Flat Earth Dome Model

Friday, April 06, 2018 - 22:00 | Author: wabis | Topics: FlatEarth, Interactive, Knowlegde | Comments(5)
Here I present an interactive Flat Eart Model that can explain Sunrise, Sunset, Moonrise, Moonset, Sun's position on Equinox, Seasons, Solar and Lunar Eclipses, Star Trails, 24 houre Day/Night at the Northpole and Antarctica, Celestial Poles, why people south of the equator can see the same Stars rotate clockwise around a singe celestial pole at the same time at different continents. But the Model still has some unsolvable flaws.

The Model

  • Intro
  • Eclipses
  • DayNight
  • Stars
  • Reset
  • <<
  • Play
  • >>
  • 0


Light-Bending: This Model shows how light rays from the Dome on the Flat Earth Model have to be bent to match the apparent positions of Sun, Moon and Stars and to produce the Tracks, Star Trails and Day-Night Terminator as observed in reality for each time and location on earth. Only by bending the light rays as shown by this Model it is possible that Sun, Moon and Stars can go apparently down below the horizon, while they are still above the Flat Earth.

Sun/Moon Tracks: During 24 hours the sky with the fixed Stars rotates about 1 degree more than 360 degrees. So in 365.25 days the star constellations at the same time are at the same place in the sky again. You can see this in the model by advancing DayOfYear step by step (place the cursor into the field and hit arrow Up or Down). The Dome grid will advance each day by about 1 degree.

If you advance the time by 24 houre steps, the Sun moves up and down between the Solstice lines during one year, causing the seasons. The Sun also moves left and right a bit so it traces a figure 8. This is caused by the tilt of the Globe earth axes against the Sun Ecliptic plane 23.44 degrees. You can see the tracks of Sun and Moon against the fixed star background (Dome Grid) by checking the options Sun Track and Moon Track. A desciption of the tracks is presented if you click the Eclipses button. These tracks correspond to what is observed in reality. The tracks are derived from the Heliocentric Model.

Retrograde Motion of Moon's Track: The Sun Track stays fixed on the Dome Grid. But the Moon Track slowly rotates retrograde against the Dome Grid and rotates one full rotation in 6798 days. This is due to the precession of the Moon Orbit caused by the distant Sun. Currently the Moon Ecliptic is such that the Track of the Moon extends the Track of the Sun North/South about 5 degrees. In about 3400 days from now the Track of the Moon lies inside the Track of the Sun about 5 degrees. This observation has no explanation in the Flat Earth Model but follows from the Heliocentric Model.

Eclipses: The intersection points of Sun and Moon Track are called Knots. There are 2 such Knots marked by a green dot. If Sun and Moon are exactly on opposite Knots, a Lunar Eclipse happens. If Sun and Moon are exactly on the same Knot, a Solar Eclipse happens (play Demo Eclipses from Step 6 on).

This Flat Earth Model can predict Solar and Lunar Eclipses. But it can not predict moons shadow on earth at Solar Eclipses or earths shadow on the Moon on Lunar Eclipses, because the required relative sizes and distances of Sun and Moon and the spherical shape of the earth are essential to compute the corresponding shadow paths. So the location on earth where the Solar Eclipses happen can not be derived from the Flat Earth Model.

Moon Phases and Orientation: The model shows the Moon Phases and the Orientation of the Moon with respect to the horizon at the location of the Observer. The apparent rotation of the Moon during the day is due to the fact, that the cameras up vector stays always perpendicular to the surface of the earth while following the path of the Moon. An Equatorial Mount for the camera or telescope does not produce such a rotation as it follows the Moon.

Equinox: This Model produces the correct apparent Sun positions at Equinox, so that the Sun raises at 6:00 AM due East and sets at 18:00 PM due West everywhere on earth.

Poles: This Model produces 24 hours day and night on the Northpole and Antarctica.

