Experiment #1 - Take a photo of tanks on a pier from 20km.
A view of the horizon from the coast of Spain. In which the Earth's curvature can be seen. Tanks are on a pier at Port de Sagunt(Saggas)
https://en.wikipedia.org/wiki/Figure_of_the_Earth#/media/File:Horizon,_Valencia_(Spain).JPG
Experiment #2 - Observe the "dip angle" of the horizon from a mountain top of a known height, and calculate the radius of the earth (dip angle = 0 = infinite radius = flat earth)
Biruni (973 - 1048) developed a new method using trigonometric calculations to compute earth's radius and circumference based on the angle between the horizontal line and true horizon from a mountain top with known height. He calculated the height of the mountain by going to two points at sea level with a known distance apart and then measuring the angle between the plain and the top of the mountain for both points. Biruni's estimate of 6,339.9 km for the Earth radius had an error of 0.0026 and was 16.8 km less than the current value of 6,356.7 km. The idea came to him when he was on top of a tall mountain near Nandana in India. He measured the dip angle using an astrolabe and he applied to the law of sines formula. He also made use of algebra in his calculation. A = Highest point of mountain B = Lowest point of mountain h = Height of the mountain C = Lowest point of true horizon visible from point A O = Centre of Earth α = Dip angle r = Earth's radius Solution: The angle AOC = α. AO=(r+h) is the hypotenuse in triangle AOC. r=(r+h).cos(α) Then the right side can be simplified to find r. r=h.cos(α)/(1-cos(α))
https://en.wikipedia.org/wiki/Spherical_Earth#/media/File:Abu_Reyhan_Biruni-Earth_Circumference.svg
Mathematical geodesists before 1900 (before NASA)
Pythagoras 580–490 BC, ancient Greece
Eratosthenes 276–194 BC, ancient Greece
Hipparchus c. 190–120 BC, ancient Greece
Posidonius c. 135–51 BC, ancient Greece
Claudius Ptolemy c. AD 83–168, Roman Empire (Roman Egypt)
Al-Ma'mun 786–833, Baghdad (Iraq/Mesopotamia)
Abu Rayhan Biruni 973–1048, Khorasan (Iran/Samanid Dynasty)
Muhammad al-Idrisi 1100–1166, (Arabia & Sicily)
Regiomontanus 1436–1476, (Germany/Austria)
Abel Foullon 1513–1563 or 1565, (France)
Pedro Nunes 1502–1578 (Portugal)
Gerhard Mercator 1512–1594 (Belgium & Germany)
Snellius (Willebrord Snel van Royen) 1580–1626, Leiden (Netherlands)
Christiaan Huygens 1629–1695 (Netherlands)
Pierre Bouguer 1698–1758, (France & Peru)
Pierre de Maupertuis 1698–1759 (France)
Alexis Clairaut 1713–1765 (France)
Johann Heinrich Lambert 1728–1777 (France)
Roger Joseph Boscovich 1711–1787, (Rome/ Berlin/ Paris)
Ino Tadataka 1745–1818, (Tokyo)
Georg von Reichenbach 1771–1826, Bavaria (Germany)
Pierre-Simon Laplace 1749–1827, Paris (France)
Adrien Marie Legendre 1752–1833, Paris (France)
Johann Georg von Soldner 1776–1833, Munich (Germany)
George Everest 1790–1866 (England and India)
Friedrich Wilhelm Bessel 1784–1846, Königsberg (Germany)
Heinrich Christian Schumacher 1780–1850 (Germany & Estonia)
Carl Friedrich Gauss 1777–1855, Göttingen (Germany)
Friedrich Georg Wilhelm Struve 1793–1864, Dorpat and Pulkovo (Russian Empire)
J. H. Pratt 1809–1871, London (England)
Friedrich H. C. Paschen 1804–1873, Schwerin (Germany)
Johann Benedikt Listing 1808–1882 (Germany)
Johann Jacob Baeyer 1794–1885, Berlin (Germany)
Sir George Biddell Airy 1801–1892, Cambridge & London
Karl Maximilian von Bauernfeind 1818–1894, Munich (Germany)
Wilhelm Jordan 1842–1899, (Germany)
Hervé Faye 1814–1902 (France)
George Gabriel Stokes 1819–1903 (England)
Carlos Ibáñez e Ibáñez de Ibero 1825–1891, Barcelona (Spain)
Henri Poincaré 1854–1912, Paris (France)
Alexander Ross Clarke 1828–1914, London (England)
Charles Sanders Peirce 1839–1914 (United States)
Friedrich Robert Helmert 1843–1917, Potsdam (Germany)
Heinrich Bruns 1848–1919, Berlin (Germany)
Loránd Eötvös 1848–1919 (Hungary)