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# The Global Grid Help (page 2)

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By McGraw-Hill Professional
Updated on Oct 3, 2011

## Parallels

For any given angle θ between and including -90° and +90°, there is a set of points on the earth’s surface such that all the points have latitude equal to θ . This set of points is a circle parallel to the equator; for this reason, all such circles are called parallels (Fig. 11-2A). The exceptions are at the extremes θ = -90° and θ = +90°; these correspond to points at the south geographic pole and the north geographic pole, respectively.

Fig. 11-2 (A) Parallels are circles representing points of equal latitude. Such circles are always parallel to the plane containing the equator. (B) Meridians are half-circles representing points of equal longitude. Such half-circles are always arcs of great circles, with their end points at the north and south geographic poles.

The radius of a given parallel depends on the latitude. When θ = 0°, the parallel is the equator, and its radius is equal to the earth’s radius. The earth is not quite a perfect sphere—it is slightly oblate—but it is almost perfect. If we imagine the earth as a perfect sphere with the oblateness averaged out, then we can regard the radius of the earth as equal to 6371 kilometers. That is the radius of the parallel corresponding to θ = 0°. For other values of θ, the radius r (in kilometers) of the parallel can be found according to this formula:

r = 6371 cos θ

The earth’s circumference is approximately 6371 × 2 π, or 4.003 × 10 4 kilometers. Therefore, the circumference k (in kilometers) of the parallel whose latitude is θ can be found using this formula:

k = (4.003 × 10 4 ) cos θ

## Meridians

For any given angle ø such that –180° < ø ≤ + 180°, there is a set of points on the earth’s surface such that all the points have longitude equal to ø . This set of points is a half-circle (not including either of the end points) whose center coincides with the center of the earth, and that intersects the equator at a right angle, as shown in Fig. 11-2B.

Fig. 11-2 (B) Meridians are half-circles representing points of equal longitude. Such half-circles are always arcs of great circles, with their end points at the north and south geographic poles.

All such open half-circles are called meridians. The end points of any meridian, which technically are not part of the meridian, are the south geographic pole and the north geographic pole. (The poles themselves have undefined longitude.)

All meridians have the same radius, which is equal to the radius of the earth, approximately 6371 kilometers. All the meridians converge at the poles. The distance between any particular two meridians, as measured along a particular parallel, depends on the latitude of that parallel. The distance between equal-latitude points on any two meridians ø 1 and ø 2 is greatest at the equator, decreases as the latitude increases negatively or positively, and approaches zero as the latitude approaches -90° or +90°.

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