The shortest distance between two points (i.e., the 'greatcircledistance' or 'as the crow flies'), according to the 'Vincenty (ellipsoid)' method. This method uses an ellipsoid and the results are very accurate. The method is computationally more intensive than the other greatcircled methods in this package.
distVincentyEllipsoid(p1, p2, a=6378137, b=6356752.3142, f=1/298.257223563)
longitude/latitude of point(s), in degrees 1; can be a vector of two numbers, a matrix of 2 columns (first one is longitude, second is latitude) or a SpatialPoints* object
as above; or missing, in which case the sequential distance between the points in p1 is computed
Equatorial axis of ellipsoid
Polar axis of ellipsoid
Inverse flattening of ellipsoid
Distance value in the same units as the ellipsoid (default is meters)
The WGS84 ellipsoid is used by default. It is the best available global ellipsoid, but for some areas other ellipsoids could be preferable, or even necessary if you work with a printed map that refers to that ellipsoid. Here are parameters for some commonly used ellipsoids:
ellipsoid 
a 
b 
f 

WGS84 
6378137 
6356752.3142 
1/298.257223563 

GRS80 
6378137 
6356752.3141 
1/298.257222101 

GRS67 
6378160 
6356774.719 
1/298.25 

Airy 1830 
6377563.396 
6356256.909 
1/299.3249646 

Bessel 1841 
6377397.155 
6356078.965 
1/299.1528434 

Clarke 1880 
6378249.145 
6356514.86955 
1/293.465 

Clarke 1866 
6378206.4 
6356583.8 
1/294.9786982 

International 1924 
6378388 
6356911.946 
1/297 

Krasovsky 1940 
6378245 
6356863 
1/298.2997381 
a
is the 'semimajor axis', and b
is the 'semiminor axis' of the ellipsoid. f
is the flattening.
Note that f = (ab)/a
Vincenty, T. 1975. Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations. Survey Review Vol. 23, No. 176, pp8893. Available here:
distGeo, distVincentySphere, distHaversine, distCosine, distMeeus
# NOT RUN {
distVincentyEllipsoid(c(0,0),c(90,90))
# on a 'Clarke 1880' ellipsoid
distVincentyEllipsoid(c(0,0),c(90,90), a=6378249.145, b=6356514.86955, f=1/293.465)
# }
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