Geodesydb - Making Measurements of the Earth, e.g.,...

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Unformatted text preview: Making Measurements of the Earth, e.g., -Locating points -Calculating distances -Determining elevation A systematic referencing scheme is needed systematic (a coordinate system). A fundamental question becomes- what is the shape and size of the earth. size Babylonian map 2500 BP Stick chart from Micronesia depicting waves and currents around islands, which are represented by shells. Early cartographers had little in the way of good information about the absolute location of places, the size of the earth or its real shape (13th century). In Robinson et al. (1995) ld_map_.281402.29 The Flat-out Truth: Earth Orbits? Moon Landings? A Fraud! Copyright 1980 Robert J. Schadewald Reprinted from Science Digest, July 1980 The facts are simple," says Charles K. Johnson, president of the International Flat Earth Research Society. "The earth The is flat." is The earth is not flat. Pythagoras (6th century B.C) taught that humans must live on a body with “perfect shape”– a sphere. Aristotle (4th century B.C.) based idea of spherical earth on observing ships as they disappeared hull-first, mast-last. It was difficult to figure out size, however… Eratosthenes was an early pioneer in earth measurement. Eratosthenes estimated the circumference of the earth. Eratosthenes’ assumptions: Syene is on the Tropic of Cancer and the Sun (23.5oN) went straight down a well at Syene at solstice. Due north at Alexandria (the same meridian), shadows were at 7degrees, 12 minutes. 7°12’ is 1/50 of a circle. He thought the distance from Syene-Alexandria was 500 mi. 500*50 = 25,000 miles vs. 24,900 actual! Dent (1996) Bolstad (2002) Bolstad Eratosthenes was lucky! Cities (Syene and Alexandria) were not due north (i.e. not on the same meridian). Syene is not on the Tropic of Cancer. “Actual” distance between cities is 453 miles, not 500. Multiple sources of error partially compensated for each other. Earth is not a sphere … Early convention held earth as spherical. Newton proposed that a consequence of gravitation would be equatorial bulging due to centrifugal force generated by rotation. In this view the “correct shape” would be an oblate ellipsoid (note that this is not quite right either). Bolstad (2002) Satellite measurements are used to define World Satellite Geodetic System 84 (WGS 84) ellipsoid. Geodetic According to WGS 84: polar flattening is 1/298.257 According But the earth is not perfectly ellipsoidal either. either. Geoid deviates Geoid from the ellipsoid in an irregular manner. manner. Mass is not constant everywhere, therefore, the effect of gravity and rotation would not be constant (the equatorial bulge due to centrifugal force). Dent (1996) Geoid The Datum • A combination of an ellipsoid, which specifies the size and shape of the earth, and a base point from which the latitude and longitude, of all other points are referenced. • Examples are NAD27 and NAD83. • The geoid is a figure that adjusts the best ellipsoid and the variation of gravity locally. How are these shapes used? Maps for large areas can be based on a spheroid to simplify mathematics of map production (e.g., projections). More detailed maps may use ellipsoid. GPS receivers computer latitude, longitude and elevation using WGS 84 ellipsoid. Geoid used for geodetic surveys when very high accuracy is needed. GPS-derived elevations can be adjusted to the geoid by subtracting difference between it and WGS 84. OK, we have a good idea of what the shape and size of the earth is- how do we used this knowledge to construct a used systematic referencing scheme? systematic Location on the sphere or ellipsoid Latitude and Longitude Early motivation- navigation Axis of rotation provides a starting point to develop concepts of location on the sphere. concepts Equator is a plane orthogonal (at a right angle) to the axis of rotation (perpendicular bisector). Dent (1996) Determining latitude (north south reference) is a matter of figuring out how far from the equator you are. One way of doing this has been know for centuries.. estimate the angle between your location and Polaris (North Star). Polaris If this is done systematically, If then we have the beginning of the graticule. Each latitude observation defines a plane that is parallel to the equator, thus the term, parallels of Dent (1996) latitude. latitude. Longitude (east/west reference) is more difficult than latitude. First, need a fixed point of reference, but there is no logical starting point-like the equator for latitude. equator The difficulty of calculating longitude The caused huge losses of life at sea. caused The solution relied on a combination of The science, technology and politics. science, Dent (1996) One solutionOne We know that the earth rotates 360° in in 24 hours – or 15°/hr (360/24 ). 