Is the earth a spinning
|Flat earth with South pole at its center.|
Could the location of the continents be the result
of radial continental drift due to centrifugal effects?
Such exotic models ignore the laws of physics that have been developed over several centuries into a unified and powerful tool for understanding the natural world. Any of these warped geometries would require rewriting every physics book and recasting every law of classical physics—laws that have worked just fine in science and engineering for centuries. No reasonable person would even try such a daunting task, and no flat earther is sufficiently knowledgeable about mathematics and physics to attempt it. It would require a "new physics" to duplicate exactly the results of the "old physics", and the newly transformed laws would be much more complicated to understand and use. So what is to be gained from such a vast exercise? Nothing new would be learned, and the result would surely be more clumsy to use in physics and engineering and all the other fields that depend upon it. Not one flat earth believer I've ever corresponded with even knows about such mathematical models, or has the ability to understand them. Ditto for their grasp of physics.
Casual believers in the flat earth usually have not heard the best arguments for a round, spinning earth, as these are generally ignored by those who promote flat earth arguments. In the summary below I've indicated with an asterisk those experiments that do not in any way depend on assumptions about the speed of light or the paths of light rays.
If you were on an large ocean liner or cruise ship sailing on a very calm day you could be below decks in your room with the portholes covered and you'd not feel any motion of the ship. No experiment you could do with available tools could detect that you were moving. Maybe you'd feel the vibration of the engines, but you wouldn't be able to tell which direction the ship was moving, or how fast, or if it was moving at all.
But some one objects. Maybe you can't detect straight-line motion, but what about spinning motion? Surely you could tell if you were on a rotating carousel, even if you were blindfolded. Yes, you certainly could, and we can, by similar means, detect the rotation of the earth even if we were in a closed room and could not observe the apparent motion of the stars. If you were on that cruise ship, and it were sailing around a circular path, you could detect that fact even below decks in a windowless room.
|Foucault pendulum at the Panthéon in Paris, 1851.|
220 feet long, 62 pound bob.
The Foucault Pendulum. There are many evidences of the earth's rotation. The one most people have heard about is the Foucault Pendulum (Léon Foucault, 1819-1868), a pendulum swinging slowly on a very long wire from a fixed support. As the earth rotates underneath the pendulum, its plane of swing relative to the room it is in slowly precesses at a constant rate, easily observed. Science museums around the world have such pendulums, and some university physics buildings do also. Pendulums at different latitudes have different precession rates, and the data confirms not only the earth's rotation, but the fact that it is round.
Gyroscopes. A spinning wheel, mounted so that it can freely turn in any direction with respect to the earth, will maintain spinning about a fixed axis as the earth turns underneath. Its behavior as a function of latitude is clear evidence that the earth is round and that it rotates. It could also tell us the earth's rotation period even if it were in a closed room.
|As light propagates down the telescope,|
the telescope moves, requiring a tilt of the telescope.
The apparent angle of the star φ differs from its true angle θ.
From The Wikipedia.
Stellar aberration. The earth's motion relative to the stars is measurable. James Bradley (1693-1762) demonstrated this, reporting his results in 1728. The earth rotates on its axis and revolves around the sun. Incoming light from stars passing into a telescope has finite speed, so from the time it enters a telescope objective to the time it reaches the eyepiece, the telescope has moved due to the motion of the earth. So the telescope must be aimed slightly forward (in the direction of its motion) to compensate for this. Measurement of this tilt angle confirms what was already known about the motion of the earth. This effect is dependent on latitude, so it also provides evidence that the earth is round.
Some flat-earthers try to explain this as an atmospheric refraction effect. They conveniently overlook the fact that such refraction would have to be biased in direction, from east to west. They have no explanation why this should be so.
|Schematic of the Sagnac interferometer.|
From the Wikipedia.
The Sagnac effect. The Sagnac interferometer sends two light beams around a closed path in opposite directions. The two beams then pass through a partially silvered mirror and recombine, forming an interference pattern. Rotation of the entire device is revealed by the shift of the interference pattern of the two beams. This effect is the basis of laser gyroscopes now often used to replace mechanical gyroscopes, and they also reveal the earth's shape and rotation. The Sagnac interferometer and the mechanical gyroscope work on entirely different principles, but they both reveal the rotation of the earth, and give the same result for its rotation speed.
