hers claim that the Sun is only about 3,000 miles above Earth, rather than 93 million miles as determined by astrophysics. Furthermore, the Flat-Earth Sun is only 32 miles in diameter, rather than 864,340 miles in conventional astronomy. Let’s discuss some of the evidence that the Sun is extremely large and very far away.
First, we consider the classic experiment carried out by the Greek scholar Eratosthenes in 205 BCE to estimate the circumference of the Earth. Eratosthenes noted that there was a day when the noonday Sun was directly overhead in Syene (modern-day Aswan, Egypt, at 24º N latitude). Since the Sun’s rays are traveling straight down relative to Earth, a pole in Syene will have no shadow at that time. However, in Alexandria (31º North latitude), poles would produce a shadow at the same hour. Eratosthenes assumed that the Earth was a sphere; he further assumed that the Sun was sufficiently far from Earth that one could approximate the Sun’s rays as reaching Earth on parallel lines. From the measured shadow length in Alexandria and some simple geometry to deduce the angular difference of the Sun’s rays between Syene and Alexandria, Eratosthenes estimated the radius of the Earth as roughly 4360 miles, which is about 10% larger than modern measurements of Earth’s radius.
Flat-Earthers point out that Eratosthenes’ experiment does not prove that the Earth is a sphere. This statement is true – Eratosthenes assumed that the Earth was spherical, and from that assumption he calculated the Earth’s radius. Flat-Earthers state that they can repeat the measurement of Eratosthenes, assuming the Earth is flat. The “Flat-Earth” measurement is shown on the left side of Fig. II.16, in contrast to the “spherical Earth” measurement on the right side. In fact, this is how some Flat-Earthers derive the distance to the Sun; they repeat the Eratosthenes measurement in Flat-Earth geometry and obtain a distance of roughly 3,000 miles.
This statement works for measuring shadows at 2 points in Egypt, Syene and Alexandria. However, we can perform the Eratosthenes experiment at many latitudes, one of which has the Sun directly overhead. If we do this, we can choose angles where Flat-Earth theory predicts shadows that increase in linear fashion with each angle. However, with the spherical-Earth measurement, the shadows will not increase linearly. In fact, if you perform the Eratosthenes measurement with two post, one of which is directly under the Sun, the calculated distance to the Sun in the flat-Earth picture differs for each distance to the second post. This explains why various Flat-Earth groups calculate different distances for the Sun.
Note that if one of the posts is placed near the North Pole, the resulting shadow for a spherical Earth will be extremely long. This is difficult to reproduce in the flat-Earth picture. This is one of the reasons Flat-Earthers are unable to state the exact distance from Earth to Sun; it varies according to the way they calculate this distance. Flat-Earthers “explain” the difference between the shadow measurements for spherical and flat Earth pictures as due to “refraction” of light (Flat-Earthers invoke “refraction” for many phenomena that cause them trouble). But they do not seem to have a consistent understanding of that term, or methods for accurately calculating refractive effects. In this case, Flat-Earthers argue that the Sun’s rays do not pass in a straight line to the Earth, but they travel in a curved path that allows them to obtain the same results as Eratosthenes.
Finally, consider the size of the Sun. Remember that the Flat-Earth Sun has a diameter of only 32 miles (this is obtained by noting that as viewed from Earth, the Sun subtends an angle of 0.5 degrees). If the Sun was only 3,000 miles away, then one can calculate that its diameter would be about 30 miles. We get a good idea of the relative size of the Sun by observing a transit of the planet Mercury. This occurs when the orbit of Mercury takes it directly between the Earth and the Sun. We then see Mercury moving across the Sun. Fig.