# Geographic coordinate system

The geographic (earth-mapping) coordinate system expresses every horizontal position on Earth by two of the three coordinates of a spherical coordinate system which is aligned with the spin axis of the Earth.

## The sexagesimal geographic coordinate standard system

Map of Earth showing lines of latitude (horizontally) and longitude (vertically); large version (pdf)

Borrowing from theories of ancient Babylonians, later expanded by the famous Greek thinker and geographer Ptolemy, a full circle is assigned 360 degrees (360°). This is also called absolute location

It defines two angles measured from the center of the Earth:

• the latitude (Lat.) is the vertical data and measures the angle between any point and the equator. Lines of constant latitude are called parallels. They trace circles on the surface of the Earth, but the only parallel that is a great circle is the equator (latitude=0 degrees),with each pole being 90 degrees (north pole +90°; south pole −90° ).
• the longitude (Long.) is the horizontal data and measures the angle east-wards from an arbitrary point on the Earth: Greenwich in London (U.K.) is the accepted zero-longitude point internationally in most modern societies (longitude=0 or 360 degrees). Longitude is measured form 0 to +360 deg, going east from the zeropoint (Greenwich or 0°), being 180 degrees the opposite point on the globe to Greenwich. Lines of constant longitude are called meridians . The meridian passing through Greenwich is the Prime Meridian. Unlike parallels, all meridians are great circles, and meridians are not parallel: they intersect at the north and south poles.

By combining these two angles, the plane position of any location on Earth can be specified.

For example, Baltimore, Maryland (in the USA) has a latitude of 39.3 degrees North, and a longitude of 76.6 degrees West (39.3° N 76.6° W). So, a vector drawn from the center of the Earth to a point 39.3 degrees north of the equator and 76.6 degrees west of Greenwich will pass through Baltimore.

This latitude/longitude "webbing" is known as the common graticule. There is also a complementary transverse graticule (meaning the graticule is shifted 90°, so that the poles are on the horizontal equator), upon which all spherical trigonometry is ultimately based on.

Traditionally, degrees have been divided into minutes ( ' ) and seconds ( " ). There are formats for degrees, all of them appearing in a Lat.-Long. order :

• DM Degree:Minute (49:30.0-123:30.0)
• DMS Degree:Minute:Second (49:30:00-123:30:00)
• DD Decimal Degree (49.5000-123.5000), generally with 4 decimal numbers.

To change from DM or DMS to DD, Decimal degrees = whole number of degrees, plus minutes divided by 60, plus seconds divided by 3600. Decimal division is now the most common and standard.

The equator is obviously an important part of this coordinate system, it represents the zeropoint of the latitude angle, and the halfway point between the poles. The equator is the fundamental plane of the geographic coordinate system. All spherical coordinate systems define such a fundamental plane.

This article originates from Jason Harris' Astroinfo which comes along with KStars, a Desktop Planetarium for Linux/KDE. See http://edu.kde.org/kstars/index.phtml

In popular GIS software, data projected in latitude/longitude is often represented as 'Geographic Coordinate System'. For example, data in latitude/longitude with datum as the North American Datum of 1983 is denoted by 'GCS_North_American_1983'.

### Notation

You can use the cardinal or the numerical only system:

• Cardinal system includes North, South, East, West (i.e., 60° E).
• Numerical system uses only numbers. i.e., 60°E is 60° and 60°W is 360°−60° = 300º.

PoLat uses instead of Equator the North Pole (North pole = 0°, Equator = 90° and South Pole = 180°). In this notation, there are no negative numbers.

The UGN (Unified Geographic Notation) uses:

• Numerical system in Decimal degrees.
• Latitude appears first, followed by a -, the latitude and UGN.
• PoLat is used for latitude.

I.e., 90.00-18.01 UGN is in the Equator (90°) and 18.01° in the east

### Geostationary coordinates

Geostationary satellites (i.e., television satellites ) are over the Equator. So, their position related to Earth is expressed in longitude degrees. Latitude does not change, and is always zero over the Equator.

### Third dimension : altitude

To completely specify a location on, in, or above the Earth, one has to specify also the elevation / height position. This can e.g., be expressed relative to a datum such as mean sea level (above mean sea level) or the geoid. The distance to the Earth's center is a practical coordinate both for very deep positions and for positions in space.

The elevation specifies the vertical position of the Earth surface.

Various elevation / height coordinates either with respect to the surface or some other datum are altitude, height, and depth.

## The proposed hexadecimal geographic coordinate system

The main meridian, zero degree hexadecimal (± Q°QQ'q), is identical to the meridian 11°15' East of Greenwich, which also crosses the city center of Florence in Italy. It traverses the equator with a continental point of confluence in Gabon.

Beginning with this main meridian the Earth is divided into both, sixteen eastern hexadecimal degrees designated plus, and sixteen western hexadecimal degrees: minus.

The meridian sixteen hexadecimal degrees: ± H°QQ'q (= 168°45' W of Greenwich) passes, maritime, in the Bering Strait next to the small uninhabited Fairway Rock Island.

Perpendicular to the longitudinal great circle Gabon — Bering Strait is situated the great circle Sumatra (in Asia) —- Ecuador (in South America), plus and minus eight hexadecimal degrees. It crosses the equator of Earth even with two continental points of confluence, respectively at +T°QQ'q (= 101°15' E Greenwich) and at -T°QQ'q (= 78°45' W of Greenwich).

In this hexadecimal geographic coordinate system, the sexagesimal main meridian of Greenwich is only one of the 32 hexadecimal main meridians spanned from pole to pole.

The North pole is located at latitude plus eight hexadecimal degrees like the South pole at latitude minus eight degrees.

The latitudes plus and minus four hexadecimal degrees correspond respectively to 45° North and 45° South. The latitudes plus and minus two hexadecimal degrees (= 22° 30') are next to the tropics, like the latitudes plus and minus six hexadecimal degrees (= 67° 30') are situated near the polar circles. (The polar circles are now at about 66°34', but at less then 66° five milleniums before. cf. Obliquity of the ecliptic.)

Among the various advantages of the hexadecimal geographic coordinate system one can annotate:

• In sexagesimal maps there is no main grid. Depending on the scale used, some maps refer to grids in distances of 10°, 4° or 3° for example. Thus even such important latitudes like 45° did not always appear. In the hexadecimal grid has a clear hierarchy of priorities. Between two gridlines, exactly in the middle, a new gridline can ever be drawed if necessary. This is very useful for zoomings.
• Generally binary map scales are more harmonic and excelsior practical; for example 1:16,384 or 1:65,536 or 1:262,144 etc. For zooming even radix two scales can be employed.
• Beyond doubt, the Earth hemispheres are better divided with one of the four cardinal meridians situated almost in the middle of Bering Strait, the natural Est-West separating line.

Example:
The city of New Orleans, Louisiana is located at 29° 57' 53" N, 90° 04' 14" W. In hexadecimal degrees, this is longitude (always first!)  - J° QB'c and latitude  + P° CJ'x. This can be pronounced: "Nine degrees, one minute and ten sixteenth East of Florence." As well as: "Two hexadecimal degrees, tenty-nine minutes and fourteen sixteenth North of the equator."