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GeoInformatics-7-2009
article both ends of the arc to measure the central angle. the principle of meridian arc measurements was used with modifications in geodetic observations up to modern times. 2.2 latitude, longitude and time being known at least three centuries bc, the lines of latitude and longitude were by a.d. 150 drawn also in the first world atlas by ptolemy, the ancient scholar with many scientific interests who s millennial fame and influence are mostly the result of his two books, one on astronomy and other on geography. in astronomy, he introduced among other things a simple but invaluable concept of subdividing an arc degree in 60 minutes (lat. partes minutae primae) and then further every minute in 60 seconds (lat. partes minutae secundae). thus, we have minutes and seconds of time and minutes and seconds of arc degrees. in his book geography ptolemy defined geography as a presentation in pictures of the whole known world together with the phenomena which are contained therein , combining data on geolocation and time. he also defined the task of cartographer, which is to survey the whole in just proportions that is, to draw maps to scale. in his maps (figure 4), ptolemy used a grid system of lati- figure 7.the triangulation of france, 1792-1799. the meriditude and longitude lines as a reference an arc stretching from dunkerque in the north to barcelona to geolocate the known items such as in the south was measured along the paris meridian between 1792 and 1799 by french geodesists delambre and lands, coasts, islands and towns on a mechain. based on these measurements the metric system map. longitude was expressed in fracwas defined and introduced first in france and then gradutions of hours while latitudes were desally around the globe. (image courtesy of ken alder, the ignated by the number of hours in the measure of all things) longest day of the year. once again, we come across relating a grid of geolocanatural phenomena to fix it down to the body tions on a map to the measures of time. of earth. ptolemy in his time has decided to the equator as the zero-degree parallel of latput its origin at the western edge of the itude was already known then and fixed from known world through the fortunate (present the laws of nature, i.e. from the observations canary) islands in the atlantic ocean northof the apparent movements of the sun and west of africa. through the centuries, the lonother celestial bodies. the astronomers knew gitude line origin has been moved back and from astronomic observations, that during the forth across the maps almost at the free will year the sun is crossing the celestial equator of later cartographers, until it finally settled twice a year on its way between the two in greenwich, uk by an international political extreme lines, where it turned around again agreement. namely, only in 1884 a conference on its yearly path. the celestial equator is an in washington of 25 world nations agreed that imaginary line, dividing the celestial sphere greenwich would be the world's prime in half, and the sun s path intersects this meridian of longitude, world time and time equator on the beginning of spring and zones. autumn, marking the vernal and autumnal equinox. two imaginary extreme lines are 2.3 from the spherical to the known as tropics, positioned at the latitudes ellipsoidal earth approximately 23.5 degrees north and south with latitude and longitude the principles of of the equator. on the other hand, the zeromapping the world were organized using a degree longitude meridian line has no such october/november 2009 figure 6. portrait of sir isaac newton (1642-1727) painted in 1689. he was a mathematician and physicist, one of the foremost scientific intellects of all time. newton identified gravitation as the fundamental force controlling the motions of the celestial bodies. in his work mathematical principles of natural philosophy, known as the principia, he developed the mathematics of orbital motion round centres of force. waters at high noon on the longest day of the year, the summer solstice on june 21, while in alexandria which lied approximately north of syene, no such event had ever been seen. instead, in alexandria the sun s rays on the same day formed an angle with the direction of the plumb line. from the length of the shadow of a vertical staff produced in a hemispherical shell, eratosthenes determined the angle as approximately 1/50 of a complete circle. this angle is equal to the central angle between these two places, as if measured from the centre of a spherical earth. eratosthenes applied the then estimated distance of 5000 stadia between alexandria and syene to provide the circumference of the earth as 252000 stadia. eratosthenes used the stade iii = 158.73 m as the unit of length. calculating in metric units the measurements of eratosthenes give a result of 40000km for the circumference of the earth and consequently the result of 6365 km for the radius of the earth ( = 252000/2 = 40100 stadia = 6365 km). this value is differing minimally from the radius 6371 km of the mean spherical earth as derived with wgs 84 ellipsoid, which represents the best global geodetic reference system for the earth available at this time for practical applications of mapping, charting, geopositioning and navigation. the principle that eratosthenes has used is the measurement of the meridian arc in which he used the same specific moment in time on latest news? visit www.geoinformatics.com 47
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