An illustrative example using the city of Bellingham, Washington, follows. It is apparent that while NAD83 and WGS84 express coordinates that are nearly identical, NAD27 is quite different, because the underlying shape of the earth is expressed differently by the datums and spheroids used.
The longitude is the measurement of the angle from the prime meridian at Greenwich, England, to the center of the earth, then west to the longitude of Bellingham, Washington. The latitude is the measurement of the angle formed from the equator to the center of the earth, then north to the latitude of Bellingham, Washington.
If the surface of the earth at Bellingham is bulged out, the angular measurements in decimal degrees from Greenwich and the equator will become slightly larger. If the surface at Bellingham is lowered, the angles will become slightly smaller. Although the earth is best represented by a spheroid, it is sometimes treated as a sphere to make mathematical calculations easier. The assumption that the earth is a sphere is possible for small-scale maps smaller than ,, At this scale, the difference between a sphere and a spheroid is not detectable on a map.
However, to maintain accuracy for larger-scale maps scales of ,, or larger , a spheroid is necessary to represent the shape of the earth. Between those scales, choosing to use a sphere or spheroid will depend on the map's purpose and the accuracy of the data. A sphere is based on a circle, while a spheroid or ellipsoid is based on an ellipse. The shape of an ellipse is defined by two radii. The longer radius is called the semimajor axis, and the shorter radius is called the semiminor axis.
What do the terms geoid, ellipsoid, spheroid and datum mean, and how are they related? The geoid is defined as the surface of the earth's gravity field, which approximates mean sea level. It is perpendicular to the direction of the force of gravity. Since the mass of the Earth is not uniform at all points, the magnitude of gravity varies, and the shape of the geoid is irregular. The website has links to images showing interpretations of the geoid under North America.
These terms are used interchangeably. For the remainder of this article, the term spheroid will be used.
A spheroid is a three-dimensional shape created from a two-dimensional ellipse. The ellipse is an oval, with a major axis the longer axis , and a minor axis the shorter axis.
If you rotate the ellipse around one of its axes, the shape of the rotated figure is a spheroid. For the earth, the semi-major axis is the radius from the center of the earth to the equator, while the semi-minor axis is the radius from the center of the earth to the pole. A particular spheroid is distinguished from another by the lengths of the semi-major and semi-minor axes.
For example, compare the Clarke spheroid with the GRS spheroid and the WGS spheroid, based on the measurements in meters below. A particular spheroid can be selected for use in a specific geographic area, because that particular spheroid does an exceptionally good job of mimicking the geoid for that part of the world.
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