Update: Real Science Answers to Flat Earth Claims

Illustration of tangential rotational velocity using Doppler radio echo from the moon’s surface. The Earth rotates from West to East (Counter-Clockwise) and for the purposes of this illustration, the direction of rotation is depicted by the blue arrow. The uplink signal is nominal and on downlink, its frequency is shifted to a higher frequency (shorter wavelength) and with the signal thus depicted as blue.

In discussing the overarching theme with Flat Earth adherents, they claim that there exists no empirical evidence for the Earth’s curve or rotation. Aside from the standard, obvious proofs presented in my series of articles published thus far on this topic that include Star Trails for both hemispheres, diurnal motion, changing elevation for Polaris based on latitude, telescopic observations of solar system objects, the Foucault pendulum, eclipses, etc., I have discovered a new, incontrovertible proof of Earth’s rotation and associated tangential velocity. This new method uses Doppler radio echo from the lunar surface, a method whose accuracy has a precision of at least four decimal places based on the accuracy and sensitivity of the radio transceiver.

1.6 Km (1 mi) section of the 3.2 Km antenna array in western Texas.

The broadcast antenna is an array of 2,560 individual dipole antennas 3.2 Km (2 mi) in length located in west Texas, approximately 160 km (100 mi) west of Dallas. It transmits a nominal carrier signal with 6 gigawatts ERP (Effective Radiated Power) at 216.9800 Mhz.  Such a combination of sufficiently high frequency that the ionosphere is completely transparent (the ionosphere is transparent to any signal above 30 Mhz) and very high ERP allows the signal to easily reach the moon and provide a detectable echo on downlink to the receiver.

Doppler technology is used almost everywhere in our everyday life, from police radar speed detectors to Doppler ultrasound medical applications. The technology is mature and very reliable. Using Doppler radio technology, radial velocity studies of our Milky Way galaxy have been conducted with an extremely high degree of precision.

A Doppler cross sectional view our Milky Way galaxy illustrating its radial (rotational) velocity as seen edge-on from our vantage point 25,000 light years from the center. Unlike the data from the lunar radio echo, the galaxy rotates clockwise as observed from above (North) and thus, the trailing (red-shifted) aspect of the image is on the right. The galactic center, the subject of several recent, high-value studies is at the center of the image.

It must be noted that the originator and owner of this website, the source of the data used here, serendipitously and quite by accident, is a licensed amateur radio operator with call sign W5SXD. He and a colleague successfully engaged in similar experiments back in 1972.  The rising moon is an ideal target for a radio echo study and was thus used in this case to determine the tangential velocity of the Earth at the transmitter’s location – the transmitter is being rotated towards the moon. As the moon continues to rise and approach the meridian, the return echo will approach the nominal transmission frequency; as the moon continues west of the meridian, the return echo will be increasingly red-shifted and the signal from the setting moon will be red-shifted by the same magnitude as the the signal from the rising moon was blue-shifted.

Receiver output of the 216.98 Mhz signal showing many jet aircraft and, most importantly, the 365 Hz blue-shifted radio echo from the rising moon. If the capture were conducted when the moon was west of the meridian, the signal would be increasingly red-shifted.

Applying the simple Doppler relation to determine velocity, where the change in frequency relative to the base frequency is directly proportional to the velocity of the object relative to the speed of light: DopplerRelation(invert) and solving for v, the tangential velocity of the Earth’s surface towards the moon at the location of the radio transmitter, we find:   DopplerRelation(solved-inverted). Substituting and solving for the velocity:

The surface of the Earth at the location of the radio transmitter (33°33’N x 98°45′ W) is rotating with a tangential velocity of
0.5043 km/sec converts to 504.3 m/sec or 1,815.48 km/hr (1,128 mi/hr) and is consistent with the result obtained using the Earth’s solar day (24 hours) of 465 m/sec.

The Doppler method thus confirms the value obtained using the Earth’s solar day.

Real Science Answers to Flat Earth Claims

Real time video from the Himawari-8 weather satellite, in geostationary orbit 35,900 Km above the equator, centered on New Guinea

I have published a variety of articles to address a new, and growing phenomenon, the belief that the Earth is flat. To my mind, it is inconceivable that, in the 21st century, when we’ve brilliantly navigated a robot craft to flyby Pluto some 7.5 billion kilometers distant, among the hundreds of other scientific milestones achieved over the previous 6 decades, let alone those of the previous 2 millennia, that there is a growing ascendance towards an ancient creation myth, that the earth is flat! Mind you, the population of individuals who now hold this belief are not children but grown adults from all walks of life who are not part of some fringe cult! Many of them are allegedly well-educated and include airline pilots(!), mathematicians, doctors(!), attorneys and an “ex theoretical physicist”. Two of my articles were specifically written to directly confront this phenomenon, “The Earth is Flat (and other nonsense)” and “Flat Earth Update“. There are other articles that speak to it by way of refernce:

GSBrooks_TheEarthIsNotFlatIndeed, a book has been published in response to the growing Flat Earth phenomenon by the intrepid Gordon Brooks, a thoughtful and accomplished writer and composer. He maintains a blog devoted exclusively to refuting Flat Earth nonsense and as a result of his advocacy for the truth, has suffered public indignities at the hands of Flat Earthers.

