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GEOG 268: Cartography. Ohio Northern University Winter 2001-2002 Hill 200. Geodesy. Mapping involves determining locations on earth, transforming positions onto flat map, graphically symbolizing those positions

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GEOG 268: Cartography

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GEOG 268: Cartography

Ohio Northern University

Winter 2001-2002

Hill 200

Geodesy

• Mapping involves

• determining locations on earth,

• transforming positions onto flat map,

• graphically symbolizing those positions

• Geographic locations determined by geographic coordinates  Latitude and Longitude

• to establish a system of geographic coordinates, we first have to know the Earth’s size and shape

Designing base map & overlay

• Generalizing process:

• Selection

• Classification: process in which objects are placed in groups with similar features

• Simplification: smoothing natural lines

• Symbolization:

• replicative, or

• abstract

• where do we start?

Size and Shape of the Earth

• The development of a base map begins from a small model of the real earth.

• Cartographer needs knowledge of earth’s geographic grid as shown on perfect sphere to create projection

• Today?: irregular surface approximating an ellipsoid

Geodesy

• Earth is very smooth geometrical figure

• smoother than a bowling ball !

• Cartography begins with approximating the Earth’s size and shape:

• increasingly accurate approximations of Earth’s shape:

• sphere

• ellipsoid

• geoid

Geodesy

• Earth’s shape?

• Pythagoras (6th century BC), and

• Aristotle  round Earth (sailing ships)

• Earth’s size?

• Eratosthenes (250 BC):

• Deep well in Aswan, sun overhead Solstice

• Next solstice: angle of sun Alexandria

• Circumference? 28,750 mi. (15% more)

• Real circumference? ~ 24,000 miles

Spherical Earth

• Earth not perfect sphere but ellipsoidal

• cartographers use sphere with same surface area as ellipsoid:

• authalic sphere: basic figure for mapping

• 3,959 mi. standard radius (WGS 84 ellipsoid)

Ellipsoidal Earth

• Until 1670s, Earth perfect sphere

• Newton: gravity causes flattening at poles

• amount ~ 1/300th polar radius vs eq. Radius

• satellite measurements = 1/298

• 3D fig. oblate ellipsoid (or oblate spheroid)

• at least 11 different values used worldwide based on location.

• Example: WGS 84 & GRS80 satellites

• Example: Clarke 1866 ground observations

Geoidal Earth

• Even more accurate figure of the earth:

• Geoid (earth-like)

• 3D “equipotential” surface (mean sea level)

• gravity everywhere = mean sea level gravity

• geoid shape - irregular surface features

• geoid deviates from ellipsoid because of

• rock density & topography

• deviates up to 300 ft. in certain places

Cartographic use of Sphere, Ellipsoid, Geoid

• All 3 are different approximations of the Earth’s surface

• Authalic sphere used as reference surface for small scale maps

• Ellipsoid used as a ref. for large scale mapping

• distances, directions and areas would be more correct at individual locations than sphere

• GPS compute lat/long and elevation using WGS 84 ellipsoid as reference surface

• Geoid

• length of degree varies from equator to poles

• used for local large scale ground based surveys