24 Keep track of time difference between Keep fixed point and local time and you can compute the difference in degrees of longitude between that point and your location. location. Determining longitude can be reduced to a “time problem”. Dent (1996) Longitude Calculation Basics 360°/24 hrs = 15°/hr If it’s noon where you are and it is 3pm at a standard fix location (e.g., Greenwich Mean Time (GMT)- the time at the prime meridian), Therefore you are at 45° West longitude (3 hrs*15°) Chronometers kept accurate time so differentials could be computed. Now radio and atomic clocks are used. Early Problem Pendulum clocks at the time they were trying to work this out (early 1700s) didn’t work well on moving (pitching, yawing) ships. The regular swings are disrupted and time is gained or lost in an unpredictable way. Dead Reckoning in the 1600s… Dead Throw overboard a “log” attached to a rope with knots at regular Throw intervals (51 ft) and using an hourglass count the number of hourglass knots in 30 seconds. Three people needed to perform an approximate task. approximate Jupiter? Jupiter is kind of difficult to see during the day and through clouds. Other “astronomical” solutions relied on observing Venus and the Moon. The astronomers had great political clout as well. Clocks were viewed as too mechanical for “real science.” Three delineations of the coast of France. Shaded version is presentThree day. Fine line is from 1679; heavy line is from 1693 when longitude day. was improved by observations of Jupiter’s satellites. was The amount of E-W stretching in this early map is caused, in part, by an inability to accurately specify longitude. accurately October 1707, 21 ships returning to England after a raid hit fog. The flagship sank in 4 minutes after hitting rocks, drowning 650 sailors. Three other ships sank with total loss at 1,647. loss This got the This attention of the British Parliament. British Longitude The British were active in exploration and conquest. They needed to know where their ships were. A contest with a large prize was begun to solve the longitude problem. The Longitude Act Parliament passed the Longitude Act (1714) which promised £20,000 to the person who could solve the longitude problem to an accuracy of half a degree of a great circle. This is approximately 34 miles. 34 Had to be “practicable and useful”. John Harrison devised a solution. An escapement connects the wheels which transmit power and indicate time, and the oscillator which dictates the speed of the clock. With each swing of the pendulum, the escapement allows one tooth to escape and transmit power to maintain pendulum’s motion. This is Harrison’s “grasshopper escapement”. pendulum’s Harrison’s H-1. Harrison’s It is 2 feet tall, took five It years to make and weighs 75 pounds. 75 Harrison could have Harrison won the prize but he was a perfectionist. A sea trial turned up some flaws that he “knew” he could fix (please note that this might be “an urban myth.” myth.” This is H-4 which was accurate enough to win Harrison the prize. It was 5 inches in diameter and weighed only three pounds. It was the culmination of three decades of work. work. In a test it lost only In five seconds after 81 days at sea. 81 John Harrison won his sought after £20,000, but 20,000, only after much effort to overcome the political machinations of his enemies who were committed to astronomical methods. Prime Meridian Lines of longitude are called meridians. Because the Britain ruled the seas at the time and because they were active in geodetic studies the so-called “Prime Meridian” was established to run through the Royal Observatory at Greenwich. Convention dictates. Other countries had their own “primes” however. France’s ran through Paris and Russia’s through Moscow. Iowa City 41° 39' 40" N , 91° 31' 48" W 41° 39' 40" N , -91° 31' 48“ (Actually we would want to convert to decimal degrees) A graticule Horizontal and Vertical Control U.S. is covered by over 200,000 points of precisely known latitude and longitude. Points are roughly 3 to 8 kilometers apart in urban areas and 6 to 25 km apart in rural areas. Location denoted by a survey monument Horizontal Control Networks Triangulation used: if you know one side (base line) and the two adjacent angles you can compute the remaining angle (Σ = 180°) and the two other sides (which define a point at the vertex). Network is built triangle by triangle; each new triangle adds a vertex point to the network. The triangulation gets “densified” as additional legs and angles are added… legs The Wisconsin horizontal control network. The position of each point with respect to neighbors is known to an accuracy of at least 1:100,000 which amounts to approx 1 ft in 19 miles. ft Most are on hill tops Most since clear line-ofsince sight is needed by sight optical equipment... optical Basic idea of Vertical Control is to make precise relative measurements precise This bench mark is for a vertical control point. point. First U.S. base line established near NY-CT border in 1833. NY-CT This network grew and This was densified, and others grew as well. others In 1927 these networks In were “adjusted” and integrated into a single national network with origin at Meades Ranch, KS. KS. North American Datum North of 1927 of NAD 83 The North American Datum of 1983 is an adjustment of NAD 27 that reflects higher accuracy in geodetic surveying. NAD 83 is tied into WGS 84 The “adjustment” from NAD 27 to NAD 83 causes some displacement in locations ...
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