Flat Earth or globe: what do you really see from up there?

A piece of evidence is an observation that one model predicts and the other does not. The simulator is built to find them: it puts the two models side by side, with the same data, and shows where they give different images.

1. Up close the two models look alike: on the seashore the difference is minimal (stop 1).
2. From afar the two models part ways: on the globe distant mountains lose their lower part, on the flat Earth they would be visible whole (Corsica, Denali).
3. From high up the horizon of the globe drops below the eye and curves; the horizon of the flat Earth does not (Everest, 39 km | 24 mi).

Anyone can compare these images with what is really visible, in the photos cited in each stop or with their own eyes.

No, because on the globe the horizon looks flat almost always.

1. From the ground we see a tiny piece of the Earth: from the shore the sea is visible up to about 5 km (3.1 mi), while the circumference of the Earth is 40 000 km (24 855 mi).
2. If the Earth were shrunk a million times, it would be a ball 12.8 m (42 ft) across, and the piece of sea seen from the shore would be 1 cm (0.39 in) wide: on a ball that big such a short stretch looks straight.
3. The curve of the horizon starts to show only very high up and with a wide view (see the question on the curvature).

So a horizon that looks flat does not tell the two models apart. Distant mountains and the dip of the horizon from high up tell them apart.

Perspective makes distant things smaller, but it does not cut them off from the bottom. A distant ship on a plane would become smaller and smaller, but it would stay whole.

On the globe, instead, a ship sailing away disappears from the bottom: first the hull, then the decks, finally the tops of the masts. This is the same effect as the distant mountains of the stops: Corsica from Livorno shows only the peaks.

The zoom does not bring the hull back: it magnifies the image, but it does not change what lies behind the curve (see the question on the zoom).

On a sphere of radius R, with the eyes at a height h above the sea, without atmosphere:

• the horizon is at a distance of about the square root of 2 × R × h;
• the horizon is below the eye line by an angle that grows with altitude;
• of an object at distance d, beyond the horizon, a height of about (d minus the horizon distance) squared, divided by 2 × R, stays hidden.

The table below gives the values without atmosphere. With the atmosphere light bends a little downward and you see a little farther: the simulator computes this with the standard atmosphere. With refraction off, from 1.6 m (5.2 ft) the simulator measures 0.041° on the sea, and the formula gives 0.041°: the same value.

In 1838 Samuel Rowbotham watched a boat along a straight canal in England, the Bedford Level, with his telescope 8 inches (20.3 cm) above the water, and wrote that he saw it for 9.7 km (6 mi) without it disappearing (Rowbotham). On a sphere, without atmosphere, about 5.1 m (17 ft) would be hidden at that distance.

Repeating the test in 1870 with poles at the same height, Alfred Russel Wallace found the curvature instead. On a canal like that, a few centimeters above the water, the air near the surface bends light a lot and the result changes with the weather and the temperature: this is why similar measurements give different results (Bedford Level).

The simulator cannot reproduce this experiment: the canal is about thirty meters wide, less than the smallest cell of the terrain. The same holds for the laser experiments on lakes: the simulator draws mountains, sea and sky, not beams of light.

Chicago, Toronto and Lake Pontchartrain are often cited cases: the Chicago skyline seen from Michigan, the Toronto skyline seen across Lake Ontario, the power lines that cross Lake Pontchartrain in Louisiana.

The simulator, however, draws only the terrain, the sea, the ice and the sky, not buildings or power lines. Showing these cases would mean inventing objects that are not in the data: this is why the journey uses only mountains and coasts, which are in the terrain measured by satellites.

Zetetic astronomy is the method proposed by Samuel Rowbotham in 1865: start only from what is observed directly, without theories. The flat Earth model of the Flat Earth Society comes from this method.

The simulator follows the same idea: no results written by hand, only what an eye would see in the two models, measured on the image. The disc is the one described by Rowbotham and by the Flat Earth Society; the globe is the one of geodesy.

No: the simulator uses no photos at all. The images are computed pixel by pixel from the data: mountains measured by satellites (Copernicus, NOAA), coasts, measured ground colors (MODIS albedo), air and sunlight. All the sources are in Data and sources.

This way the image does not depend on a photo that someone might consider retouched: it depends on public numbers, which anyone can check one by one.

The Flat Earth Society proposes “universal acceleration”: the disc would rise continuously, pushing everything upward (Universal Acceleration).