Plumb bobs. A mass suspended on a long wire leans from true vertical by a slight angle, always toward the equator. The lean angle is least (zero) at the equator and at the poles, greatest at latitude 45°, and its variation with latitude demonstrates two things (1) the sphericity of the earth, and (2) the fact that the earth spins about its polar axis. This is a centrifugal effect, well understood and easily demonstrated in the laboratory with rotating systems of other kinds. Physics students experiment with such systems in freshman laboratories, measuring and confirming the physics of this bit of physics.*
Atmospheric cyclones and anticyclones, demonstrate earth's rotation and the direction of that rotation. These are examples of Coriolis effects. The fact that they have opposite sense of rotation in the northern and southern hemispheres is evidence of an antisymmetry about the equator. This would not be the case even on a spinning flat disk earth. Ocean currents have the same sort of symmetry, though these depend on several influences, including winds, water density and the Coriolis effect. They also support the fact of earth's rotation, but the interpretation of the evidence is complex.*
|The Compton tube apparatus.|
The Compton tube. Physicist Arthur Holly Compton (1892-1962) devised a neat way to demonstrate earth's rotation in 1913. It is called the "Compton tube". Seldom is it mentioned in textbooks. It uses a large 1 meter diameter glass torus filled with liquid having small particles in suspension. It is aligned in a plane east-west allowed to stabilze for a day or more, then quickly rotated 180 degrees about its diameter. The suspended particles are observed with a microscope and for a few seconds they rotate with respect to the tube, the motion damping out in about 20 seconds. This motion occurs because the liquid and the particles were initially moving with the tube around the earth's axis. After the tube flips, the liquid and the particles, are now moving in the opposite direction inside it. Their speed can be observed with the microscope. This device not only indicates the direction of North, but also shows which direction the earth rotates. I find only one brief mention of this on the Internet. See: Science World, Compton tube. Compton proposed this as an inexpensive and practical method for demonstrating the earth's rotation in a school laboratory. *
Long distance projectiles and unguided missiles must be launched at a calculated angle and direction if they are to hit their targets. This requires taking the earth's rotation into account in the calculations. They must also use the fact of the earth's surface curvature. *
During a World War I naval engagement near the Falkland Islands British gunners were puzzled why their precisely aimed guns were falling to the left of the German ships. Their guns had been corrected for the Coriolis effect—but for the Northern hemisphere. The Falkland islands happen to be in the Southern hemisphere. So the guns failed to correctly account for the earth's rotation. Who says it doesn't matter whether you accept the rotation of the earth?
Launching earth satellites into orbit takes advantage of the earth's rotation. With the exception of satellites intended for polar orbits, they are launched heading eastward. This requires the least fuel. If launched westward they would need to gain as much speed as the earth (in the wrong direction) plus the additional speed to achieve orbital speed. Satellites in low orbit must reach speeds of about 17,500 mph. The launch rocket on the launching pad already has velocity toward the East due to the Earth's rotation. Launches near the equator gain 1,000 mph from Earth's rotation. *
The Doppler effect is the shift of frequency of light (or any electromagnetic radiation) due to the relative velocity of source and receiver. If they are moving toward each other, the frequency rises; if they are moving apart, the frequency decreases. We now have orbiting earth satellites that can image the earth with Doppler radar, primarily for gathering atmospheric data. This data confirms (a) the round shape of the earth, and (b) its rotation. We even put a cube corner light reflector on the moon that allows us to send a beam of laser light to the moon, which directly reflects back to the earth station that originated it. This can accurately measure the distance to the moon as it changes due to its orbital eccentricity. This can even measure the change in this distance due to the earth's rotation relative to the moon, confirming the round shape of the earth. Similar confirmation of the earth's shape and rotation comes from global positioning systems (GPS). *
Falling bodies. A stone dropped down a deep vertical mine shaft is deflected slightly eastward. This is because its velocity at the earth's surface is greater than the velocity of the earth at the bottom of the shaft, which is nearer earth's center. This is true in either hemisphere of earth, but the amount of deflection depends on latitude, being greatest at the equator and reaching zero at the poles. The deflection also happens with a stone dropped from a high tower. This effect is also clear evidence of the sphericity of earth. *
In fact this experiment has a long history. Some early philosophers denied the rotation of the earth. They argued that if it were rotating, a stone dropped from the mast of a ship would not fall to a point on deck directly below, but would fall behind the mast. Experiment proved otherwise, because, as Galileo argued, the stone at the top of the mast was initially moving just as fast as the deck below, and retains that speed as it falls. So he concluded that even on land, if the earth moves, a stone dropped from a high tower falls to a point directly below. So the earth's rotation, he said, doesn't affect motion of objects on earth.
