The shortest distance between two points on an ellipsoid (the 'geodetic'), according to the 'Meeus' method. distGeo
should be more accurate.
1  distMeeus(p1, p2, a=6378137, f=1/298.257223563)

p1 
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 
p2 
as above 
a 
numeric. Major (equatorial) radius of the ellipsoid. The default value is for WGS84 
f 
numeric. Ellipsoid flattening. The default value is for WGS84 
Parameters from the WGS84 ellipsoid are 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  f 

WGS84  6378137  1/298.257223563 

GRS80  6378137  1/298.257222101 

GRS67  6378160  1/298.25 

Airy 1830  6377563.396  1/299.3249646 

Bessel 1841  6377397.155  1/299.1528434 

Clarke 1880  6378249.145  1/293.465 

Clarke 1866  6378206.4  1/294.9786982 

International 1924  6378388  1/297 

Krasovsky 1940  6378245  1/298.2997381 

more info: http://en.wikipedia.org/wiki/Reference_ellipsoid
Distance value in the same units as parameter a
of the ellipsoid (default is meters)
This algorithm is also used in the spDists
function in the sp package
Robert Hijmans, based on a script by Stephen R. Schmitt
Meeus, J., 1999 (2nd edition). Astronomical algoritms. WillmanBell, 477p.
distVincentyEllipsoid, distVincentySphere, distHaversine, distCosine
1 2 3 
Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.
Please suggest features or report bugs with the GitHub issue tracker.
All documentation is copyright its authors; we didn't write any of that.