With a push equal everywhere, however, weight should be identical at every point. The measurements say otherwise: gravity is 9.7803 m/s² at the equator and 9.8322 m/s² at the poles, that is 0.5% more (WGS84). The flattened, rotating globe predicts exactly this difference.

The simulator does not use gravity to draw: it cites it only as a comparison.

The altitude depends on how wide the view is, that is on the field of view. The most cited study (Lynch, Applied Optics, 2008) says:

• with a wide view, 90° or more, the curvature starts to show from about 10 700 m (35 000 feet);
• with a narrow view, under 60°, it does not show at that altitude;
• pilots describe it as evident from about 15 000 m (49 213 ft) and obvious from about 18 000 m (59 055 ft).

The Flat Earth Society also writes that on the globe about 18 300 m (60 000 feet) would be needed.

In the simulator, at 10 000 m (32 808 ft) and with the natural field of view, the curve is barely visible (Pacific); at 39 km (24 mi) it is clearly visible (Roswell).

1. On the globe the horizon drops below the eyes as you rise, but only a little: 0.037° from the shore, 3.014° from an airplane, 2.78° from Everest.
2. These are small angles. Two and a half degrees is as much as five full Moons side by side: without a horizontal reference nearby, the eye does not notice it.
3. With a spirit level, or with the eye line of the simulator (the dashed green line), you can see instead that the horizon is below.

On the flat Earth, with the atmosphere, the horizon would be a little above the eyes at every altitude (see the question on the flat Earth below).

Because the window shows a stretch of horizon that is too narrow. At 10 000 m (32 808 ft) the curve is there (Pacific), but over a stretch a few degrees wide the difference between the center and the edges is minimal.

The same holds from a mountain, and the surrounding terrain also covers the horizon. What you can notice, if you know where to look, is that the horizon is below the eyes (Everest).

The rule says how far the sea drops below a straight line tangent to the Earth: 8 inches (20.3 cm) times the miles squared. At 100 km (62.1 mi) it gives 785 m (2 575 ft).

But the rule does not say what you see, because it counts as if the eyes were at water level. With the eyes at 1.6 m (5.2 ft) the horizon is already at 4.5 km (2.8 mi): the hidden part is calculated only beyond that point, and at 100 km (62.1 mi) the hidden part is 715 m (2 346 ft), not 785 m (2 575 ft).

Those who use the rule without the height of the eyes find a number that is too large, and then a mountain that “should” be hidden turns out to be visible. The simulator takes into account the altitude of the eyes, the true shape of the Earth and the air.

The stops of the journey answer with real cases. Where the observer is low, only the upper part of the distant target is visible (Corsica, Denali).

Record photos beyond 250 km (155 mi), like the one of Pic Gaspard, succeed only rarely and show only the peaks: on the flat Earth those mountains would be visible whole on every clear day.

Still water is level over short distances: in a glass, in a lake, the curvature is too small to see. Over 1 km (0.62 mi) the sea surface drops 8 cm (3.1 in) below a straight line.

Water follows the direction of gravity, which on the globe always points toward the center: over large distances the sea surface curves together with the Earth. This is what the sea stops show (Corsica, Denali).

Refraction is light bending as it crosses air of different density: it is measured, and surveyors and navigators use it every day.

The simulator computes it from the 1976 standard atmosphere (U.S. Standard Atmosphere) and from the air index of Ciddor, the same in the two models. The refraction button (J key) turns it off, so you can see what changes.

On ordinary days refraction lets you see a little farther, but not enough to cancel the curvature: the distant mountains of the stops stay cut off at the bottom. The exceptional days, with cold air near the ground, are rare: this is why records beyond 250 km (155 mi) are rare (Pic Gaspard).

Haze fades distant mountains, but it does not cut them off from the bottom: it makes them lighter all in the same way, from the base to the summit.

In the simulator the air is that of a very clear day: there are fewer suspended particles than those measured on the cleanest days at Mauna Loa, one of the places with the clearest air in the world. At sea level the eye sees up to about 236 km (147 mi), and with perfectly clean air up to 322 km (200 mi).

Beyond 300-400 km (186-249 mi) even the cleanest air lets very little light through: this is why record photos are taken at dawn or at sunset, with the mountain dark against the bright sky.

1. On a plane without atmosphere the farthest point you see is extremely far away: you see it practically at the height of your eyes.
2. With the atmosphere light bends downward. A ray that leaves your eye slightly upward bends and falls back onto the distant plane.
3. The ray of light behaves like a stone thrown far: to make it go far you have to throw it slightly upward. So you see the distant plane a little above the horizontal.
4. This is why from Ostia, on the flat Earth, the horizon is 1.4° above the eye. With refraction off, it goes back almost onto the eye line.

