gsfc.nasa.gov/12390

Fourth problem: And what about eclipses? A solar eclipse is one in which the moon passes before the sun and blocks it from our view. This type of eclipse would be possible in the solar flashlight model as the moon can block the sun if its orbit is below that of the sun.

But a lunar eclipse is one in which the moon falls behind the earth’s shadow. That’s simply not a possible configuration in the solar flashlight model because the earth is never positioned between the sun and the moon. So solar eclipses are possible in the solar flashlight model, but lunar eclipses are not.

Actually they have an explanation for lunar eclipses. They claim that there is a Shadow object that circulates through the heavens and which periodically blocks the light of the moon. It’s a convenient notion. But if it were actually true then the Shadow object would block out the light of the stars as it circulates through the skies. This has in fact never been observed. So we may dismiss this idea as nothing more than an attempt to dress up a lame hypothesis with a very poorly thought out fix.

Summary: The solar flashlight model is astounding for its evident denial of experimental facts. We know that flat earth propagandists refuse to consider any evidence from satellites, from manned space missions, or from photographs. But the advocates of the solar flashlight model go much farther than that. They deny the reality of the Cavendish experiment, of Newton’s three laws of motion, and of the many lunar eclipses that humanity has witnessed over the last many thousands of years. This is truly an extraordinary model for the breathtaking reach of its denial of physical reality. It is not a physically possible hypothesis, though it does appear to be quite popular.

Written 2019-03-09.

The Flat Earth model, part 4: Movement

Does the earth move? That simple question has been the subject of more than 2,000 years of philosophical, theological, and scientific dispute. The Ptolemaic theory of planetary movement asserted that the earth is fixed and immovable at the center of the universe, as the bible says:

Yea, the world is established; it shall never be moved.
Psalm 93:1, Revised Standard Version

Yea, the world is established, it shall never be moved.
Psalm 96:10, RSV

Thou didst set the earth on its foundations, so that it should never be shaken.
Psalm 104:5, RSV

A Greek astronomer by the name of Aristarchus described a heliocentric (sun-centered) model of the universe in the early 200s BCE. He first estimated the size and distance of the moon and then used those results to estimate the size and distance of the sun. His calculations told him that the sun is about seven times larger than the earth. He made these estimates without the benefit of telescopes or spacecraft or even a value of pi. But from his findings he rightly concluded that it would be ridiculous to assume that the sun revolves around the earth since the sun is much larger than the earth.

This is a very interesting conclusion as it implies that Aristarchus was assuming that if one body of mass is orbiting another, then the larger mass must be the one that is stationary and the smaller mass must be the one that is moving. Newton’s universal law of gravitation made that view explicit, but the reasoning of Aristarchus shows that it was implicit even in the earliest thinking about the motion of the planets. Aristarchus might not have been able to express his thoughts about this dynamic in words, but he must have been imagining that the larger body exerts a force on the smaller body. It is the concept of a centrally directed force that was the key to Kepler’s insights about planetary motion, and this concept was clearly nascent in the thinking of Aristarchus.

The radius of the sun is actually about 109 times larger than that of the earth, not seven times. Aristarchus’s calculations were wrong– chiefly because it is very difficult to measure the angle of incidence of light on the surface of the moon with nothing more than the human eye. But Aristarchus was right to conclude that it must be the sun that is stationary, not the earth.

If the earth moves then it should be possible to see nearby stars shift in relative position as compared to more distant stars as the earth moves through its orbit. This phenomenon is known as parallax.

Parallax of the stars was not observed by ancient astronomers. But that’s not surprising, given that the stars are vastly farther away from earth than ancient astronomers imagined. Parallax can in fact be observed with present day ground based telescopes. But no such technology was available to ancient astronomers. As a result the geocentric (earth-centered) model gained broad acceptance.

There were other arguments against the motion of the earth too. If the earth were moving through space wouldn’t we feel a wind? But we don’t feel a wind. Therefore we must not be moving. If the earth were spinning on an axis we would be feeling a constant dizziness. And we don’t feel dizzy. So we must not be moving. All of these various observations led people to believe that the earth is immobile.

