 "Graticule" redirects here and may mean: a wire or cross
lines in an optical focusing system.
A
geographic coordinate system is a
coordinate system that enables every
location on Earth to be specified in three coordinates, using
mainly a
spherical
coordinate system.
The Earth is not a
sphere, but an irregular
shape approximating an
ellipsoid; the
challenge is to define a coordinate system that can accurately
state each topographical point as an unambiguous
tuple of numbers.
Latitude and longitude
Latitude phi (φ) and Longitude lambda
(λ)
Latitude (abbreviation: Lat.,
φ, or phi) is the angle from a point on the Earth's
surface to the
equatorial plane, measured
from the center of the sphere. Lines joining points of the same
latitude are called
parallels,
which trace concentric circles on the surface of the Earth,
parallel to the equator.
The north pole is 90° N; the south pole is 90° S. The 0° parallel of latitude is
designated the
equator, the
fundamental plane
of all geographic coordinate systems. The equator divides the globe
into Northern and Southern Hemispheres.
Longitude (abbreviation: Long.,
λ, or lambda) is the angle east or west of a
reference meridian between the two geographical poles to another
meridian that passes through an
arbitrary point. All meridians are halves of great circles, and are
not parallel. They converge at the north and south poles.
A line
passing to the rear of the Royal Observatory, Greenwich (near London in the UK) has been
chosen as the international zerolongitude reference line, the
Prime Meridian. Places to the
east are in the eastern hemisphere, and places to the west are in
the western hemisphere. The
antipodal
meridian of Greenwich is both 180°W and 180°E.
In 1884, the United States hosted the
International Meridian
Conference and twentyfive nations attended. Twentytwo of them
agreed to adopt the location of Greenwich as the zeroreference
line.
San Domingo voted against the adoption of that motion, while
France and Brazil
abstained. To date, there exist organizations around the
world which continue using historical prime meridians before the
acceptance of Greenwich and the illattended conference became
commonplace.
The combination of these two components specifies the position of
any location on the planet, but does not consider
altitude nor
depth.
For
example, Baltimore,
Maryland (in the USA) has a
latitude of 39.3° North, and a longitude of 76.6° West. So,
a vector drawn from the center of the Earth to a point 39.3° north
of the equator and 76.6° west of Greenwich will pass through
Baltimore.
This latitude/longitude "webbing" is known as the
conjugate graticule.
In defining an
ellipse, the vertical
diameter is known as the
conjugate
diameter, and the horizontal diameter —
perpendicular, or "transverse", to the conjugate — is the
transverse diameter. With a sphere or
ellipsoid, the conjugate diameter is known as the
polar axis
and the transverse as the
equatorial axis. The graticule
perspective is based on this
designation: As the longitudinal rings — geographically
defined, all great circles — converge at the poles, it is the
poles that the conjugate graticule is defined. If the polar vertex
is "pulled down" 90°, so that the vertex is on the equator, or
transverse diameter, then it becomes the
transverse
graticule, upon which all
spherical trigonometry is ultimately
based (if the longitudinal vertex is between the poles and equator,
then it is considered an
oblique
graticule).
Degrees: a measurement of angle
There are several formats for writing degrees, all of them
appearing in the same Lat, Long order.
 DMS Degrees:Minutes:Seconds (49°30'00"N,
123°30'00"W)
 DM Degrees:Decimal Minutes (49°30.0',
123°30.0'), (49d30.0m,123d30.0')
 DD Decimal
Degrees (49.5000°,123.5000°), generally with 46 decimal
numbers.
Geodesic height
To completely specify a location of a topographical feature on, in,
or above the Earth, one has to also specify the vertical distance
from the centre of the sphere, or from the surface of the sphere.
Because of the ambiguity of "surface" and "vertical", it is more
commonly expressed relative to a more precisely defined
vertical datum such as
mean sea level at a named point. Each country
has defined its own datum.
In the United Kingdom, the reference point is Newlyn. The
distance to Earth's centre can be used both for very deep positions
and for positions in space.
Cartesian coordinates
Every point that is expressed in spherical coordinates can be
expressed as an (
Cartesian)
coordinate. This is not a useful method for recording a position on
maps but is used to calculate distances and to perform other
mathematical operations. The origin is usually the center of the
sphere, a point close to the center of the Earth.
Shape of the Earth
The Earth is not a sphere, but an irregular shape approximating a
biaxial ellipsoid. It is nearly
spherical, but has an equatorial bulge making the radius at the
equator about 0.3% larger than the radius measured through the
poles. The shorter axis approximately coincides with axis of
rotation. Mapmakers choose the true ellipsoid that best fits their
need for the area they are mapping. They then choose the most
appropriate mapping of the spherical coordinate system onto that
ellipsoid. In the United Kingdom there are three common latitude,
longitude, height systems in use. The system used by GPS,
WGS84, differs at Greenwich from the
one used on published maps
OSGB36 by
approximately 112m.
The military system ED50,
used by NATO, differs by
about 120m to 180m.