Without refraction, at the center of the image the instrument measures the mountains of Sardinia, at 343 km (213 mi), 0.201° above the eye: on the flat Earth they would stand above the sea, but the haze hides them.

On the globe refraction lets you see a little farther, but the horizon stays below the eye line.

With both eyes we see about 214° horizontally, counting side vision; we see details, however, only in the central 60° or so (Strasburger and others, 2011, corrected in 2024).

The screen is like a window: it shows only the part of the world that lies behind it. The simulator opens with the “natural” field of view of your window, that is the angle the screen really covers in front of your eyes, at about 71 cm (28 in) away (the reference pixel of the W3C), never below 20°.

You change the field with the mouse wheel, with two fingers or with the “Field of view” control, from 10° to 120°; the F key goes back to the natural one. The wider the field, the smaller and farther things look, as in a wide-angle photo.

Many lenses, like those of action cameras, bend straight lines: a straight horizon can look curved, and a curved one can look straight or bent the other way, depending on where it sits in the frame.

The simulator uses a projection without distortion, like a perfect lens: straight lines stay straight. If the horizon of the globe looks curved, as at 39 km (24 mi) in the Roswell stop, the curve belongs to the Earth, not to the lens. On the flat Earth, at the same altitude, the horizon stays straight.

1. On the flat Earth, with the atmosphere, the horizon appears a little higher than the eye, about 1.4°, in every direction.
2. A photo, or the screen, is like a flat sheet held in front of the eye. The center of the sheet is close to the eye, the edges a little farther.
3. Something that is 1.4° above the eye must be drawn on the sheet the higher, the farther the sheet is: like a tilted laser beam, the farther away you stop it, the higher it reaches.
4. This is why at the edges of the photo the horizon comes out a little higher than at the center. The horizon does not really rise: the flat sheet draws it that way.

On the globe the opposite happens: the horizon is below the eye, so at the edges of the photo it comes out a little lower.

The zoom magnifies what reaches the eye, but it does not change the path of light. If the lower part of a mountain lies behind the curve of the sea, no ray of light arrives from there, and no zoom can show it.

The zoom instead shows small things better if they were already above the horizon, for example the distant peaks. The Corsica stop has the same view with the naked eye and with the zoom: with the zoom the peaks are clearer, but the lower part of the island does not come back.

• all the values used are in Data and sources, each with its public source;
• no result is written into the program: horizon, distances and altitudes are read on the computed image;
• the two models use the same data and the same optics: you can switch from one to the other at the same point and compare;
• every stop opens in the simulator exactly as in the image, and from there you can go wherever you want: with a double click on the scene or on the map you choose a point and go there;
• you can compare the images with the real photos cited in the stops, or with what you see yourself.

Walls of ice do exist on the coast of Antarctica: they are the fronts of the ice shelves, like the Ross Ice Shelf, tens of meters high (last stop). According to the Flat Earth Society (Ice Wall) the wall is 45.72 m (150 ft) high.

In the simulator the wall is as high as the data say, in the two models. What changes is the length of the wall: the Antarctic coast is 56 691 km (35 226 mi) on the globe and 310 554 km (192 969 mi) on the disc, where it surrounds all the land.

Behind the walls the ice continues for thousands of kilometers to the South Pole, where there is a scientific station inhabited all year round: Antarctica has been crossed on foot, by sledge and by airplane.

Richard Byrd flew over the South Pole on 28 November 1929, in a Ford Trimotor airplane: the round trip took 18 hours and 41 minutes (Richard E. Byrd).

Operation Highjump, in 1946-1947, was a United States Navy expedition organized by Byrd: about 4 700 men, 13 ships and 33 aircraft, to build the Little America IV base and photograph coasts and ice from the air (Operation Highjump).

Byrd's words about a land “beyond the Pole” are cited as evidence of lands beyond an ice wall. The expeditions found the coasts, mountains and ice of Antarctica, not a wall around the world (Logically Facts).

No. The Antarctic Treaty, signed in Washington on 1 December 1959, is an agreement of peace and science. The official text is on the website of the Secretariat of the Antarctic Treaty. This is what it says:

• Article I: Antarctica shall be used for peaceful purposes only; military bases, maneuvers and weapons tests are prohibited;
• Article II: scientific research is free;
• Article III: scientific observations and results shall be exchanged and made freely available;
• Article V: nuclear explosions and radioactive waste are prohibited;
• Article VII: observers may go at any time to any area of Antarctica, and “aerial observation may be carried out at any time over any or all areas of Antarctica”.

