Is the earth a spinning
|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 can also tell us the earth's rotation period even if the gyroscope 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.
[Not to scale; the angle is very much smaller.]
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 size of 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 stellar aberration is biased in direction, because of the earth's rotation. Atmospheric refraction would be seen in all directions.
|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 then are recombined, 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. 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.
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, and water density. These 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". It is seldom 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 (parallel to the equator) and allowed to stabilze for a day or more, then it is 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 earth's rotation, but the correction was 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 source and receiver 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 left 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 the moon's 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. Supercooled cesium-133 has been used for this for several decades. Now atoms of strontium-87 and ytterbium-171 offer a threefold increase in the 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-87 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 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 10% 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.*
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.*
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 by using a flat earth model.*
Radio transmission. Radio waves refract and reflect from ionized layers of earth's atmosphere. This has been observed and utilized in radio communications, and is well known to ham radio enthusiasts. This refection of radio waves allows radio signals to go far around the curvature of the earth.
|Radio waves. Source: NASA.|
Very high frequency radio waves have the smallest reflection. Lower frequency waves reflect strongly, at heights that depend on the frequency. Measusrement of the intensity and direction of waves at the receiving antenna confirms the curvature of earth and atmosphere, as well as the height of the reflecting layers. The interpretation is complex, just as for the seismic waves of the previous section.
That invalid 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. Without gravity 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 their assumed severe distortion of distances on earth's surface, varying 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.
Bending of the path of light is called refraction. It occurs when the light path traverses materials of different optical density. There is one refraction 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. The atmosphere acts as a huge lens wrapped around the earth. This allows us to see a bit "around" the curve of the earth. The cause of this refraction is the decrease of atmospheric density with height. It also distorts the shape of the rising and setting sun and moon (flattening them), an effect easily observable by anyone. This causes the sun to rise earlier and set later than would be expected if there were no atmosphere. Stars and other celestial objects that would otherwise be "over the horizon" can be seen. This is why, above the Arctic Circle one can see the sun move all the way around the sky near the summer solstice, remaining above the horizon all the way around the sky. 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 to be confused with the localized and temporary optical phenomena due to temperature inversions near the ground. See the discussions of atmospheric refraction and looming, sinking towering and similar refraction phenomena in the Wikipedia. These are confined to situations where the light path is very close to the earth's surface, usually, but not always, over water.
Historically, such observations have been used by all 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 just right, a ship that ought to have already disappeared "over the horizon" actually seems to rise above the water (looming), or even rise up above the apparent horizon. Sometimes it will appear upside down, and this is called an illusion, though it is also a refraction phenomena. All these effects 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. We also do 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 messy, complicated and selective 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.
In the 18th century accurate maps were important for commerce, so land surveys were made. These used triangulation and optical surveying instruments. They depended on accurate determination of distances to use as baselines of triangles. Surveyor's optical transits were used to measure angles with great precision—far better than anything Eratosthanes had. Of course, these relied on the assumed straightness of light paths. As these surveys were over land, atmospheric refraction was not usually an issue and could be avoided or corrected for. These results clearly indicated that the triangles could not be lying on a flat surface. Over large areas, the curvature of earth's surface could be calculated. This was not surprising, for we already had abundant evidence that the earth was round. Such surveys were even precise enough to show that the earth was not exactly a sphere, but was slightly "flattened" at the poles, bulging at the equator. It is a very small effect, but was confirmed by many such surveys, especially those at higher latitudes.
Does this alone "prove" that the earth is a round ball? No, for if the earth were a hollow shell of the same size with us walking on the inside, the triangulation results would be the same! This is a result of Euclidean geometry. This fact might be welcomed by proponents of the notion that the earth is really a hollow sphere with us on the inside, but they are not well enough versed in mathematics to even understand it. [See the link to "The Hollow Earth" at the end of this document.] But land surveys conclusively show that the earth is not flat.
Those who deny the round, spinning earth and deny 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 physics 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 predictive power, such that it accounts 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 rationalizations. It is usually 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. Many even deny the laws of geometry and physics entirely. 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 that flat earthers are serious. One suspects they are just having fun challenging accepted science. It is easy for them, of course, for they assume no obligation to present testable hypotheses, gather precise data, or 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 fantastic 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 account for all experimental evidence from all fields of physical science. They should be 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. Before I wrote this docuement I used to test 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. [I had to give some of them directions how to find the library.] 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.
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