But he was only approximately correct. There's more to this story. Galileo had not considered the fact that on a round rotating earth the top of a high tower actually moves faster than the ground at the base of the tower, due to it being farther from the center of the earth. So the stone at the top is also moving faster than the ground below, and retains this velocity all the way down. So it gets ahead of the ground and falls to the east of the point just below, opposite to the prediction of the flat earthers. The effect is small, because the difference in velocity at top and bottom is so small, but it is measurable with precision instruments. Flat earthers predicted the ball would fall beind the mast if the earth were moving, but it actually falls ahead of the mast. So the flat earther's experiment actually is another evidence for a round, rotating earth. *
Atomic Clocks. Standards of length and time are now based on the microwave radiation from atomic energy level transitions. Cesium-133 has been used for this for several decades. Now strontium atoms offer a threefold increase in precision in such measurements. Einstein's special relativity theory predicts that clocks suffer time dilation when they are moving, and this has been experimentally conclusively confirmed. Now, with strontium clocks we can even compare the difference in speed between networked clocks located at different places on earth. In 2017 Pacóme Deva of the Paris Observatory and his colleagues did this, using optical fiber links between London and Paris, and one between Paris and Braunschweig, Germany. While this was reported in the press as a test of special relativity, it also serves as a measure of earth's axial rotation and its sphericity, since the cities being compared are at different latitudes, and therefore different distances, from the earth's axis, and have a different velocity due to that fact. [New Scientist, 25 March 2017, p. 11,] *
The night sky. Early civilizations were quite aware of the starry night sky, with its apparently fixed patterns of stars, leading to those patterns (constellations) being given names. These patterns were reliably constant and unchanging in shape. Ocean navigators knew them well, and used them for determining latitude at sea. As they traveled south, the north star's elevation decreased, and in the southern sky constellations, previously not visible, were now above the horizon. Either the entire sky dome had obligingly shifted northward as they sailed south, or they were sailing on a round earth.
|Sun's position at Alexandria and Syene|
at the same time of the day.
The ancient Greeks also knew the size of the round earth. Eratosthenes of Syene (276-194 BCE) calculated that by geometric triangulation, using a measured baseline from Alexandria to Syene (now Aswan). His baseline data wasn't very accurate, but his method was sound and his result was within 1% of the modern value. High school physics students sometimes repeat this experiment, using baselines spanning several U.S. states. *
The Internet makes it possible for near instant communication anywhere on earth. A group of people in various countries could do this experiment. They would observe, at a pre-agreed time, the length of the shadow of a perfectly vertical pole. The data, combined with their geophysical coordinates, would allow a repeat of Eratosthenes measurement of the size of the round earth. *
Seismology gives further evidence. Earthquakes propagate waves through the body of the earth. The direction and arrival times of these disturbances at surface monitoring stations allow us not only to pinpoint the location of the earthquake epicenter, but also to learn the composition of the inner earth itself, and how the inner shells refract seismic waves. All of these consistently support the spherical shape of the earth and its inner shells. No flat earther has ever even tried to account for this massive body of data, using a flat earth model. *
The equatorial bulge is a result of the earth's rotation, which distorts the earth into a slightly oblate ellipsoid of revolution. Isaac Newton (1642-1726/27) gave a mathematical proof of this rotation effect in his Principia (1687). He showed that a rotating self-gravitating near-spherical elastic body would increase its radius at the equator and decrease its radius at the poles. This is a very small effect, but is measurable by precise surveying techniques along with measurements of stellar positions at various latitudes. These measurements, along with Euclidean geometry, determine the variation in the length of one degree of latitude as a function of latitude. During the 17th and 18th centuries scientific expeditions were sent to Northern countries to measure the "polar flattening", and the effect was confirmed. Today GPS systems further confirm it in both hemispheres, and the fact that the effect is nearly symmetric about the equator not only confirms the fact that the earth is round and that it is rotating about its polar axis, but also confirms the correctness of Newton's gravitational law. *
But that conclusion ignores the force due to the earth's gravity, which not only keeps us on the surface of the earth, but also holds the earth together; otherwise the earth would never have formed in the first place.
