Great circle
- Distance on the mean sphere
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Great circle
Two places, typed or set by two clicks on the map. The distance and the initial bearing are on the sphere that uses the GRS80 mean radius, …. The rhumb-line distance is beside it, so the two paths can be compared.
Looking at the globe from the middle of the great circle. The blue line is the great circle. The brown line is the rhumb line. A part of a path that is on the far side is left out.
- Great circle, and place A
- Rhumb line, and place B
Initial bearing
- Clockwise from true north
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Rhumb line
- Constant bearing
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What this page shows
The great-circle distance is the shorter arc on the sphere. The initial bearing is the direction of that arc at place A, clockwise from true north. The rhumb line is the path of constant bearing. On a sphere it is longer than the great circle, or the same length when the two paths coincide, as they do along the equator and along a meridian.
The preset is Stockholm to Sydney. Stockholm is 59.3293° N, 18.0686° E, the city position used on the other pages. Sydney is 33.8688° S, 151.2093° E, the city position used for the Sydney preset on the Polaris page. They are not surveyed pins, and there is no airport list.
Assumptions
- The sphere’s radius is the GRS80 mean radius from the shared geometry module, …. The page does not keep a second radius.
- The distance uses the haversine. The bearing is atan2 of the east and north parts of the departure. It is left blank when the places are the same, when they are opposite each other, or when place A is a pole, because one bearing is not defined there.
- The rhumb distance uses the meridional parts. To a pole, the rhumb line is the meridian. Longitude is taken the short way, across the antimeridian when that is shorter.
- The map draws the great circle, and the rhumb line as a dashed brown path. A path that crosses the antimeridian is split so the map does not join it the long way across the picture.
- Hold Ctrl and scroll to zoom the map. The scroll wheel alone moves the page. The map requests tiles from OpenStreetMap. The coordinates are used only in this browser.
Sources
- Moritz, H. (1980). Geodetic Reference System 1980. Bulletin Géodésique, 54, 395–405. The radius is the mean radius from that system, taken from the shared geometry module.
- The great-circle formulae are the spherical haversine and the initial course. The rhumb line is the loxodrome on the sphere.
- Stockholm, 59.3293° N, 18.0686° E, and Sydney, 33.8688° S, 151.2093° E, the city positions already used on this site.
- Map tiles © OpenStreetMap contributors.