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In any ellipsoid, the length of a degree of longitude at the equator is exactly 60 geographical miles. The Earth's radius at the equator in the GRS80 ellipsoid is 6,378,137.0000 m, [3] which makes the geographical mile 1,855.3248 m. The rounding of the Earth's radius to metres in GRS80 has an effect of 0.0001 m.
The greatest length of any of these paths is the diameter of the graph. A central vertex in a graph of radius r is one whose eccentricity is r —that is, a vertex whose distance from its furthest vertex is equal to the radius, equivalently, a vertex v such that ϵ(v) = r.
Vincenty's goal was to express existing algorithms for geodesics on an ellipsoid in a form that minimized the program length (Vincenty 1975a). His unpublished report (1975b) mentions the use of a Wang 720 desk calculator, which had only a few kilobytes of memory.
When calculating the length of a short north-south line at the equator, the circle that best approximates that line has a radius of (which equals the meridian's semi-latus rectum), or 6335.439 km, while the spheroid at the poles is best approximated by a sphere of radius , or 6399.594 km, a 1% difference. So long as a spherical Earth is assumed ...
A graphical or bar scale. A map would also usually give its scale numerically ("1:50,000", for instance, means that one cm on the map represents 50,000cm of real space, which is 500 meters) A bar scale with the nominal scale expressed as "1:600 000", meaning 1 cm on the map corresponds to 600,000 cm=6 km on the ground.
The above formula can be rearranged to solve for the circumference: = =. The ratio of the circle's circumference to its radius is equivalent to 2 π {\displaystyle 2\pi } . [ a ] This is also the number of radians in one turn .
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