The roughly spherical shape of Earth can be empirically evidenced by many different types of observation, ranging from ground level, flight, or orbit. The spherical shape causes a number of effects and phenomena that when combined disprove flat Earth beliefs. These include the visibility of distant objects on Earth's surface; lunar eclipses; appearance of the Moon; observation of the sky from a certain altitude; observation of certain fixed stars from different locations; observing the Sun; surface navigation; grid distortion on a spherical surface; weather systems; gravity; and modern technology.
Observations involving the horizon Visibility of distant objects on Earth's surface
On a completely flat Earth without obstructions (mountains, hills, valleys or volcanos), the ground itself would never obscure distant objects. A spherical surface has a horizon which is closer when viewed from a lower altitude. In theory, a person standing on the surface with eyes above the ground can see the ground up to about away, but a person at the top of the Eiffel Tower at can see the ground up to about away.
This phenomenon permits a way of confirming that Earth's surface is locally convex: If the degree of curvature is determined to be the same everywhere on Earth's surface, and that surface was determined to be large enough, the constant curvature would show that Earth is spherical. In practice, this method is not reliable because of variations in atmospheric refraction, which is how much the atmosphere bends light traveling through it. Refraction can give the impression that Earth's surface is flat, curved more convexly than it is, or even that it is concave (this is what happened in various trials of the Bedford Level experiment).
The phenomenon of variable atmospheric bending can be seen when distant objects appear to be broken into pieces or even turned upside down. This is often seen at sunset, when the Sun's shape is distorted, but has also been photographed happening to ships, and has caused the city of Chicago to appear normally, upside down, and broken into pieces from across Lake Michigan (from where it is normally below the horizon).
When the atmosphere is relatively well-mixed, the visual effects generally expected of a spherical Earth can be observed. For example, ships travelling on large bodies of water (such as the ocean) disappear over the horizon progressively, such that the highest part of the ship can still be seen even when lower parts cannot, proportional to distance from the observer. Likewise, in the days of sailing ships, a sailor would climb up a mast to see farther. The same is true of the coastline or mountain when viewed from a ship or from across a large lake or flat terrain. In certain places, the curvature is visible via fixed objects. This includes the Lake Pontchartrain Causeway visible from a Metairie hotel, and the 85 pylons carrying of powerlines over Lake Pontchartrain, visible from I-10 Bonnet Carré Spillway Bridge.
Dip of the horizon
The dip of the horizon refers to the angle between the true and astronomical horizon. Because the Earth is spherical, the true horizon always lies below the astronomical horizon, with the dip becoming larger as altitude increases. Celestial navigation often needs to be precise enough that the dip of the horizon must be known when measuring the angle between the apparent horizon and a star. To obtain a more accurate altitude angle, the dip must be subtracted from the sextant reading so that the angle properly references the astronomical horizon. For convenience the Nautical Almanac provides a table with dip corrections for navigators to use, and also provides the formulae used to calculate them which were derived using Earth's radius. The dip of the horizon can be easily observed, for example, by looking through the head up display on an aircraft at high altitudes.
Lunar eclipses
The shadow of Earth on the Moon during a lunar eclipse is always a dark circle that moves from one side of the Moon to the other (partially grazing it during a partial eclipse). The only shape that casts a round shadow no matter which direction it is pointed is a sphere, and the ancient Greeks deduced that this must mean Earth is spherical.
The effect could be produced by a disk that always faces the Moon head-on during the eclipse, but this is inconsistent with the fact that the Moon is only rarely directly overhead during an eclipse. For each eclipse, the local surface of Earth is pointed in a different direction. The shadow of a disk held at an angle is an oval, not a circle as is seen during the eclipse. The idea of Earth being a disk is also inconsistent with the fact that a given lunar eclipse is only visible from half of Earth at a time.
