Sun Minimum Angular Elevation

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Sun’s angular elevation

It’s easy to calculate the expected angular elevation of the sun for the flat earth.  Flat Earthers often claim the sun is 3,000 miles above the flat earth, sometimes more, sometimes, less.  We will use 3,000 miles.  It doesn’t change the outcome much, use your own numbers if you prefer.


To calculate the angular elevation we use a simple right triangle.  We place the sun at point “B”, and the observer at point “A”.  We use the elevation of the sun, 3,000 miles for side “a” and measure the distance the observer is from the point under the sun for side “b”.

Use “Side Angle Side” to calculate all the sides and angles of the triangle manually.  It’s easier to use an online calculator like this one.  For this problem, use calculator #2 on that web site.

The AE map is used for this example, but any flat earth map imaginable could be used with similar results.  I have used Walter Bislin’s Creating Flight Plans for Flat Earth web page to calculate distances on the flat earth AE map.  If you have a different method to calculate distances on the flat earth, send feedback to and I’ll include alternative measurements in all my calculations.

Let’s examine a couple sample locations and also pick the most extreme possible observer location in favor of a flat earth.

Example 1: Quito, Ecuador, EquinoxQuito, Ecuador farthest sun location

Quito is on the equator, at 0°N 78.5W.  We will calculate the minimum angular elevation of the sun on the day of the equinox.  At local solar noon the sun is directly overhead so the angle is 90°.  At local solar midnight the sun will be directly over Indonesia on the opposite side of the world, still on the equator.  The distance is 12,436 miles.  Plugging in to the triangle calculator we get an angular elevation of 13.56°.

Example 2: Minneapolis, Northern SolsticeMinneapolis, MN, USA farthest sun location on the Northern Solstice

Minneapolis, MN, USA is at 45°N 93W.  On the Northern Solstice the sun travels over the Tropic of Cancer at 23.5° North latitude.  At local solar noon the sun is the closest to Minneapolis it ever will be all year, directly over the Gulf of Mexico, 1,486 miles away.  At local solar midnight, the sun is directly over Myanmar, 7,676 miles away.  Plugging into the triangle calculator we get an angular elevation of 21.35°.

This means, according to flat earth theory, in the middle of the night in Minneapolis, the sun’s elevation is 21.35° above the horizon.

Example 3: Puerto Williams, Southern SolsticePuerto Williams, Chile farthest sun location on Southern Solstice

Puerto Williams is on the far southern tip of Chile at 54°56′S 67°37′W.  It’s one of the southernmost cities on the earth.  On the day of the southern solstice, at local solar midnight, the sun is over the western tip of Australia, 17,861 miles away from Puerto Williams.  Plugging that distance into the triangle calculator we get an angular elevation of 9.53°

This is the absolute lowest angular elevation possible for the sun on the AE map from land other than Antarctica.  Everywhere else on Earth will always have a higher angular elevation at local solar midnight.

Example 4: Forcing the outcome, Total imagination

What conditions are required for the sun to get really close to the horizon if the earth were flat?  How far away and how low would the sun need to be to make it work?

  • Lower the sun to 1000 miles and use the same distance as Example 3, the angular elevation is 3.20°, still too high to even consider to be setting.
  • How about 1,000 miles high and 30,000 miles away?  That is 1.91°, still too much.  For reference, the angular size of the moon is 0.5°.  That’s more than 3 moon widths above the horizon.
  • How about 1000 miles high and 100,000 miles away?  The elevation is 0.57°, a little more that the width of the moon.  Still a clear noticeable gap between the horizon and the sun.
  • The visible limit of the human eye is about 1 arcminute or 0.02°, this is considered the vanishing point.  In order for the sun and the horizon to be within 0.02° of each other, the sun must be 1,000,000 miles away and only 350 miles high.
  • What if we left the sun at 3,000 miles elevation and forced the sun to be in the vanishing point of the flat earth horizon?  How far away would it need to be?  The sun would need to be 8,500,000 miles away to appear on the horizon.

Physical Model

This is pretty easy to model physically.  Find a hallway, measure it’s length and height so you know the limits of what you can model.  Select the angular elevation you want to model and plug the numbers into a triangle to find the length and height.Light in Hallway 9.53 degrees.png

I have a 120-foot long hallway that is 8 feet high.  To model the example that is the most in favor of a flat earth, Puerto Williams, we need an angular elevation of 9.53°.  I have a light with a magnet that will stick to the ceiling, it’s 6 inches long.  Calculating a triangle with a 7.5-foot elevation and 9.53° the observer needs to be 45 feet away from the point directly under the stand-in sun.

