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A "true circumnavigation" of Earth is defined, in order to account for the shape of Earth, to be about 2.5 times as long, including a crossing of the equator, at about 40,000 km (25,000 mi). [24] On the flat Earth model, the ratios would require the Antarctic Circle to be 2.5 times the length of the circumnavigation, or 2.5 × 2.5 = 6.25 times ...
The full moon covers only about 0.2 deg 2 of the sky when viewed from the surface of the Earth. The Moon is only a half degree across (i.e. a circular diameter of roughly 0.5°), so the moon's disk covers a circular area of: π ( 0.5° / 2 ) 2, or 0.2 square degrees. The moon varies from 0.188 to 0.244 deg 2 depending on its distance from ...
Equal-area Johann Heinrich Lambert: Cylindrical equal-area projection with standard parallel at the equator and an aspect ratio of π (3.14). 1910 Behrmann: Cylindrical Equal-area Walter Behrmann: Cylindrical equal-area projection with standard parallels at 30°N/S and an aspect ratio of (3/4)π ≈ 2.356. 2002 Hobo–Dyer: Cylindrical Equal ...
The concept of a spherical Earth dates back to around the 6th century BC, [2] but remained a matter of philosophical speculation until the 3rd century BC. The first scientific estimation of the radius of the Earth was given by Eratosthenes about 240 BC, with estimates of the accuracy of Eratosthenes's measurement ranging from −1% to 15%.
The central angle of a square is equal to 90° (360°/4). The external angle of a square is equal to 90°. The diagonals of a square are equal and bisect each other, meeting at 90°. The diagonal of a square bisects its internal angle, forming adjacent angles of 45°. All four sides of a square are equal. Opposite sides of a square are parallel.
If the shape is complex, 2 π times the offset, times the absolute value of its turning number must be added. [ 1 ] This diagram gives a visual analogue using a square: regardless of the size of the square, the added perimeter is the sum of the four blue arcs, a circle with the same radius as the offset.
Posidonius calculated the Earth's circumference by reference to the position of the star Canopus.As explained by Cleomedes, Posidonius observed Canopus on but never above the horizon at Rhodes, while at Alexandria he saw it ascend as far as 7 + 1 ⁄ 2 degrees above the horizon (the meridian arc between the latitude of the two locales is actually 5 degrees 14 minutes).
The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian. Hence, in this figure θ = A/2 and r = 1. The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2 θ, is the area of a spherical cap on a unit sphere