Even in Newton's time critics dismissed gravity as an "occult force", for they couldn't get their minds around the notion that bodies could exert forces on other bodies without touching them, and without anything material between them.
Flat earthers usually dismiss and deny the existence of gravitational force. They say, "Things fall because they are heavy. What else do we need to know?" Scientists want to know more.
They must assume some equally mysterious cause for the severe distortion of distances from N to S pole. Their justification for these is, "That's just is the way it is." Gravity deniers called Newton's gravity an "occult" force. This is clearly a double standard, for whatever might cause their light path bending is also an "occult" force.
There is one light path bending effect that argues for the round earth and against the flat earth. The atmospheric blanket of the round earth is curved, and therefore refracts light in a way well understood from laboratory experiments. It allows us to see a bit "around" the curve of the earth. This is due to the decrease of atmospheric density with height. It distorts the shape of the rising and setting sun and moon (flattening them), an effect easily observable by anyone. This also causes the sun to rise earlier and set later than would be expected if there were no atmosphere. It also allows us to see stars and other celestial objects that would otherwise be "over the horizon". This is why, at the North or South poles one can see the sun move all the way around the sky near the summer solstice, remaining above the horizon all the way around. It is also the reason that in some cases a total lunar eclipse at sunset or sunrise can be seen when both the sun and moon are above the horizon. Astronomers, even amateur ones, must be aware of, and compensate for, this effect when observing stars near the horizon. This is not a mysterious effect, but one due to atmospheric refraction, and the physics of it is well understood. It is quite different from the sort of severe light bending that flat earthers must assume to support their earth model.
This atmospheric refraction is constant and ever-present. It is not the localized and temporary phenomenon that causes mirages due to temperature inversions near the ground. See the discussions of atmospheric refraction and looming and similar refraction phenomena in the Wikipedia.
Historically, such observations have been used by "both sides" of the earth shape question. Those who accepted the round earth cited the fact that ships sailing toward the horizon are seen to disappear gradually, from the hull then to the top of their masts. That's the usual case, when there are no temperature gradients along the line of sight. When conditions happen to be right, a ship that ought to have already disappeared "over the horizon" actually seems to rise above the water, or even rise up and appear upside down. These are commonly referred to as mirages and can be seen over land as well. Flat earthers ignore those cases. They look only at those cases where local conditions give the result they want.
Then there's an interesting phenomenon not generally well known to most people. The surface of the ocean is of variable curvature, and sometimes over considerable distances, is nearly flat! This is because the surface level is affected by the profile of the ocean floor beneath it—a gravitational effect. Over an undersea mountain, the water level actually rises. Over an undersea hollow or trench the level is depressed into a slight valley. This is confirmed by satellite radar observations. So the ship you are looking at with binoculars may actually be higher than you assumed, sailing up the slope of one of those water surface "humps". Your line of sight may be over a relatively flat ocean surface, or even across a surface "valley". Your magnified view of the ship may, on a calm day, be stable, without the shimmering or distortion that you would expect of a mirage.
For evidence of earth's shape and spin, we look to "cleaner" experiments (described above) that aren't confused by variables difficult to control and measure. And look to confirm results by doing many independent and fundamentally different sorts of measurements to see whether they agree with each other. Those experiments have been done.