When I did this, the fluorescent light on the ceiling completely out-glared the light I stuck to the ceiling.  As you can see in the picture the stick light is not visible.  For this model, this is highly in favor of the flat earth theory.  The light source is significantly larger than the sun would be, yet it is still a long way from the floor.  There is still a large visible gap between the light and the floor.

Special Case: Dome

A lot of people see this impossibility and reach for the dome claim to resolve it.  I figure the thought is “the sun is literally high up, the dome is curved, that must make it appear lower, duh, MCToon, you’re stupid”.

Of course, there is no evidence of a dome at all, but people really love their dome.  So, I’ll make an exception for the dome: model the dome.  Do the math, calculate the angles, plot it out.  Use 3D apps, whatever.  Do it for the three examples above.  Then, use to get the observed sunrise, local solar noon and sunset locations for the three examples above and include these observations into the same dome model.  Then use the same dome model to model the angular size of the sun to match the observed size of the sun, about 30 arcminutes, all day every day.

If you can model the dome to account for just these three examples, for just these three observations, I’m in.  I’ll post a video showing the model.  I’ll contact all my globe head friends and beg them to mirror the details on this revolutionary information.

If you can’t model the dome, provide evidence of the dome.  How far is it?  How was the distance measured?  What is it made of?  What are the refractive properties?  Are the sun, moon, and stars projected on it from inside or outside?  Provide real, substantial evidence.

If you can’t model the dome or provide evidence of the dome, don’t bring it up.  I’m not gullible, you shouldn’t have been.


At the location most beneficial to flat earth, the lowest angular elevation of the sun in the middle of the night is 9.53°.  This is too high for any known phenomenon to account for a setting sun.  There is absolutely no way this could be considered a sunset.

When someone claims the sun sets due to:

  • Perspective
  • Circular perspective
  • Atmospheric lensing
  • Refraction
  • Diffraction
  • Reflecting off the dome
  • Bendy light
  • Electromagnetic acceleration
  • Angle of attack
  • Rayleigh criterion
  • Projections
  • Holograms
  • Luminaries
  • Or anything else

Just ask them to explain the phenomenon responsible for dropping the apparent location of the sun by at least 9.53°.   Since this is likely an as-yet unknown phenomenon, be sure to request formulas, derivations, and calculations to account for this angular declination.

Are you are a flat earther and think I’m wrong?  I’m open to your ideas.  Please send your response to  Any polite emails will be added directly below.


Twitter user @T__E__S__L__A:   “What should I prove you wrong about? That webpage speaks about linear perspective and it does not apply to Sun.”

dwr448iwkaem2y4If I understand this odd claim, he is suggesting that the sun is inexplicably exempt from the regular behavior of literally everything else humans have ever seen or experienced.  Instead, the sun follows “circular perspective”.  He has an image as well posted her for reference.  Unfortunately, there is zero supporting evidence for this claim.  When asked for this supporting evidence, he was unable to provide any.  No formulas, no derivations, nothing to support this.  Since there’s no evidence, it gets dismissed.

Back to Sunset and Moonset on Flat Earth

4 thoughts on “Sun Minimum Angular Elevation

  1. If you really want to make their heads hurt, ask them to explain how an equatorial telescope mount works on their FE “model”. Of course it can’t possibly work, but then again I doubt they can even understand how they work on a correct spherical earth, in a heliocentric solar system.