The flat earth model has generally been associated with the hypothesis of an immovable earth. One can imagine a flat disk-shaped earth that moves, and one can imagine a spherical earth that is fixed and immobile. So it isn’t necessarily the case that if the earth is flat it must be immobile, or that if it is spherical it must move.

The heliocentric model puts the sun at the center of our solar system, and the earth and all of the other planets in orbit around the sun. That, in fact, is why it is called a “solar” system. Is there any evidence for the heliocentric model?

Absolutely, there is. In fact the motion of the earth has been measured.

In 1838 F.W. Bessel reported that the star 61 Cygni has a parallax of 0.314 arcseconds. That puts the star at a distance of 3.2 parsecs from earth, or roughly 10.4 light years away. So Bessel proved that parallax is real and that it can indeed be used to measure the distances to the stars. If parallax is real, then it must be because the earth moves.

The Hipparcos satellite was launched by the European Space Agency in the 1990s to measure the positions and parallaxes of about 118,000 stars with very high precision. The satellite orbited earth, and so it was able to take advantage of the diameter of the earth’s orbit for its observation of parallax.

In the 1720s James Bradley and Samuel Molyneux made the first successful measurement of stellar aberration, a phenomenon that causes stars to appear to be in a different location to an observer on earth than it would to an observer on the sun. Their efforts resulted in a calculated velocity of the earth as just short of 30 kilometers per second.

The earth does in fact move. We have had proof of that fact for at least 2300 years. The earth revolves around the sun with a period of one year. Because the earth is about 93 million miles from the sun the earth’s orbital velocity is about 66,660 miles per hour, or about 18 miles per second. That equates to about 30 kilometers per second.

But the earth’s movement is more complicated than that. Our solar system revolves around the center of the galaxy. The solar system is about 28,000 light years from the center of the galaxy and it rotates about the galactic center once about every 230 million years. That works out to about 230 kilometers per second, or roughly 7.6 times as fast as the earth is orbiting around the sun.

And in addition our galaxy is moving. The universe is expanding, and our galaxy is moving in the direction of the galaxy Andromeda. Beyond that, our galaxy is one of several in a cluster of galaxies known as the Local Group that is moving collectively in the direction of Virgo at a rate of about 410 kilometers per second. The earth moves, our solar system moves, our galaxy moves, and in fact everything in the universe is moving.

Written 2019-01-27.

The Flat Earth Model, part 3: Gravity

The flat earth model is based on a highly fanciful model of gravity. In fact I honestly doubt that any advocate of the flat earth model understands gravity at all. So let’s begin with a simple question: What is gravity?

Isaac Newton conjectured that all bodies of matter in the universe exert an attractive force on all other bodies of matter. He summarized this idea in his universal law of gravitation, which says that the attractive force between two bodies of matter is proportional to the product of their masses divided by the square of the distance that separates their centers of mass:

Figure 1: Newton’s Universal Law of Gravitation

The constant G in the above equation is the constant of proportionality; F is the force; M is the mass of one of the two bodies, m is the mass of the other; and R is the distance that separates them.

This conjecture has two key components. The first is that it applies to all bodies of matter equally– there isn’t one class of bodies that exert a gravitational force and other classes that don’t. This is different from the electric force, for example, in that some types of matter are electrically neutral.

The second key component is that Newton claimed that the gravitational force radiates in all directions uniformly– there isn’t a privileged direction. One often repeated objection to the spherical earth model is that people standing on the “bottom” of the earth would fall off. That’s a perfect example of the failure to understand that Newton’s universal law of gravitation does not identify a privileged direction. In Newton’s universe “down” is the direction that points to the nearest large body of matter. For persons standing on the “bottom” of a spherical earth “down” points toward the center of the earth, just as it does for persons standing on its “top”.

This example illustrates another fundamental principle of our universe, namely its relativity. Every observer’s perception of physical phenomena such as length, mass, time, and down is different from that of any other observer not in the same inertial frame.

But was Newton’s conjecture correct? Is there an attractive force that behaves as he described and can one measure it? In 1797 Henry Cavendish performed the first experiment to observe and measure the force of gravity operating on objects in a laboratory. His experimental design is described in many articles that are available on the Internet.

