Empirical Earth · Shape, Curvature & the Horizon

Curvature, the horizon & Eratosthenes

The claim

“No measurable curvature — the horizon rises to eye level; Eratosthenes is just a small, nearby Sun.”

What is true

At eye level on flat ground the horizon does look flat, and the drop is too small to see from a beach.

What is measured

With nothing but shadows, Eratosthenes measured the Earth’s circumference at about 40,000 km back in 240 BCE. The modern value is 40,075 km. More on refraction and the curve. The two-stick measurement of the globe is Eratosthenes and his test.

What would show this is wrong

a horizon that never drops as you climb, and three equal-height markers staying in a straight line over many miles.

Sources

  1. World Geodetic System 1984 (WGS 84). NGA Standardization Document, defining ellipsoid parameters (a, f, b). National Geospatial-Intelligence Agency. WGS 84 link
  2. Refraction, Snell's law & refractive index of air/water. Standard optics; refractive index of air via the Ciddor/Edlén equations. E. Hecht, Optics ; NIST refractive-index references. Snell's link
  3. Eratosthenes' measurement of Earth's circumference (~240 BCE). Cleomedes, On the Heavens ; standard history of science — Syene/Alexandria gnomon shadows, 1/50 of a circle, 250,000 stadia. Er link
  4. Modern geodesy fixes Earth’s size to the meter. The World Geodetic System 1984 (WGS84) defines the equatorial radius as 6,378,137 m and the flattening as 1/298.257223563, giving an equatoria link
  5. Measuring flatness with light. An optical flat under monochromatic light shows interference fringes; two adjacent fringes mark one-half wavelength of height difference (about 316 nm for a 63 link
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