Heliocentric Model: In reality ovserved Tracks of Sun, Moon and Stars (Star-Trails), the Equinox and Solstice Knots and the Day-Night Terminator can not be derived from the Flat Earth Model itself. They have to be assumed without any cause or reason. This Model derives them using the Heliocentric Model. On the Heliocentric Model they are simply a consequence of Gravity in play and the angles between the orbital planes of Sun and Moon. You measure the positions of Sun and Moon on their Orbits at any time and all future and past positions can be calculated using Newtons universal law of gravity.

Shapes on the Dome: The shape of Sun, Moon and star constellations on the Dome have to be distorted exactly like shapes of the real Globe world are distorted when mapped onto the Flat Earth. So the Sun and Moon on the Dome sould be squeezed circles, bent along a latitude line of the Dome. This distorted shapes get corrected by the bending of light as shown in the model, so the observer sees perfect spheres for Sun and Moon and the correct star constellation shapes.

All features of this Model are derived from the Heliocentric Model to produce an almost working Flat Earth Dome Model.

Problems with the Model

Lightrays: There are no known physical laws that can bend light so much and in this exact fashion to produce the real observations as shown in this Model. There are an infinte number of possible lightray paths that could be choosen to model the bent light. There is no physical cause to choose a specific one. So this Model chooses Bezier curves to model the light rays. The Bezier control points can be adjusted with the magenta slider. The smaller RayParam ist, the stronger the curve, the bigger RayParam, the smoother the curve.

Impossible Light-Bending: Atmospheric effects can never bend light that much. Not even known materials for lenses can achieve this. Even if such bending could be achieved by the atmosphere or something else, I can not derive any constant density gradient to produce just the right bending to connect each location on the Dome to each location on the Flat Earth at the right time.

No South-Pole: The Southpole makes serius problems. There can be no Southpole Star, because on the Flat Earth Model this star has to be smeared around the whole border of the Flat Earth.

Light bending over Night-Shadow: To produce 24 hours Daylight on Antarctica the Sun rays have to be bent over a region of Night shadow to the observer.

Moon Phases and Orientation: The Moon Phases on the Flat Earth can not be explained by the interplay of Sun and Moon with respect to the Observer. The Moon has to have it's own light. The Moon Phases and its orientation are complicated and can not be modeled by a simple rule on the Flat Earth. The Model derives the Moon Phases and its Orientation, as they can be observed in reality, from the Heliocentric Model. The Orbits and Distances of Sun, Earth and Moon are essential to derive the Moon Phases.

Shadows of Eclipses: Although the Model could predict the date of Eclipses, the Shadows on Lunar and Solar Eclipses, and therefore the locations and times on earth, where they can be observed, can not be calculated with the Flat Earth Model, because to compute the shadows you need the full 3D positions and sizes of the objects. You can't compute them from flat projections. All projections onto planes or domes lose the third dimension.

Brightness and Heat from the Sun: How does the sun produce the right amount of light and heat for each observer? The inverse square law does not work here because the individual distances between Sun and Observers in the model does not reflect reality, so the brightness and heat would never match observations. The Sun would have to produce light and heat different for each location on earth without any physical explanation.

Purpose of the Model

The purpose of this model is to show to what extent a Flat Earth model with a Dome can produce observations that match reality. This can only be accomplished by strong light bending. The model also shows, that many observations of reality can not be modeled with a Flat Earth Dome model.

The basic idea of my model is: The Flat Earth is a projection of the 3D Globe onto a flat plane. What if we project 3D space with Sun, Moon and Stars (and Planets) onto a 2D Dome? That is what my model does.