The validity of the round earth model does not depend on one rather messy, complicated and selective set of observations such as the horizon observations. We need to look at the abundance of diverse evidences (cited above), and the fact that they all lead to the same conclusion about the earth's round shape, and all agree on its spin (and its direction of spin). These agree on size and spin rate to great precision.
The departures from sphericity of the earth are relatively small. For example, the equatorial bulge raises the equator about 22 km, which is only 0.4% of the earth's radius. All other bulges and surface features are much smaller. This is an example of how sensitive our measuring instruments have become—that we can even measure this. Suppose we made a scale model of the earth the size of a bowling ball, with the highest mountains and deepest ocean trenches to scale. This model would be smoother than a regulation bowling ball. And it would appear, to the unaided eye (or to a camera), perfectly round. The atmosphere, on this scale, would be a coat of clear varnish. If you doubt this, do the calculations yourself. Flat earthers hardly ever show any mathematics to support their claims. One wonders why.
Those who deny the round, spinning earth and gravity do not know or appreciate the abundance of confirmatory evidence from many independent sources. Though the evidence arises from diverse experiments, it all fits (is consistent with) the laws of physics and our understanding of the geometry of the universe to a precision equal to that of our most sensitive instruments. The deniers generally treat all physics laws as separate and independent. They do not grasp the fact that the laws are all part of a rigorous, integrated and unified logical/mathematical network. This is the beauty and strength of physics. Deniers have not constructed any system based on the flat earth model that can equal conventional physics in comprehensiveness and power, such that we could use it to account for all of the evidence. They complain that conventional physics is "too complicated" for their comprehension. But where is their simpler model that can equal conventional physics in its precise and experimetally confirmable results?
Flat earth believers reject all evidences for a round, rotating earth with contrived and often absurd and inconsistent arguments, or dismiss some of them as hoaxes. Their arguments are hand-waving, rationalizations, empty unsupported assertions and contrived hypotheses. It is generally not worth anyone's time to refute their incredibly lame assertions and arguments by using mathematics and physics because those who accept those arguments do not have sufficient understanding of mathematics and physics. However, even sophomore physics majors know enough classical physics to find the flat earth arguments laughable, and cannot imagine how anyone could believe them.
It is difficult to believe the flat earthers are serious. One suspects they are just having fun challenging others. It is easy for them, of course, for they assume no obligation to present testable hypotheses, gather precise data, and do the necessary mathematics to make correct interpretations and inferences from that data.
Another possible explanation is that some people really don't care about scientific evidence and solid arguments. They prefer to live in a fantasy world of their own devising, untroubled by any necessity to justify it by scientific inquiry. They love to repeat unverified or invented "facts" and "magical" concepts. To refute every one of their bogus "evidences" would occupy a diligent researcher a lifetime. It would be futile anyway, for the believers would just invent some other arguments.
None of them ever feel any obligation to square their fantasies with physics and mathematics. None have ever tried to develop a comprehensive alternative physics that would support their claims and all experimental evidence from all fields of physical science. They are obligated to do this, for their claims certainly are not supported by conventional physics. Their pretensions are not science, but science fiction and fantasy.
I must admit that there are also many people who accept the round, rotating earth, yet cannot defend their position, don't know the evidence, and haven't sufficient understanding of physics and mathematics to argue for their position. This document is a small effort to remedy that. I have tested this with college students by asking them to write a short essay defending their notion of the shape of the earth, supporting their position with hard evidence and sound argument. Most failed miserably on the first attempt. (These were not science majors.) I encouraged them to consult reliable library references. After several attempts one student complained, "I'm frustrated. I don't know why the earth is round. All my teachers said it was, and I believed them. Isn't that enough?" I responded, "No, that is not enough." Education is a failure for many, because they "learn" only by memorizing empty assertions and slogans without understanding the underlying evidence and arguments.
This document ©2017 by Donald E. Simanek. Input and suggestions are welcome. Please use the address to the right when responding, and please indicate the specific document of interest.