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1. Definition

2D position reference is not limited to a flat plane. Geographic coordinates, latitude and longitude, have been used for centuries as an absolute positioning system. Sea bound navigators used flat paper maps which were plotted using latitude and longitude.

Assuming the Earth is a sphere, geographic coordinates are angular values with their verticies at the Earth's center, Figure B-1

Figure B-1
Geographic Coordinates

As long as the directional suffixes are included, geographic coordinates are non-ambiguous.


2. Drawbacks?

Geographic coordinates are simple, but they do have some disadvantages.

a. Spherical trigonometry

(1) Distances

Distances between points are arcs, Figure B-2. Their lengths are angular and must be determined using spherical trigonometry.

Figure B-2
Arc Distance

Survey distances are measured in linear units so another computational layer is added to make them work with geographic coordinates

(2) Angle Conditions

Multi-sided figures have curved sides and the Σ (interior angles)=(n-2)x180° angle condition does not apply, For example, the interior angle sum of triangle CDE in Figure B-3 can exceed 180°00'00".

Figure B-3
Spherical Triangle

The amount by which the angle condition is exceeded is called spherical excess and accumulates at approximately 0°00'01" per 70 square miles of enclosed area.

b. Meridian convergence

(1) Directions

Meridians are parallel at the equator and converge to a point at the poles, Figure B-4 

Figure B-4
Convergence
Figure B-5
Length Variation

c. The earth isn't round

Geographic coordinates are based on a sphere. Unfortunately the Earth is not spherical. A different geometric model is needed which complicates things. We still use latitude and longitude positions, but their geodetic counterparts, not geographic. This may seem a trifling difference, but it isn't, and will be covered in a subsequent chapter.

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