There are others too, who actively write in support of the truth.

One may wonder why I have devoted so much time and energy to this topic when, by any standard, it would normally be dismissed as complete nonsense, those kinds of tall tales that are told to children to explain the world in terms a child can understand. Ironically, and one would be surprised to learn, the mind of a small child can readily grasp and accept the very plain, simple truth that the Earth really is a big, spinning ball that orbits the sun. The children are filled with awe and wonder at the thought of this, they’re exited and inspired and it is for them that I, Gordon and others continue to shine the light of reason and truth into the darkness. How dare these imposters and frauds poison the minds of the young, the uneducated, the ignorant and uninformed! Through no fault of their own, many individuals are invincibly ignorant to the true nature of our natural world and the universe and are easily led down this path of error and fall prey to the “easy science” and seeming logic that Flat Earth proponents claim to possess. It is for these individuals, the children and the coming generations that we do this, so that humanity’s progress will not have been in vain.

In this article, I will directly debunk and explain several popular themes and myths that the Flat Earthers hold up as their Holy Grail, arguments that the misinformed or uneducated often fall prey to.

The Sun is Not 93,000,000 Miles Distant
We define the solar constant to be the radiant energy received from the sun at a particular distance. For the Earth, the solar constant is 1,400 Joules/m²/second or 1.4 K-Watts/m². This is a measured quantity that is widely used in science in ways too numerous to list here; it is a value that goes into the manufacture and design of solar panels, solar energy systems and other green technologies. The Flat Earthers at least concede that the sun subtends an angle of 1/2 degrees on the sky, a measurement that will allow us to compute its size. The distance to the sun, they claim, is 4,800 km (3,000 mi). For starters, if the sun were 4,800 km distant its diameter would be 42 km or 26 miles, a value over 100 times smaller than the size of the Earth, flat or not! Ok, for the moment, lets accept that, as preposterous as it sounds. Extrapolating the intrinsic luminosity (power) of the sun using the solar constant for the Earth and the claimed distance, the energy output of the sun would be 4.05 E+17 Joules/sec (E = powers of 10, 2 E+3 = 2×10³) or 4.05 E+17 Watts (4.05 E+14 Kw), a value 1 part in one billion of its actual value of 3.85 E+26 Watts (3.85 E+23 Kw). That’s not all, an object that outputs 4.05 E+17 Watts of power and is only 42 km in diameter (21 km radius) would have a surface energy density of 73 million Watts/m², a value 10 million Watts/m² greater than its actual value of 63 million Watts/m², from an object whose volume of space is 36 trillion times smaller!

The Earth is Fixed and Doesn’t Move
This assertion of the Flat Earthers applies to both the rotational and orbital aspects of the Earth’s motion. Regarding the orbital motion of the Earth, with the claim that the Earth is fixed and motionless in space at the center of the universe (Geocentric cosmology), noting that the change in the rising time of any star from one night to the next will be earlier by 4 minutes each night. Over a period of 90 days (1/4 year), that same star will rise 90×4=360 minutes (6 hours) early. This change in the rising and setting time is attributable to the (360/365) = 1° degree change in the Earth’s orbital position every day. This motion is separate from diurnal motion, the apparent rising and setting of any celestial object, an aspect of the Earth’s rotation about its axis. Any beginning amateur astronomer’s telescope is equipped with a “clock drive”, a small motor that moves the telescope at the same rate as the rotation of the earth and thus, the object of interest remains centered in the telescope’s field of view. Why would this be necessary if the earth was “fixed” and immovable?

A night view of the SALT (South African Large Telescope) observatory, housing the largest single optical telescope in the southern hemisphere. Clearly visible is the blurred image of the Large Cloud of Magellan and star trails, centered on the South Celestial Pole. Such observations are only possible for observers located on a rotating spherical platform.

