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Latitudes at regular intervals of longitude can be found and the resulting positions transferred to the Mercator chart allowing the great circle to be approximated by a series of rhumb lines. The path determined in this way gives the great ellipse joining the end points, provided the coordinates ( ϕ , λ ) {\displaystyle (\phi ,\lambda )} are ...
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
The disk bounded by a great circle is called a great disk: it is the intersection of a ball and a plane passing through its center. In higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space R n + 1. Half of a great circle may be called a great ...
The point can be illustrated with an east–west passage over 90 degrees of longitude along the equator, for which the great circle and rhumb line distances are the same, at 10,000 kilometres (5,400 nautical miles). At 20 degrees north the great circle distance is 9,254 km (4,997 nmi) while the rhumb line distance is 9,397 km (5,074 nmi), about ...
Pilots use aeronautical charts based on LCC because a straight line drawn on a Lambert conformal conic projection approximates a great-circle route between endpoints for typical flight distances. The US systems of VFR (visual flight rules) sectional charts and terminal area charts are drafted on the LCC with standard parallels at 33°N and 45 ...
Gnomonic projection of a portion of the north hemisphere centered on the geographic North Pole The gnomonic projection with Tissot's indicatrix of deformation. A gnomonic projection, also known as a central projection or rectilinear projection, is a perspective projection of a sphere, with center of projection at the sphere's center, onto any plane not passing through the center, most commonly ...
Together, a meridian and its antimeridian form a great circle that passes through the geographic poles. 2. The 180th meridian in particular, i.e. the meridian of longitude that is exactly 180 degrees both east and west of the Prime Meridian, with which it forms a great circle dividing the Earth into the Eastern and Western Hemispheres.
The longitude on the ellipsoid and the distance along the geodesic are then given in terms of the longitude on the sphere and the arc length along the great circle by simple integrals. Bessel and Helmert gave rapidly converging series for these integrals, which allow the geodesic to be computed with arbitrary accuracy.