for geodesics on the
earth, see
geodesics on an ellipsoid. for geodesics in
general relativity, see
geodesics in general relativity. for other uses, see
geodesic (disambiguation).
a geodesic triangle on the sphere. the geodesics are
great circle arcs.
geodesy 


fundamentals
 geodesy
 geodynamics
 geomatics
 history

concepts
 geographical distance
 geoid
 figure of the earth (earth radius and earth's circumference)
 geodetic datum
 geodesic
 geographic coordinate system
 horizontal position representation
 latitude / longitude
 map projection
 reference ellipsoid
 satellite geodesy
 spatial reference system
 spatial relations

technologies
 global nav. sat. systems (gnsss)
 global pos. system (gps)
 (russia)
 (china)
 (europe)
 (india)
 (japan)
 discrete global grid and geocoding

standards (history) ngvd 29  sea level datum 1929  osgb36  ordnance survey great britain 1936  sk42  systema koordinat 1942 goda  ed50  european datum 1950  sad69  south american datum 1969  grs 80  geodetic reference system 1980  iso 6709  geographic point coord. 1983  nad 83  north american datum 1983  wgs 84  world geodetic system 1984  navd 88  n. american vertical datum 1988  etrs89  european terrestrial ref. sys. 1989  gcj02  chinese obfuscated datum 2002  geo uri  internet link to a point 2010 
 international terrestrial reference system
 spatial reference system identifier (srid)
 universal transverse mercator (utm)


in differential geometry, a geodesic (/^{[1]}^{[2]}) is a curve representing in some sense the shortest path between two points in a surface, or more generally in a riemannian manifold. it is a generalization of the notion of a "straight line" to a more general setting.
the term "geodesic" comes from geodesy, the science of measuring the size and shape of earth. in the original sense, a geodesic was the shortest route between two points on the earth's surface. for a spherical earth, it is a segment of a great circle. the term has been generalized to include measurements in much more general mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph.
in a riemannian manifold or submanifold geodesics are characterised by the property of having vanishing geodesic curvature. more generally, in the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it. applying this to the levicivita connection of a riemannian metric recovers the previous notion.
geodesics are of particular importance in general relativity. timelike geodesics in general relativity describe the motion of free falling test particles.