Though early navigators thought of the sea as a flat surface that
could be used as a vertical datum, this is far from reality. The
Earth can be thought to have a series of layers of equal
potential energy within its
gravitational field. Height is a
measurement at right angles to this surface, and although gravity
pulls mainly toward the centre of Earth, the geocentre, there are
local variations. The shape of these layers is irregular but
essentially ellipsoidal. The choice of which layer to use for
defining height is arbitrary. The reference height we have chosen
is the one closest to the average height of the world's oceans.
This is called the
geoid.
The Earth is not static as points move relative to each other due
to continental plate motion, subsidence, and diurnal movement
caused by the
Moon and the
tides. The daily movement can be as much as a metre.
Continental movement can be up to a year, or in a century. A
weather system highpressure area can
cause a sinking of .
Scandinavia is
rising by a year as a result of the melting of the ice sheets of
the last ice age, but neighbouring Scotland is only rising by . These changes are
insignificant if a local datum is used, but are significant if the
global GPS datum is used.
Expressing latitude and longitude as linear units
On a spherical surface at
sea level, one
latitudinal second measures
30.82 metres and one latitudinal minute
1849 metres, and one latitudinal degree is
110.9 kilometres. The circles of longitude,
meridians, meet at the geographical poles, with the westeast width
of a second being dependent on the latitude. On the
equator at sea level, one longitudinal second
measures
30.92 metres, a longitudinal minute
1855 metres, and a longitudinal degree
111.3 kilometres. At 30° a longitudinal second is
26.76 metres, at Greenwich (51° 28' 38" N) is
19.22 metres, and at 60° it is
15.42 metres.
The width of one longitudinal degree on latitude
\scriptstyle{\phi}\,\! can be calculated by this formula (to get
the width per minute and second, divide by 60 and 3600,
respectively):
 ::::\frac{\pi}{180^{\circ}}\cos(\phi)M_r,\,\!
where
Earth's
average meridional radius \scriptstyle{M_r}\,\! approximately
equals . Due to the average radius value used, this formula is of
course not precise. You can get a better approximation of a
longitudinal degree at latitude \scriptstyle{\phi}\,\! by:

:\frac{\pi}{180^{\circ}}\cos(\phi)\sqrt{\frac{a^4\cos(\phi)^2+b^4\sin(\phi)^2}{(a\cos(\phi))^2+(b\sin(\phi))^2}},\,\!
where Earth's equatorial and polar radii, \scriptstyle{a,b}\,\!
equal
6,378,137 m,
6,356,752.3 m,
respectively.
Length equivalent at selected latitudes in
km
Latitude 
Town 
Degree 
Minute 
Second 
±0.0001° 
60° 
Saint Petersburg 
55.65 km 
0.927 km 
15.42m 
5.56m 
51° 28' 38" N 
Greenwich 
69.29 km 
1.155 km 
19.24m 
6.93m 
45° 
Bordeaux 
78.7 km 
1.31 km 
21.86m 
7.87m 
30° 
New Orleans 
96.39 km 
1.61 km 
26.77m 
9.63m 
0° 
Quito 
111.3 km 
1.855 km 
30.92m 
11.13m 
Datums often encountered
Latitude and longitude values can be based on several different
geodetic systems or
datum, the most common being
WGS 84 used by all GPS equipment.
Other datums however are significant because they were chosen by a
national cartographical organisation as the best method for
representing their region, and these are the datums used on printed
maps. Using the latitude and longitude found on a map may not give
the same reference as on a GPS receiver. Coordinates from the
mapping
system can sometimes be changed into another datum using a
simple
translation. For example, to
convert from ETRF89 (GPS) to the Irish Grid add 49 metres to the
east, and subtract 23.4 metres from the north. More generally one
datum is changed into any other datum using a process called
Helmert transformations. This
involves converting the spherical coordinates into Cartesian
coordinates and applying a seven parameter transformation
(translation, threedimensional
rotation),
and converting back.
In popular GIS software, data projected in latitude/longitude is
often represented as a 'Geographic Coordinate System'. For example,
data in latitude/longitude if the datum is the
North American Datum of 1983 is denoted by 'GCS North
American 1983'.
Geostationary coordinates
Geostationary satellites (e.g.,
television satellites) are over the equator at a specific point on
Earth, so their position related to Earth is expressed in longitude
degrees only. Their latitude is always zero, that is, over the
equator.
See also
Notes
 A Guide to coordinate systems in Great Britain
v1.7 Oct 2007 D00659 accessed 14.4.2008
 http://wwp.millenniumdome.com/info/conference.htm
 The French Institut Géographique National (IGN) still displays
a latitude and longitude on its maps centred on a meridian that
passes through Paris
 DMA Technical Report Geodesy for the Layman,
The Defense Mapping Agency, 1983
 WGS 84 is the default datum used in most GPS
equipment, but other datums can be selected.
 Making maps compatible with GPS Government of
Ireland 1999. Accessed 15.4.2008
References
 Portions of this article are from Jason Harris' "Astroinfo"
which is distributed with KStars, a desktop
planetarium for Linux/KDE. See [7837]
External links