Note that although the Dome itself may be 3D, it only represents a 2D surface. Of course applying the known physical laws of light propagation, on the Flat Earth we would see a completely different imgage of reality than we can observe. Sun, Moon and Stars on the Dome never go physically below the horizon. So you have to invent things like the Flat Earth Perspective, which does not work as needed either. But if you assume light bending as shown in my model, it can really produce the images that we observe to a certain extent, if you don't look too close into it. Exceptions are Solar and Lunar eclipses for example. Although you can predict the dates of this events, like the ancient astronomers could by observing the sky, but you can not predict the locations on earth, where this events happen. They can only be seen on certain locations and times, which we can only predict using the Heliocentric model.

Some other points I wanted to show with my model are:

Sun and Moon trace specific paths on the celestial sphere. This paths have no cause on the Flat Earth model. The only explanation is, a creator has created it that way. But in the Heliocentric model all paths follow automatically from the law of universal gravity. You only have to measure the current positions, velocitys, sizes and distances of Sun, Planets and Moons and you can calculate all past and future locations and how they appear from the earth or any other place by applying the law of gravity alone. You can predict the exact locations and times where solar eclipses can be seen (from the shadow that the Moon traces on earth).

The Moon phases and its apparent orientation for any observer on any place on earth, as shown in my model, can not be explained by the Flat Earth model. They have no relations to the flat earth sun too, so the moon has to have "its own light". My model can predict this observations for any place on earth by using the Heliocentric model.

The Day/Night Terminator on the Flat Earth that matches reality has a very peculiar shape that changes over the course of a year. The shape depends somehow on the location of the sun. This shape can only be explained with the Heliocentric model by projecting the Terminator from the Globe Earth with a tilted axis onto the Flat Earth. The shown light bending in my model would produce this terminator line correctly. But this light bending is not a thing that arises naturally, but is computed explicitly in a way to produce the real observations.

To have a Dome means, all heavenly bodies are located on or near the Dome. The real solar system is a 3D space with big objects very far away from each other orbiting around each other. The Dome is a 2D projection of this 3D space, very similar to the 2D projection of the Globe Earth onto the Flat Earth plane. This produces inevitable distortions you have to correct somehow (by bending light). By loosing the third dimension you loose a lot of information to produce and predict real observations. So Flat Earther have to "make things up" to explain observations that follow automatically from the real 3D universe we live in.

Last but not least, the Flat Earth does not represent the real shapes and sizes of the continents. This can never be accomplished. A 3D sphere, as the Earth really is, can never have a similar surface as its flat projection. This is geometrically impossible. That's the reason why a sphere looks different than a plane in the first place, because their surfaces hav different curvature. They can never match globally. You can only make small flat maps of the Globe surface that get not distorted too much to be usefull for finding local places. But you can never accurately measure real distances from any flat map projection. Global navigation has to, and always did, use spherical coordinate systems, like the current WGS84 model, used by GPS and aricraft navigation systems.


Some observations like the positions of Sun, Moon and Star Constellations as well as Sun/Moon-Rise and -Set can be explained by a Flat Earth Model if we allow strong light bending in a specific way. Even the date of Eclipses can be predicted from this model.

But observations as the southern celectial pole, Moon Phases and its Orientation and apparent Rotation as well as the track of the Shadow of the Moon on solar Eclipses can not be computed from the Flat Earth Model, because you need the correct size and orbits of Sun, Moon and Earth to compute this. The essential third dimension is lost if you assume a Dome over the Flat Earth, where Sun and Moon are close and small.

There is no explanation or scientific model that can physically explain why and how light is bent as needed by this Flat Earth Model.

Equinox, Solstice, Azimuth, Elevation

The Model assumes a perfect circular Orbit of the Earth around the Sun and a perfect circular Orbit of the Moon around the Globe Earth. This results in a slight divergence of the dates of Equinox and Solstice from reality a few days.

The Model chooses to match:

  • Spring Equinox at 20. March 2017 12:00 UT
  • Solar Eclipse at 21. August 2017 18:00 UT

Azimuth and Elevation of Sun and Moon are also slightly inaccurate due to the use of circular orbits instead of elliptical orbits. This affects also the Moon Phases.

