u/Grand-Ring9184

I am trying to calculate the earth's circumference with Eratostene's method but I have a big problem. I need a way to independently calculate the vertical distance between the two cities, and all of the ways I can think of imply circular logic (using data that already implies the knowledge about the earth's circumference). is there really a way? I obviously can't send people to walk and count their steps as Eratostene did.