So the Treaty does not forbid overflights: it expressly provides for them. The official languages of the Treaty are English, French, Russian and Spanish; the quotation is from the English text.

Original document.

The disc is drawn like the map of the Flat Earth Society, the same idea as the Gleason map of 1892: the North Pole at the center and every place at its true distance from the North Pole, along its meridian.

The equator is 10 002 km (6 215 mi) from the center and the edge of the disc 20 003.9 km (12 430 mi). This is why the southern lands, like Australia, South America and Antarctica, are stretched on the disc.

In the simulator the map at the bottom left shows the globe or the disc, zooms in up to 512 times, and with a double click takes you to any point.

Qantas flight QF27 flies non-stop from Sydney to Santiago, Chile, in about 12.5 hours, with a Boeing 787 (flight schedule).

On the globe the shortest route between the two airports is 11 363 km (7 061 mi) long: in that time the airplane averages 909 km/h, the normal speed of an airliner.

On the flat Earth map, with the North Pole at the center, Sydney and Santiago lie far apart, on two sides of the disc: the straight line between the two airports is 25 637 km (15 930 mi) long. To cover it in the same time the airplane would have to fly at 2 051 km/h, more than twice as fast.

The two distances come from the same code as the simulator: on the globe along the WGS84 ellipsoid (GeographicLib), on the disc as on the Gleason map. The coordinates are those of the airports of Sydney and Santiago.

The Sun and the Moon are in the same direction in which we really see them, at the chosen date and time.

The Flat Earth Society describes a small, nearby Sun that circles above the disc (The Sun): a Sun like that would never set, see the question on the sunset.

So as not to draw a sky that nobody observes, the simulator puts the Sun and the Moon where they are really seen, the same in the two models.

1. On the flat Earth of the Flat Earth Society the Sun circles above the disc, a few thousand kilometers high (Distance to the Sun). As it moves away it gets lower, but it cannot go below the horizon: it always stays a few degrees above.
2. The Sun of the flat Earth is like a street lamp in a huge, flat square: the farther you walk away, the lower you see it, but it never disappears behind the pavement.
3. The Flat Earth Society explains the sunset with perspective or with light that bends, but it gives no way to calculate when the Sun sets (Sunrise and Sunset).
4. This is why in the simulator the Sun of the flat Earth is where it is really seen, at that place and at that time: it is the choice most favorable to the flat model.
5. Even so the sunset does not add up. On the flat Earth the air raises the horizon above the eye line (question on the horizon), so in the evening the Sun disappears behind it before the real sunset, and in the morning it rises later: this is why, in the Pic Gaspard stop, the flat Earth image was taken 17 minutes after the globe one.

At night the stars turn around a fixed point in the sky. In the northern hemisphere the point is near the North Star; in the southern hemisphere it is the south celestial pole, near the star Sigma Octantis, which you find by following the Southern Cross (Celestial pole, Sigma Octantis).

From Sydney, from Santiago, Chile, and from Cape Town, those who look south see the same pole, with the same stars around it. On the globe this is natural: from the three cities south points toward the same point of the sky, beyond the South Pole. On the flat Earth, with the North Pole at the center, the south of every city points toward the edge of the disc, in three directions far apart: three observers looking in such different directions cannot see the same point of the sky.

The Flat Earth Society wiki proposes two explanations: perspective (Southern Celestial Rotation) or a second pole, with a sky that turns above the south (Bi-Polar Model). The second one is a different model from the single-pole map the simulator uses.

The simulator puts the stars in the direction in which they are really seen, the same in the two models, like the Sun and the Moon: this is why the difference does not show in a single image, but in the comparison between observers in distant cities.

The firmament is the solid vault of the sky of biblical cosmology (Firmament). Some supporters of the flat Earth take it as a real dome above the disc.

No rocket, satellite or balloon has ever met a dome. On 24 October 1946 the V-2 No. 13 rocket, launched from New Mexico, took the first photo of the Earth from space from 105 km (65.2 mi) (V-2 No. 13). The International Space Station circles the Earth at about 400 km (249 mi), 15 and a half times a day, and it has had people on board without interruption since 2 November 2000 (International Space Station).

The simulator rises up to 100 000 m (328 084 ft), where space conventionally begins, and it puts no dome in either of the two models.