Cavendish used lead spheres in his testing, but he could just as readily have used spheres of stone, cement, iron, wood– anything. Newton called his law of gravitation universal because he believed it to apply to all material objects, whatever they are made of.

So yes, there is indeed an attractive force between all bodies of matter in the universe, just as Newton had conjectured. But does that force obey an inverse square law as Newton had hypothesized?

This aspect of Newton’s theory of gravitation is due to its second key element, the fact that it is omnidirectional. Think of a body of mass emitting lines of gravitational force. Now surround the body by a concentric sphere. The lines of force intercept the sphere with a density that represents the strength of the gravitational field. Now imagine the sphere increasing in size. As its radius increases its surface area increases in proportion to the square of the radius, and the density of the lines of force intercepting the sphere falls simply because the surface area of the sphere is increasing. The inverse square relationship of Newton’s law is simply a consequence of the fact that the gravitational force radiates in all directions.

In Cavendish’s experiment the attraction between the lead balls was exerted horizontally, not vertically. So we have hard physical evidence that the gravitational force doesn’t only pull vertically.

How would this attractive force work on a disk shaped earth? The standard answer one hears from the advocates of the flat earth model is that it would pull everything “down”. But is that claim really true?

Let’s consider the gravitational force exerted by a disk shaped earth. We’ll construct our disk in such a way that it has the same surface area as our spherical earth, and the same volume. A little mathematics shows that such a disk would have a radius of about 8,000 miles (rather than the spherical earth’s 4,000 miles) and a thickness of about 1500 miles.

Now imagine a building constructed at the very center of a disk shaped earth. For the sake of simplicity we will think of this building as consisting of a stack of stone or concrete blocks.

Figure 2: A disk shaped earth with a building at its center

Now let’s consider the force acting on one cubic inch of the building due to the gravitational force of the earth. The key point we have to consider is the first part of Newton’s universal law of gravitation– namely that all bodies of matter in the universe exert an attractive force. So to account for the gravitational force exerted by a disk shaped earth we have to consider the force exerted by every cubic inch of the earth’s mass, and then we have to sum up all of the resulting forces.

To do that let’s think about a cubic inch of the tower, P, and a cubic inch of the earth directly below it, Q some distance below the surface. The direction of the force exerted by Q pulls directly down, as shown in the diagram below:

Figure 3: The force exerted on a point P of the building by a point Q of the disk shaped earth

Now let’s consider a cubic inch of earth that is some distance horizontally from the vertical, as shown in the diagram below:

Figure 4: The force exerted by a point R offset from the vertical

The diagram shows that the gravitational attraction between the points P and R can be resolved into two components: a vertical component and a horizontal component.

Because a disk is symmetrical around its central axis it is always possible to find another cubic inch of matter in the earth that is at the same depth below the surface, the same distance horizontally from the vertical, and 180 degrees opposite to point R, The diagram below shows the point S that satisfies this condition:

Figure 5: Showing a point S with the same horizontal component as point R

The important fact about point S is that its horizontal component is of the same magnitude as that of point R, but it points in the opposite direction Therefore the horizontal components for points R and S will cancel out with the result that we only have to consider the vertical components. Hence the net force operating on the building will be directed vertically down into the planet, just as we would hope.

Now let’s consider another building close to the outer edge of the disk, with a point R offset from the vertical, as shown in the picture below:

Figure 6: A building at the edge of the disk shaped earth

As before the diagram shows the gravitational force resolved into a vertical and a horizontal component. But in this case there is no mirror point with which to offset the horizontal force. So the horizontal component of the force exerted by point R would not be offset by that of any other point. And this would be true for every cubic inch of matter of the earth that is horizontally offset from the building.

The net result is that there will be an overwhelming horizontal force that will pull the building horizontally to the left, causing the building to collapse. As a result there would be only one truly safe location on which to build any building on this fantasy earth– at its very center. A building built anywhere else will be ripped down by the planet’s gravitational force.

Incidentally this would give us a very simple way of finding the edge of a disk shaped earth. All one would need is a plumb bob. The outer edge of the disk would be in the direction opposite to that toward which the plumb bob is pulled.