Computing Day-Night Terminator

The Day-Night Terminator is derived from the Heliocentric Model to match reality:

  1. A circle perpendicular to the axis Earth-Sun in the Sun coordinate system is computed depending on the Sun's position at a certain date and time relative to the intersection knot of the equatorial plane of the earth and the ecliptic plane of the Sun.
  2. This circle is then transformed to the Globe Earth coordinate system.
  3. Each point of the circle is then transformed to the corresponding Flat Earth coordinate system, which produces the shadows as shown in this Model.
  4. At Equinox the transformation to the Flat Earth coordinate system fails at the south pole, because on Flat Earth the south pole is everywhere on the border of the disc. The corresponding points of the Terminator line had to be generated explicitly and have no real cause.

The special shape of the Night-Shadow produced by the mapping of the Globe Night-Shadow onto the Flat Earth results automatically, if the light rays are bent as shown in this model.

Computing Moon Phases

The Moon Phases and their orientations with respect to the Horizon at the Observer can only be computed from the Heliocentric Model as follows:

  1. The relative positions of Sun and Moon from the Heliocentric Model with respect to the Geocentric coordinate system determines the Phase of the Moon and its axes as observed from Earth. The distances of Sun and Moon from the Earth have to be correct to produce the correct phases.
  2. The Coordinate System of the Observer's Camera is computed in such a way, that the Camera points to the Moon and the Up direction of the Camera is perpendicular to the Globe Surface at the Observer.
  3. The Axes of the Moon Phase is transformed to the local Coordinate System of the Observer.
  4. The Orientation of the Moon Phase is computed from the Axes in the local Coordinate System of the Observer by transforming it to the Camera Coordinate System.

Used distances:

  • Earth-Sun: 149,600,000 km
  • Earth-Moon: 384,000 km

URL Parameters

The App can be called with some URL parameters to set a specific App State:

You can use the Save/Restore Panel with the Button Get App URL to get an URL from the current state of the App. Copy this URL into any Web-Form (e.g. YouTube comment) and by clicking the link this page is opened with the saved state from the URL.

  • To start a certain Demo with the URL, append
    &demo=DemoName to the page URL, where DemoName is the Name of some of the Demo Buttons above the App Dispalay.
  • To set a demo to a specific position, append
  • To run a demo from a specific position, append
  • To speed up or slow down all animtion, append

Some parameters may be combined in one URL, eg, &demo=Intro&play=3&speed=3

The App changes the URL in the adressbar of the browser to reflect the current state of the App. You can copy the URL to and post it in a comment. With the Back and Forward browser buttons you can jump from state to state.


1Dave 4/7/2018 | 17:25

Please do this with a geocentric model as the flat earther theory is inside the dome and if any flat earther tries to say that it is possible that the sun is outside the dome, they then flaw every attempt to prove its flat

2wabiswalter@bislins.ch (Walter Bislin, Author of this Page) 4/8/2018 | 16:33

It is not relevant for this model whether the sun is inside or outside of the dome. The dome shown in this model is simply a visual grid to show the locations of the sun and moon. You can imagine the real dome to be farther out if you wish. That does not change anything.

By the way: you can modify the height and size of the dome with the blue sliders.

3Greg McCormick 4/10/2018 | 10:13

Thank you for this splendid piece of work. I hope you will use it as the basis for some videos.

Your model should also force the correct elevation of Polaris by latitude. I tried to derive a vertical profile of refractive index that would mimic the observed relationship. I gave it a boundary condition that the refractive index should match that of air up to about 20000 metres. By having a varying refractive index above this height (in the region of 1.2) it is possible to get a match plus or minus 5 degrees. So far I have not been able to do better, and I suspect it may not be possible to do better with these boundary conditions but I have not yet proved this.
There is an amusing consequence of the bending. If this is due to refraction, all flat earth estimates of sun height must be wrong except those made at the equator, and all flat earth estimates of Polaris's height must be wrong except those made at the North pole. And those two "heights" of course exactly match the known radius of the earth.