Appearance of the Moon
The Moon's tidal lock to Earth results in the Moon's always showing only one side to Earth (see animated image). If Earth were flat, with the Moon hovering above it, then the portion of the Moon's surface visible to people on Earth would vary according to location on Earth, rather than showing an identical "face side" to everyone. If Earth were flat, with the Moon revolving around it tidally locked, then the Moon would be seen simultaneously at all places on Earth at once, but its apparent size, the portion facing the viewer, and facing side's orientation would gradually change for each viewer as its position moved across the sky over the course of the night.Archived at Ghostarchive and the Wayback Machine:
Observation of the sky from altitude with the aid of a diagram
On a perfectly spherical Earth, not considering obstructions and atmospheric refraction, its surface blocks almost half the sky for an observer close against the surface (see horizon). Moving away from the surface of Earth means that the ground blocks less and less of the sky. For example, when viewed from the Moon, Earth blocks only a small portion of the sky because it is so distant. This effect of geometry means that, when viewed from a high mountain, flat ground or ocean blocks less than a hemisphere of the sky. With the presumption of a spherical Earth, an expedition commissioned by caliph al-Ma'mun used this fact to calculate Earth's circumference to within of the correct value of around , and possibly as accurately as .
The rate of change in the angle blocked by Earth as altitude increases would be different for a disk than for a sphere. The amount of surface blocked would be different for a mountain close to the edge of a flat Earth compared to a mountain in the middle of a flat Earth, but this is not observed. Surveys from all over Earth show that its shape is everywhere locally convex, confirming that it is very close to spherical.
Observation of fixed stars from different locations The fixed stars, for example the Pole Star (Polaris), can be demonstrated to be very far away by diurnal parallax measurements. Such measurements show no shifts in the stars' positions. Unlike the Sun, Moon, and planets, they do not change position with respect to one another over human lifetimes; the shapes of the constellations are constant. This makes them a convenient reference background for determining the shape of Earth. Adding distance measurements on the ground allows calculation of Earth's size.
The fact that different stars are visible from different locations on Earth was noticed in ancient times. Aristotle wrote that some stars are visible from Egypt which are not visible from Europe. This would not be possible if Earth was flat.
A star has an altitude above the horizon for an observer if the star is visible. Observing the same star at the same time from two different latitudes gives two different altitudes. Using geometry, the two altitudes along with the distance between the two locations allows for a calculation of Earth's size. Using observations of the star Canopus at Rhodes (in Greece) and Alexandria (in Egypt) and the distance between them, the Ancient Greek philosopher Posidonius used this technique to calculate the circumference of the planet to within perhaps 4% of the correct value. Modern equivalents of his units of measure are not precisely known, so it is not clear how accurate his measurement was.
The Andalusian astronomer Ibn Rushd went to Marrakesh (in Morocco) to observe the same star in 1153, as it was invisible in his native Córdoba, Al-Andalus. He used the different visibility in different latitudes to argue that the Earth is round, following Aristotle's argument.
Observation of constellations on North and South hemispheres at different seasons The North Pole is in continuous night for six months of the year. The star Polaris (the "North Star") is almost directly overhead and therefore at the center of this rotation. Some of the 88 modern constellations visible are Ursa Major (including the Big Dipper), Cassiopeia, and Andromeda. The other six months of the year, the North Pole is in continuous daylight, with light from the Sun blotting out the stars. This phenomenon, and its analogous effects at the South Pole, are what defines the two poles. More than 24 hours of continuous daylight can only occur north of the Arctic Circle and south of the Antarctic Circle.)
At the South Pole, a completely different set of constellations are visible during the six months of continuous night, including Crux, and Centaurus. This 180° hemisphere of stars rotates clockwise once every 24 hours around a point directly overhead.
From any point on the equator, all of the stars visible anywhere on Earth on that day are visible at some time during the year as the sky rotates around a line drawn from due north to due south. When facing east, the stars visible from the north pole are on the left, and the stars visible from the south pole are on the right.
The direction any intermediate spot on Earth is facing can also be calculated by measuring the angles of the fixed stars and determining how much of the sky is visible. For example, New York City is about 40° north of the equator. The apparent motion of the Sun blots out slightly different parts of the sky from day to day, but over the course of the entire year it sees a dome of 280° (360° - 80°). So for example, both Orion and the Big Dipper are visible during at least part of the year.
Making stellar observations from a representative set of points across Earth, combined with knowing the shortest on-the-ground distance between any two given points, makes an approximate sphere the only possible shape for Earth.
Observing the Sun On a flat Earth, a Sun that shines in all directions would illuminate the entire surface at the same time, and all places would experience sunrise and sunset at the horizon at about the same time. With a spherical Earth, half the planet is in daylight at any given time and the other half experiences nighttime. When a given location on the spherical Earth is in sunlight, its antipodethe location exactly on the opposite side of Earthis in darkness. The spherical shape of Earth causes the Sun to rise and set at different times in different places, and different locations get different amounts of sunlight each day.