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GeometricalGeodesy Thomas H. Meyer, Ph.D. Department of Natural Resources Management & Engineering University of Connecticut

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Surveying is… “Measuring distance, angles, heights, etc., to determine the relative locations of points on the Earth” -- NGS Glossary. what you do to make a map applied trigonometry

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Technology 1. Global Positioning System

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Technology 2. Optomechanical

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The job is to collect observations of features to be mapped and thereby determine their coordinates observations are things, such as angles and distances, a surveyor “observed” using an instrument maps are drawn using the coordinates of the features

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Surveying Observables zenith angle

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Surveying Observables, cont. bearings angles in the horizontal plane between features of interest slant distances

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Derived Quantities horizontal distance vertical distance

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bounds metes

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Suppose… you have a properly leveled instrument. you site an object in the distance… at a zenith angle of exactly 90 degrees. Is that object above, below or level to you?

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How do you know the Earth is round?

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The Flat-Earth Assumption causes objects to appear lower and farther away than they really are.

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Is this a practical problem? if a = 6378137 m then a one centimeter error occurs at c = 357.159 m Typical surveying accuracy for a 3500 m line is around one millimeter

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Ok, so far we’ve been using a coordinate system… it’s Cartesian In what reference frame does that coordinate system reside within?

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Geodesy “The science concerned with determining the size and shape of the Earth.” --NGS Glossary

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Why study geodesy?

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With inches to spare…

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going aground in the Panama Canal is bad…

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fender benders…

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Barge-Bridge Collision

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A horizontal geodetic datum.. is a system by which latitude and longitude coordinates are assigned to places of interest i.e., the foundation of spatial coordinates note bene: height is not included

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Surveying on the Sphere To construct and use geodetic datums we must be able to determine latitude and longitude coordinates from surveying observations. That requires spherical trigonometry

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Spherical Triangles

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Our fundamental figure

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Geodetic Coordinates

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Radii of Curvature in Geodesy radius of curvature in the meridian radius of curvature in the prime vertical radius of curvature in the normal section

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Radius of Curvature in the Meridian

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Radius of Curvature in the Prime Vertical

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Normal Section

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Radius of Curvature in the Normal Section

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GeometricalGeodesy Thomas H. Meyer, Ph.D. Department of Natural Resources Management & Engineering University of Connecticut Thomas.meyer@uconn.edu

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