and
NAD83, in metres The locations of points in 3D space most conveniently are described by three
cartesian or rectangular coordinates,
X,
Y, and
Z. Since the advent of satellite positioning, such coordinate systems are typically
geocentric, with the Z-axis aligned to Earth's (conventional or instantaneous) rotation axis. Before the era of
satellite geodesy, the coordinate systems associated with a geodetic
datum attempted to be
geocentric, but with the origin differing from the geocenter by hundreds of meters due to regional deviations in the direction of the
plumbline (vertical). These regional geodetic datums, such as
ED 50 (European Datum 1950) or
NAD 27 (North American Datum 1927), have ellipsoids associated with them that are regional "best fits" to the
geoids within their areas of validity, minimizing the deflections of the vertical over these areas. It is only because
GPS satellites orbit about the geocenter that this point becomes naturally the origin of a coordinate system defined by satellite geodetic means, as the satellite positions in space themselves get computed within such a system. Geocentric coordinate systems used in geodesy can be divided naturally into two classes: • The
inertial reference systems, where the coordinate axes retain their orientation relative to the
fixed stars or, equivalently, to the rotation axes of ideal
gyroscopes. The
X-axis points to the
vernal equinox. • The co-rotating reference systems (also
ECEF or "Earth Centred, Earth Fixed"), in which the axes are "attached" to the solid body of Earth. The
X-axis lies within the
Greenwich observatory's
meridian plane. The coordinate transformation between these two systems to good approximation is described by (apparent)
sidereal time, which accounts for variations in Earth's axial rotation (
length-of-day variations). A more accurate description also accounts for
polar motion as a phenomenon closely monitored by geodesists.
Coordinate systems in the plane archive with
lithography plates of maps of
Bavaria In geodetic applications like
surveying and
mapping, two general types of coordinate systems in the plane are in use: •
Plano-polar, with points in the plane defined by their distance,
s, from a specified point along a ray having a direction
α from a baseline or axis. •
Rectangular, with points defined by distances from two mutually perpendicular axes,
x and
y. Contrary to the mathematical convention, in geodetic practice, the
x-axis points
North and the
y-axis
East. One can intuitively use rectangular coordinates in the plane for one's current location, in which case the
x-axis will point to the local north. More formally, such coordinates can be obtained from 3D coordinates using the artifice of a
map projection. It is impossible to map the curved surface of Earth onto a flat map surface without deformation. The compromise most often chosen — called a
conformal projection — preserves angles and length ratios so that small circles get mapped as small circles and small squares as squares. An example of such a projection is UTM (
Universal Transverse Mercator). Within the map plane, we have rectangular coordinates
x and
y. In this case, the north direction used for reference is the
map north, not the
local north. The difference between the two is called
meridian convergence. It is easy enough to "translate" between polar and rectangular coordinates in the plane: let, as above, direction and distance be
α and
s respectively; then we have: :\begin{align} x &= s \cos \alpha\\ y &= s \sin \alpha \end{align} The reverse transformation is given by: :\begin{align} s &= \sqrt{x^2 + y^2}\\ \alpha &= \arctan\frac{y}{x}. \end{align} == Heights ==