The Flat Earthers claim that the “Firmament”, comprised of the stars, all fixed upon the sky, rotates about the North Pole with Polaris marking the “Center” with the South Pole inaccessible, surrounded by an impenetrable ice wall. With the exception of an observer at the North Pole (the real North Pole), the observed diurnal motion of the stars is inconsistent with this model. All stars appear to rotate around the North Celestial Pole, conveniently marked by Polaris during this epoch in history to within 1° of the true North Celestial Pole, the imaginary analog on the sky of the Earth’s rotational axis. Using a simple camera/tripod setup, “star trails” can be recorded for exposures of five minutes or longer if the camera is pointed towards Polaris. The elevation of Polaris (the North Celestial Pole) above the northern horizon is equivalent to the observer’s latitude. For an observer on the equator, the NCP (and thus, Polaris) is on the northern horizon with the SCP (the South Celestial Pole) on the southern horizon. There is no “marker” for the SCP such as Polaris for the NCP and such, the Flat Earth model cannot account for the apparent conundrum of star trails visible from places like Cape Town, South Africa in the southern hemisphere. They have no explanation except to say that it is a matter of “perspective”, a catch-all phrase they use to explain what cannot be explained logically and simply using their model.

The Earth Is Enclosed Under a Clear Impenetrable Dome

The Chelyabinsk meteor was a superbolide caused by a near-Earth asteroid that entered Earth’s atmosphere over Russia on 15 February 2013

They claim that the flat earth is enclosed under a clear, impenetrable dome or canopy. If this were true, we would be protected from any extra-terrestrial threats such as incoming asteroids or meteors. Gone is the idea of a terminal, extinction level event that changed the course of life on Earth or Earth’s planetary history. Using this model, it would be one or two logical steps to quite easy eliminate the Chicxulub asteroid event or any similar, existential threat to life on Earth. Thus, no extinction level event and no dinosaurs, another of their propositions. The problem with the clear, impenetrable dome are such remnants as the Arizona Meteorite Crater, the Tunguska Air Burst Event and, more recently, the Chelyabinsk bolide that leveled buildings, broke windows and was witnessed by thousands of Russians. There is no clear, impenetrable dome.

The Earth is Flat No Matter How High You Go, There is no Curve and no Spin
This is probably the most widely trumpeted claim the Flat Earthers make. Empirical determination of the Earth’s circumference was made by Eratosthenes almost 2,300 years ago. He measured the change in the sun’s altitude between Alexandria and Elephantine Island near Syene (modern Aswan, Egypt) on the Summer Solstice and, by setting up a distance ratio between the two locations, relating the Earth’s full circumference and the distance between Alexandria and Elephantine Island with the angular separation between them, he was able to determine the circumference to within 5% of its actual value. The Earth’s spin was first empirically determined by Jean Bernard Léon Foucault in 1851. The Foucault Pendulum demonstrates that the earth is a rotating sphere that didn’t depend on any celestial observations. By suspending a weight just above the floor from the zenith point of the observatory, Foucault empirically demonstrates that the earth is rotating by measuring the precession of the pendulum’s swing over the course of 24 hours. One may wonder why its necessary to evoke experiments from the 3rd century BC and the mid-19th century. Most Flat Earthers will not accept the untold thousands of video and still images produced of the spherical, rotating Earth as evidence, claiming that they’re “fake” or produced using “CGI”, even when those images and video were produced decades before CGI was developed.

For a sense of scale, the largest animal life form on the planet, a blue whale, are like tiny mites crawling around on the back of an elephant when comparing our physical size to the Earth. It’s instructive to visualize what the back of an adult elephant might look like to a mite or a flea; actually a flea would be too large. The Earth is huge compared to even the largest life forms, hence the reason it appears to have “no curve”. Amateur rockets have attained altitudes of 115 km (72 miles), the transition layer between the Mesosphere and the Thermosphere, the boundary layer recognized as the “edge of space”.

Pilot Felix Baumgartner of Austria just before his 2012 jump from an altitude of 39 Km (24 miles). The Earth’s curvature is clearly visible from this altitude.

Even when the Earth’s curvature can be clearly observed from that altitude, when confronted with video and still-image content from these amateur rocket flights, the evidence is dismissed for obvious reasons, citing “fakery”. Most Flat Earthers claim that humans have never been to space, even denying the Russians achieved this with Yuri Gagarin’s low-orbital flight in 1961. NASA is widely viewed by them as a huge, evil conspiracy so any content that’s linked to NASA is automatically dismissed. The level of absurdity continues to grow and is boundless as the sky above, given that even the video and images from Felix Baumgartner’s recent plunge from 39 Km (24 miles) was dismissed and labeled as “Fake” by the Flat Earthers.


