Equator, meridian and a mean circle
Circumference 2πR is exact for a circle. Earth’s equator uses its equatorial radius, while a meridian follows an ellipse through both poles. Substituting a mean spherical radius answers a third, approximate question. State which path a quoted circumference describes.
A shadow turns an angle into a distance
If nearly parallel sunlight produces a signed zenith-angle difference Δz along meridian separation d, a sphere gives C = 360d/|Δz|. The constructed 800 km and 7.2° example yields 40,000 km. An angle uncertainty of 0.1° is substantial compared with that 7.2° difference.
More sites test more than one fitted size
Two sites supply a slope, but a nearby lamp over a plane can also fit two angles. A third non-symmetric site tests whether angles vary linearly with surface distance or follow one shared lamp’s arctangent curve. Record local solar noon and the sign of the shadow, not only its length.