A spherical earth doesn’t have this problem for the simple reason that a sphere doesn’t have an edge. For any location on a spherical earth it is always possible to find a point of matter with which to counterbalance any point that is offset from the vertical, as shown in the diagram below.

Figure 7: A building on a spherical earth

This is not a problem that flat earth propagandists can fix. This problem is the result of the proposed shape of the earth– that is, disk shaped. The only way it can be fixed is by adopting a model that is based on a different shape for the earth– one that has no edge And the only shape that meets that condition is the sphere.

Written 2019-01-26.

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:

https://www.tfes.org

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:

https://images.nasa.gov/

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.

The Flat Earth model, part 2: Daylight

There are many observable facts that advocates of the flat earth model do not accept. Daylight is one of them.

There are two major facts about daylight that any model of the shape of the earth must explain. These are its longitudinal and latitudinal variations.

Anyone who has ever spoken to another person who lives in another time zone is familiar with the longitudinal variation of daylight. At any given point in time one half of the earth is in darkness and one half is in light, and that variation falls along longitudinal lines.

I live in the Pacific time zone; my brother lives in the Eastern time zone. So we are always 3 hours different in time. If I call him at 7 PM my time it’s 10 PM his time. I’m in late evening and he’s in night.

If it is noon in the Pacific time zone at a time of year when no time zone is observing Daylight Savings the time will be:

1 PM in Denver Colorado
2 PM in Chicago
3 PM in New York City
8 PM in London
9 PM in Berlin
11 PM in Moscow Russia
4 AM in Beijing
5 AM in Tokyo
10 AM in Anchorage Alaska

This is not just a human imposed artifice. When it is 11 PM in Moscow it really will be dark outside. When it is 3 PM in New York City it really will be mid-afternoon and therefore daylight outside.

The flat earth model cannot account for this fact. Once the sun appears above the horizon of a flat earth all regions of the planet will experience daylight equally. None will be in darkness.

The spherical earth model accounts for longitudinal variation in daylight quite simply and naturally. From a single point source of light– i.e. the sun– only one half of a sphere can be illuminated at any one time. We have a huge number of confirmations of this phenomenon in the form of photographs that have been taken from artificial satellites and manned space vehicles. For example, this photo was taken by the crew of the Apollo 15 mission:

https://images.nasa.gov/details-as15-91-12343.html

The photo shows Africa and Europe in shadow while South America is in daylight. Here’s another that was taken on the Apollo 13 mission that shows a portion of North America in daylight:

https://images.nasa.gov/details-as13-60-8588.html

And here’s one that shows the earth as a crescent:

https://images.nasa.gov/details-as4-01-750.html

None of these photographs would be possible if the earth were shaped like a disc.

These variations in daylight are longitudinal in that they fall along the lines of the earth’s meridians– that is, lines of longitude. Latitudinal variations are those that have to do with the distance a location on the earth’s surface is from the equator. Regions that are closer to the North and South poles experience far more hours of daylight during their summer months than do equatorial regions, and far fewer hours of daylight during their winter months. I live close to the 47th parallel. At the summer solstice we receive about 16 hours of sunlight in the day, and at the winter solstice we receive about 8.5 hours. A person living on the equator would receive 12 hours of sunlight every day of the year. Here is a short video that shows what it is like to live north of the Arctic Circle in the summer:

Furthermore the northern regions experience summer when the southern regions are in winter. In winter the sun never rises above the horizon on at least one day per year for any location north of the Arctic Circle.

The flat earth model cannot explain this phenomenon. When it is daylight in any one region of the flat earth it would be daylight for all. But that is not true on planet Earth.

The spherical earth model explains this phenomenon quite simply and elegantly. The earth is inclined at an angle of about 23 degrees relative to its plane of rotation about the sun. That inclination means that regions close to the north pole are tilted toward the sun by 23 degrees during the summer months and are tilted away from it by 23 degrees during the winter months. When tilted toward the sun the polar regions will see the sun above the horizon for more hours; when tilted away the sun will appear above the horizon for fewer hours.

This variation in daylight is directly related to latitude, as it is dependent on the distance a region is from the equator. It is the basis of the seasons, something that most people do believe in– maybe even most flat earth propagandists.

Written 2019-01-24.