Nikola Tesla Debunked Gravity, Disagreed With Einstein
Nikola Tesla was a brilliant physicist and inventor and what happened to him in the end was tragic. Much of the electric infrastructure we take for granted in today’s modern society was pioneered and developed by him. Many Flat Earthers use a public disagreement between he and Albert Einstein on the nature of gravity to call into question Einstein’s then newly developed theory of gravity, General Relativity. Without considering the data and images from the 1919 Total Solar Eclipse that famously confirmed key aspects of the theory, Tesla dismissed it as being rife with errors and an offense to common sense. Tesla, in support of the aether theory, where light and all electromagnetic radiation would require this invisible, undetectable medium to propagate, he publicly declared the theory of relativity “a mass of error and deceptive ideas and opposed to common sense“. Further, to bolster the veracity of Relativity, the testing and detonation of the first nuclear weapon a short while later was a confirmation of a key aspect of Special Relativity, E=mc², developed by Einstein in 1905, 10 years before publication of his General Theory. All these events are a matter of history and of science, in spite of how Flat Earthers misrepresent that history. Einstein has been repeatedly vindicated numerous times with many, varied experiments during the intervening 101 years since the publication of his General Theory. What happened to Nikola Tesla in the end was tragic but that does not change history and does not change the fact that he was wrong.

We Never Went to the Moon

Michael Light, from the project FULL MOON, 1999 First Stage Separation of Saturn V Rocket, 41 Miles Above Earth; Photographed by Robotic Camera, Apollo 6 (Unmanned), April 4, 1968 Direct-digital c-print; 24.5"x24.5"; edition 50 Transparency NASA; digital image ©1999 Michael Light
First Stage Separation of Saturn V Rocket, 66 Km (41 mi) above Earth, photographed by Robotic Camera, Apollo 6

This can be filed under the “Humans Have Never Achieved Space Flight” category, in spite of thousands of eye witnesses on the beach in Florida for each of the seven Apollo mission launches, worldwide coverage by all the major networks of each launch, the earth-shaking liftoff of the giant Saturn V booster for each of the seven launches, six of which made it to the moon. To any reasonable person, the question begs asking, where did the rockets and the astronauts go and why spend untold millions of dollars for each launch to scuttle it, for what purpose? This would be sufficient for a reasonable person but since the launches were conducted by and through NASA, they’re automatically dismissed as being part of a massive hoax and conspiracy that had the entire world fooled.

Laser Ranging Experiment
When the Apollo XI astronauts left the moon in 1969, they left behind the “Laser Ranging Experiment“, an experiment that continues to this day. The purpose of the experiment was to precisely measure and monitor the distance to the moon. Using high-power, ground based lasers integrated with large, ground-based telescopes, it monitors the distance to the moon with a precision of +/- 3 cm (1.25 inches). Up until 2009, when NSF cut the funding for them, the McDonald Observatory in Texas was one of several high-profile venues that was a continuous participant in the experiment, monitoring the moon’s distance faithfully for four decades. As of today, the remaining venues that are still participating are the Lick Observatory, the Air Force Cambridge Research Laboratories Lunar Ranging Observatory in Arizona, the Pic du Midi Observatory in France and the Tokyo Astronomical Observatory. The data collected by these observatories through this experiment is public access and in the case of some, there is full public access to the experiment and its operation. As it turns out, this experiment confirms the inexorable outward motion of the moon, a result consistent with all modern theories of gravity including but not limited to Einstein’s General Theory of Relativity. The experiment has “tested Albert Einstein’s general theory of relativity to unprecedented accuracy”. The theories on gravity put forth by Galileo Galilee and famously by Isaac Newton with his Universal Law of Gravitation are both vindicated. The full public access aspect of the experiment is problematic for the Flat Earth adherents. This single experiment destroys almost every aspect of their model and is the nail in the coffin. It is because of this that they so viciously attack Galileo, Newton and Einstein and any mention of the experiment’s success :

  1. Full public access means the public can witness the experiment in person and first hand, destroying the notion that NASA is a giant evil conspiracy, that the moon landings were a Hollywood production and that we never went to the moon. The simple fact that such an experiment exists -on the moon- is, of itself, enough to discredit this and other such claims;
  2. Since the angular size of both objects is known, and is about 1/2º for both, the sun must be larger and more distant since the moon completely covers it during a total eclipse of the sun. When the moon is positioned directly between the earth and the sun during an eclipse and, in the case of most eclipses it is a perfect geometric cover, it logically follows that the sun must be larger and more distant.
  3. That the moon’s distance has been determined to be 384,467 km (240,292 mi) with the laser ranging experiment and, since we’ve established that the sun must be larger and more distant than the moon, the sun cannot be 3,000 miles distant as claimed but is, in fact, 150 M Km (93,000,000 mi) distant.

These examples by no means represent an exhaustive list and numerous variations on any of these themes abound with new and imaginative ways of self delusion and denial by Flat Earthers manifesting themselves on a frequent basis.

To conclude, I don’t suspect many Flat Earthers will read this article nor any other article in this blog. These articles aren’t really intended for them as if they were, the need to publish them would already be moot; it is intended to assist those who are sincerely struggling with this topic or any aspect of science or the natural universe.

Imagination is more important than knowledge 585px-Albert_Einstein_signature_1934(invert)
An index of all articles in this blog can be found here.


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