Free Notes II (Patreon)

• The people of Nareth know that the world is round.  The Master-Scholars of Jelaytha, being the clever people they are, discovered that their capital city of Jelay rests on what is known on Earth as the Tropic of cancer; 

Basically, during the summer solstice, the sun hangs directly above the city, casting light directly into wells without hitting the well walls. People already knew about this, and festivals were created to honor this strange phenomena, but it is only in recent times when Jelaythans actually questioned the "why" and "how". Especially considering they knew the planet to be spherical, they wanted to know how big the planet was. I will try to simplify how they went about this with the least amount of math possible.

1) The Sun hangs directly, once a year.

2) If the sun simply hovered around the sky and the planet is flat, why does this not happen more than once?  

3) Researchers went around their island and planted poles during the event, each recorded their findings. One even did this in Trevalyn.

4) The poles far away from the Jelay had shadows, proving that the sun was not directly above the entire island even though it was in the capital.

5) This made sense, as they knew there to be a curvature to the planet as the famed seamen they are, they knew that a ship's hull could disappear while the tall mast could still be seen from a distance when sailing over the horizon. It was also already known that the planet would cast a round shadow on the moon during a lunar eclipse.

6) Using the distance from one city to the capital, all one had to do now was measure the length of the shadow and the height of the pole, dividing the two. This is because the sun's position itself became a baseline measurement that one could do their math on.

7) The resulting length of the shadow was 7.12 degrees. If the planet is a sphere, this means it had to be 360 degrees, so divide 360 by 7.2, which results in 50.

8) The actual equation is 360/7.2 = circumference-of-the-planet/distance-between-the-two-cities. 

9) Thankfully, the city distance was easy to round up. It was about 500 Narethian miles (or 800 Imperial kilometers)

10) Remember that 360/7.2 = 50? Multiple that by the distance! The answer turns out to be 25,000 Narethian miles (or 40,000 Imperial kilometers)

11) They then multiple those measurements with square Narethian miles and Imperial kilometers.

11) Their conclusions? The planet is big as shit.

Bonus: This was all inspired by the ancient Greek scholar Eratosthenes, who was within a margin of error of 2% in regards to his calculations to the circumference of the Earth. Hilariously, there's a great what-if in here somehow. From the Khan Academy: A century after Eratosthenes, the Greek astronomer Posidonius of Rhodes (c. 135–51 BCE) calculated the Earth’s circumference. Posidonius used the star Canopus as frame of reference: when the star is visible at the horizon in Rhodes, it is 7.5 degrees above the horizon in Alexandria. His first calculations came out almost exactly correct, but he revised the distance between Rhodes and Alexandria, which resulted in a number comparable to about 18,000 miles (about 29,000 kilometers), some 28 percent smaller than the actual circumference. Ptolemy reported the calculations of Posidonius instead of those of Eratosthenes, and it was Ptolemy’s writings that found their way to Christopher Columbus. If Ptolemy had used Eratosthenes’s larger, more accurate figure for Earth’s circumference, Columbus might never have sailed west.

Why did I do this? So that Master Feren could test our MCs!