Using an equatorial sundial you can demonstrate that the sun moves through 15 degrees every hour, no matter what time of day it is.

Example construction of such a sundial:

This has several implications, all of which are problematic for flat earth theory.

**A) DISTANCE TO THE SUN**

If you know the distance between two points at any given latitude between the two tropics (e.g, between say Ziguinchor, Senegal, and Gondar, Ethiopia at 12.6 degrees N - at most about 7400 km), you can calculate the exact distance to the sun. If you believe in longitude, you can just go by the angle difference in longitude. If you don't believe in longitude, you could send a team of two people, one to each location, and measure the exact time the sun passes over head as well as the angle the sun makes at the time the sun passes overhead the other location. Since that is exactly what longitude is, it will work out to the same value.

For this particular example, Google thinks you can drive from one to the other in about 7400km, and the longitude difference is 53.7 degrees. This means that at noon at Gondar the day the sun is directly overhead, the sun is at a 53.7 degree angle in Ziguinchor, and vice versa.

On a flat earth, this means you can draw a triangle where one leg is the line on the flat earth between the two locations, one leg is vertical from the location where the sun is directly overhead, and one leg is from the sun to the other location. This triangle would have angles of 53.7, 90, and 36.3 degrees. The length of the earth leg is at most the driving distance between the two cities, and the vertical distance from the earth to the sun at the location is the tangent of 36.3 degrees * at most 7400km, or about 3400 miles.

**B) ANGULAR SIZE OF THE SUN**

Because you now know how far the sun is from the earth, you can determine how much farther away the sun is at a time other than noon. In the above example, the sun would be 7400km/cos(36.3 degrees) at the location that is not directly under the sun, or about 5700 miles away. This is 1.7 times farther away than the sun is at noon, meaning that the angular size of the sun should be significantly smaller at the location where it is not noon.

However, the angular size of the sun is always about 1/2 of a degree, this means the sun's distance from you does not change significantly during the day, or the shape of the sun is weirdly shaped such that from different angles it appears larger. Such a weirdly shaped sun would be impossible to eclipse, for example.

**C) PERSPECTIVE**

Since the angular velocity of the sun is constant, in flat earth theory this means that the sun must be moving faster when it is farther away from you. However, if that were the case, people in different areas of the earth would see the sun moving more quickly overhead, because while it is 4 PM where you are, it's noon somewhere. Either the person where it is noon would see the sun moving faster, or you would see the sun moving slower.