4Jason 4/25/2018 | 19:46

The Earth has already been irrefutably proven to be flat and stationary. The smart phone in your pocket provides proof by itself. So any phenomena must be put in context of a flat, stationary Earth. Your theory of bending light is definitely an intriguing approach to take, and your animating model is much appreciated. Great start for a flat Earth model in motion using your theory!


Provide a setting to show how the light paths from one star would be bent in many directions at the same time, along a single Latitude line in the night time areas of the Earth, so we can see the three dimensional shape of all the curved lines together

Provide a setting to show how the light paths from the Sun would be bent in many directions at the same time, forming the daylight areas of the Earth, so we can see the three dimensional shape of all the curved lines together.

The 'celestial sphere' seems to be much too big. Allow the user to change the size and proportion of the 'celestial sphere'.


Magnetic field lines of force are all curved. Dielectric field lines of force are all curved. Light can be bent dramatically by electromagnetic fields. The Earth has field lines of force, including the lay lines.

The 'firmament is not a dome, but instead a volumetric field, the bottom of which is about 70 miles altitude above us.

The consideration of any atmospheric refraction of any light from above would be a 'last second' distortion that might be ignored for this particular model.

In your descriptions, consider leaving out any reference to the heliocentric model because it's irrelevant for this experiment.

It's possible the Sun is not a bright ball but instead an electromagnetic projection created by crossing field lines of force, so the Sun appears in a different, predictable spot in the sky depending on your location.

Thanks for taking the time to put this together. Really cool.

5wabiswalter@bislins.ch (Walter Bislin, Author of this Page) 4/25/2018 | 22:09
The Earth has already been irrefutably proven to be flat and stationary.

On the contrary. There is not a single observation that is not also a prediction of the globe model but uncountable observations that contradict the flat earth model. Not to speak of the technical achievements we have like airplanes navigating using GPS satellites and inertial reference units that depend on gravity, time and the rotation of the earth to function. Only to name some.

The 'celestial sphere' seems to be much too big. Allow the user to change the size and proportion of the 'celestial sphere'.

The size of the celectial spheres has no influence at all. It is a virtual image as it appears to the observer. I don't want to add too much features. But thanks for the suggestions. Maybe later...

Magnetic field lines of force are all curved. Dielectric field lines of force are all curved. Light can be bent dramatically by electromagnetic fields.

This is a wrong conclusion without any experimental support. In fact mainstream physics (Maxwells theory of EM) and all experiments tell us, that light is not bent by electric and magnetic fields. Try to bend a light ray with a strong magnet. In old TV tubes there are extremely strong electric fields, but light passes this fields unaffected. Light does not interact with itself either (except in very special circumstances we never experience on earth).

Before light gets influenced by any electric or magentic field, they have to be so strong, that their energies would destroy everthing that comes close to it. Atoms get smashed befor light is affected.

The 'firmament is not a dome, but instead a volumetric field, the bottom of which is about 70 miles altitude above us.

Evidence? Did you send ballons up there to check this hypothesis? We send rockets into space almost daily and never found a dome of any kind.

In your descriptions, consider leaving out any reference to the heliocentric model because it's irrelevant for this experiment.

It would suit you that way. Flat Earthers tend to deny things that do not fit their believe or imagination of reality.

The Heliocentric model is very relevant! One of the main purposes of this model is to show, that most celestial observations can only be explained with the Heliocentric model. Some aobservations are even impossible on a FE model, like the fact that solar eclipses are local phenomena, because the shadow of the moon produced by the distant sun crosses only a small parts of the earth. The Moon phases as shown in my model, matching the observations to a precision of some minutes, are computed from the Heliocentric model. I have no way to compute it from the FE model.

Thanks for taking the time to put this together. Really cool.

Thank's for that!

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