The flat earth dome model had to be derived entirely from the heliocentric model which results are then simply projected onto the flat earth and the dome. To connect the flat earth projections with the dome projections, light must bend in a physically impossible way.
Link to here: walter.bislins.ch/FED
With the Flat Earth Dome Model I intended to show, that the geometric and physical aspects of celestial events and observations, in contrast to cyclic time events, can only be derived from the Heliocentric model. Further the model shows that the observations can only be explained by strong light bending.
The basic idea behind the 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, Planets and Stars onto the Flat Earth Dome in the same manner? What is the relation between the bodies on the dome and observers on the flat earth? How have I to bend the light from the objects on the dome to the observer to match observations?
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.
To explain the cause for the problems with celestial observations on the Flat Earth, I have to explain some aspects of the Heliocentric model.
The Heliocentric model consists roughly of three sets of properties: geometric and physical properties and cycles.
Geometric properties are for example: sizes, distances, inclinations of orbits, constellations of sun, earth and moon and the tilt of earth's axis. The geometry of the observations also depends on the location and orientation of the observer.
Physical properties are for example the heat distribution on earth from the sun that causes the seasons, solar winds that cause Auroras, the heat emission of the earth into space that is responsible for the mean temperature on earth, terrestrial and astronomical refraction due to a density gradient of the atmosphere that influences how much of obejcts are hidden behind the curvature of the earth and how much celestial objects and constellations are squeezed at the horizon and the variations in the gravitational acceleration and coriolis forces due to the ellipsoidal shape and rotation of the earth.
Cycles can be derived from the geometric properties of the Heliocentric model by applying the laws of physics, which results in the Keplerian parameters, or calculated to some extend from careful observations. So the dates of cyclic events can be predicted either from properties of the Heliocentric model, or from observations of previsous cyclic events, for both flat earth and globe.
But you can not calculate the geometric and physical properties of events and observations without knowing the geometry of the Heliocentric model and the physics of sun and earth. The Dome Model calculates the geometric properties of events from a rough Heliocentric model and projects the resulting geometric data onto the flat earth model. You can not derive this geometric data from the flat earth model itself, because the geometry of the flat earth model is completely different than the geometry of the Heliocentic model. Flat earth lacks the necessary third dimension of space and a physical model for sun, moon and earth.
This things can not be calculated from previous observations without applying the Heliocentric model:
Light-Bending: This Model shows how light rays from the Dome on the Flat Earth Model have to be bent to match the apparent size and positions of Sun, Moon and Star constellations 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 hours 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 motion and 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.
Distances: The biggest problem are distances on the flat earth. Only distances exactly north-south are correct. All other distances are wrong, especially south of the equator, eg. Australia is 2.5 times too wide on the flat earth. Only if we deform the flat earth until it is a globe we can get all distances right.
Celeatial Sphere: 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, velocities, 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).
Moon Phases and Field Rotation: 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.
Missing the third Dimension: 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 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.
Light-Bending: Atmospheric effects can never bend light as shown in the Dome Model. Even if such bending could be achieved by the atmosphere or something else, I cannot derive a 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 way. The light bending due to atmospheric refraction on the Globe Model follows simple physical laws and can be predicted by measuring atmospheric properties.
There are no known physical laws that can bend light in a gas 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 light bending. The correct one would have the one that matches observations in any altitide too. This is not modeled correctly. So this Model chooses Bezier curves to model the light rays only for observers on sea level. 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.
It is not possible to create a light bending model that matches observations for any altitude. For instance, if you follow a light ray on the Globe Earth from the ground towards the sun, you travel in a straight line and see the sun always at a constant elevation angle if you don't change your orientation. On this Flate Earth model you would have to travel along a curved light ray and you would have to change your orientation and fly steeper and stepper to keep the sun at the same elevation angle as on ground. You would finally end upside down on the southern hemisphere. Does this happen in reality?
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.
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: Because the bending of the light as shown in this model preserves the size, orientation and location of star constellations, it also causes that the angular size of sun and moon match observations, if we ignore the small varuations due to elliptical orbits. This would also produce the right heat distribution of the sun on the flat earth to cause seasons. But if the sun with enough power to heat the earth is inside or near the dome then the atmosphere near the sun would be as hot as the sun. This does not match the known temperature profile of the real atmosphere.
Some observations like the positions of Sun, Moon and Star Constellations as well as Sun/Moon-rise/set can be explained by a Flat Earth Model if we allow strong light bending in a specific way and restrict the observers to sea level. 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 sizes 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. Observations other than from sea level can not match reality.
There is no explanation or scientific model that can physically explain why and how light is bent as needed by this Flat Earth Model. It is not possible to derive a light bending model that works for any altitude.
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 have different curvatures. They can never match globally. You can only make small flat map projections 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, aricraft navigation systems and google earth.
The Model implements 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 of a few days.
The Model chooses to match:
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.
The Day-Night terminator is derived from the Heliocentric Model to match reality as follows:
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.
The Moon Phases and their orientations with respect to the Horizon at the Observer can only be computed from the Heliocentric Model as follows:
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