  2. Great stuff. All that while the flerfs have… � No working model, or map. � No way to determine proper distances, or directions between two point on the earth not sharing the same longitude. � No explanation for how the sun and the moon circle the earth, or how the sun migrates from the tropic of Capricorn to the tropic of Cancer and back over the year. � No idea why the ancient Greeks such as Pythagoras, Aristotle, Eratosthenes and Aristarchus believed the earth was a sphere. � No idea what P and S shockwaves detected by seismology equipment tells us about the internal structure of the earth, and the shape and dimensions of the surface of the earth. � No idea what powers the sun and the stars. � No idea of the distance to the stars. � Clueless as to why almost all stars don’t appear to change position in the sky from opposite sides of earth’s orbit around the sun when the phenomena of parallax says they should, and why we can only use the parallax method for measuring the distance of stars that are closest to the earth. Luckily, Polaris is one that we can determine the distance to using parallax, because it is also a Cepheid variable star, which allows the distance to be measured to much more distant stars where the parallax method not longer works. � No idea of the distance from the earth to the planets, or even much about them at all. � No idea why binary stars obey Newton’s law of gravitation. � No explanation as to why we can only see 59% of the total surface area of the moon when, from a flat earth perspective we should be able to see most of it, including the dark side of the moon. � No idea why the moon appears upside down in the southern hemisphere compared to how it looks in the northern hemisphere, and why the phases of the moon are on opposite sides of the Moon, and why it looks circular from all vantage points on the earth. � No idea why sunspots rotate in the opposite direction in the southern and northern hemispheres, or even what sun spots are. � No believable explanation for how GPS is implemented across the world. � No explanation as to why aircraft carry ring laser gyros onboard capable of detecting the rotation of the earth. � No idea how it is possible to develop gravitational maps of the earth’s surface, or why anyone would want one, or how they could be used. � No explanation for how eclipses work, especially lunar eclipses, or how to predict them correctly. � No idea why the Humber bridge, the Verrazzano Narrows bridge are built to account for the earth’s curvature. � No idea why CERN, LIGO and the Stanford linear accelerator vacuum rings and arms are constructed to take account of the earth’s curvature. � No idea why physicists working on LIGO, the gravity wave detector, were awarded Nobel prizes in physics. � No idea why geodetic surveyors keep claiming the earth is an oblate spheroid. � No idea why Google Earth does not publish its underlying flat earth model that allows it to project the earth as a globe. � No explanation as to why the sun rises due east for everyone on the earth on the equinox. � No explanation as to why the sun’s ground speed at june and december solstices are equal. � No idea why there should be a discernible horizon that looks like the edge of the ocean viewed from a beach. The horizon should really be a blur as the farther we look out across the flat earth, the more light is scattered and the more particles in the atmosphere obscuring the view. � No idea how it is possible to see the sun set twice simply by changing your height above the earth (quickly by just a few tens of metres). � No reasonable explanation as to how Polaris can be used in conjunction with a sextant in the northern hemisphere to determine latitude. � No explanation as to why the Artic and Antarctic experience months of days and nights at different times of the year. � No explanation why bright little objects called satellites by some are regularly visible in the night sky following a predicted path across the sky � No explanation for how tides work. � No explanation how (most times) boats disappear over the horizon when they should be visible on a flat earth. � No explanation as to why the horizon does not rise to eye level. � No credible explanation why helium balloons fitted with non-fish eye cameras often detect the curvature of the earth. � No credible explanation for the existence of the “Downward” force called gravity. � No explanation that does not implicitly make use of the theory of gravity for the atmospheric pressure gradient from high to low pressure with altitude, especially if we live in a dome. � No idea why (almost without exception) hurricanes and typhoons rotate in opposite directions in northern and southern hemispheres respectively. � No explanation for the Coriolis effect observable in controlled experiments such as those conducted by Ascher H. Shapiro in the 1960s. � No explanation as to why the northern celestial pole rotates counter clockwise in the northern hemisphere, and the southern celestial pole rotates clockwise in the southern hemisphere. � No idea what Antarctica even looks like, and where the South Pole is physically located. � No idea why Venus has phases. Bye bye Geocentric system. � No idea why planets, e.g. Mars, exhibit retrograde motion. Hello Heliocentric system. � No idea why the planets and their moons in the solar system appear to be obeying Newton’s laws of planetary motion. � No explanation whatsoever why Stellar Aberration occurs. � No idea why clouds are illuminated from the bottom at sun set. � Can’t explain how a commercial aircraft can fly from Perth to Sydney in only 4 hours 10 mins across the flat earth, as to achieve this, it would need to fly faster than an F18 on afterburner all the way. � No idea why the CO2 atmosphere of Mars appears to “Cling” to the exterior of its spherical spinning surface without the need for physical containment. This phenomenon is observable on others planets too. � No idea why the sun and the moon don’t change in angular size from rising to setting by a factor of 2 to 3 since they are local to the earth, and no idea why the sun according to the inverse law of radiation is not 4 to 9 times brighter at midday than at sunset and sunrise when viewed from Australia. � No credible reason why millions of people (mostly scientists, engineers and technicians ) over decades would lie to keep the globe earth alive, and why nations and commercial enterprises, accountable to the voters and shareholders respectively, would spend (waste) $2 trillion a year , each and every year to maintain the globe lie. � No idea how it is possible to measure the value of G, the universal gravitational constant and in so doing, verify the theory of gravity. � No scientific papers published in the last 100 years supporting the flat earth. � No clue on how Mercury can pass in front of the Sun like it did on Nov.11,2019..


  3. I don’t think they kow about the existence of many of those. In some cases they might even be in denial about their existence.


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