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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 ...
A rhumb line (blue) compared to a great-circle arc (red) between Lisbon, Portugal, and Havana, Cuba. Top: orthographic projection. Bottom: Mercator projection. Practically every marine chart in print is based on the Mercator projection due to its uniquely favorable properties for navigation.
Parameters of a circle of equal altitude. The center of the CoP, is the geographical position (GP) of the observed body, the substellar point for a star, the subsolar point for the sun. The radius is the great circle distance equal to the zenith distance of the body.
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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 ...
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 ...