History of geodesy
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- See also the main article on geodesy.
Man has been concerned about the Earth on which he lives for many centuries. During very early times this concern was limited, naturally, to the immediate vicinity of his home; later it expanded to the distance of markets or exchange places; and finally, with the development of means of transportation man became interested in his whole world. Much of this early "world interest" was evidenced by speculation concerning the size, shape, and composition of the Earth.
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[edit] Early concepts of the figure of the Earth
Primitive ideas about the figure of the Earth, still found in young children, hold the Earth to be flat, and the heavens a physical dome spanning over it. Lunar eclipses, e.g., always have a circular edge of approx. three times the radius of the lunar disc; as these always happen when the Earth is between Sun and Moon, it suggests that the object casting the shadow is the Earth and must be spherical (and four times the size of the Moon, the lunar and solar discs being the same size). Also an astronomical event like a lunar eclipse which happened high in the sky in one end of the Mediterranean world, was close to the horizon in the other end, again suggesting curvature of the Earth's surface.
[edit] Classical Greece
The early Greeks, in their speculation and theorizing, ranged from the flat disc advocated by Homer to the spherical body postulated by Pythagoras — an idea supported one hundred years later by Aristotle. Pythagoras was a mathematician and to him the most perfect figure was a sphere. He reasoned that the gods would create a perfect figure and therefore the earth was created to be spherical in shape. Anaximenes, an early Greek scientist, believed strongly that the earth was rectangular in shape.
Since the spherical shape was the most widely supported during the Greek Era, efforts to determine its size followed. Plato determined the circumference of the earth to be 40,000 miles while Archimedes estimated 30,000 miles. Plato's figure was a guess and Archimedes' a more conservative approximation. Meanwhile, in Egypt, a Greek scholar and philosopher, Eratosthenes, set out to make more explicit measurements.
He had observed that on the day of the summer solstice, the midday sun shone to the bottom of a well in the town of Syene (Aswan). Figure 1. At the same time, he observed the sun was not directly overhead at Alexandria; instead, it cast a shadow with the vertical equal to 1/50th of a circle (7° 12'). To these observations, Eratosthenes applied certain "known" facts (1) that on the day of the summer solstice, the midday sun was directly over the line of the summer Tropic Zone (Tropic of Cancer) - Syene was therefore concluded to be on this line; (2) Alexandria and Syene lay on a direct north-south line. Legend has it that he had someone walk from Alexandria to Syene to measure the distance: that came out to be equal to 500 miles.
From these observations, measurements, and "known" facts, Eratosthenes concluded that, since the angular deviation of the sun from the vertical direction at Alexandria was also the angle of the subtended arc, the linear distance between Alexandria and Syene was 1/50 of the circumference of the Earth or 50 x 500 = 25,000 miles. The circumference of the Earth over the poles is 40000 km by definition, i.e. 24855 statute miles. The actual unit of measure used by Eratosthenes was called the "stadion" (see Ancient Greek units of measurement). No one knows for sure what the stadion that he used is in today's units. The measurements given above in miles were derived using one stadion equal to one-tenth statute mile.
It is remarkable that such accuracy was obtained. His measurements had these inaccuracies: (1) although it is true that the sun at noon is directly overhead at the Tropic of Cancer on the day of the summer solstice, Syene is not exactly on the tropic of Cancer but 37 miles to the north; (2) the true distance between Alexandria and Syene is somewhat smaller than Eratosthenes had measured (453 miles instead of the reported 500); (3) Syene lies 3° 30' east of the meridian of Alexandria; (4) the difference of latitude between Alexandria and Syene is 7° 5' rather than the rounded (1/50 of a circle) value of 7° 12' that Eratosthenes obtained.
Another ancient measurement of the size of the earth was made by the Greek, Posidonius. He noted that the star Canopus was hidden from view in most parts of Greece but that it just grazed the horizon at Rhodes. Posidonius measured the elevation of Canopus at Alexandria and determined that the angle was 1/48th of circle. Assuming the distance from Alexandria to Rhodes to be 500 miles, he computed the circumference of the earth as 24,000 miles. While both his measurements were approximations when combined, one error compensated for another and he achieved a fairly accurate result.
[edit] Ancient India
The great Indian mathematician Aryabhata (476 - 550 AD) was a pioneer of mathematical astronomy. He describes the earth as being spherical and that it rotates on its axis, among other things in his work Aryabhatia. Aryabhatiya is divided into four sections. Gitika,Ganitha (mathematics), Kalakriya (reckoning of time) and Gola (celestial sphere). The discovery that the earth rotates on its own axis from west to east is described in Aryabhatiya ( Gitika 3,6; Kalakriya 5; Gola 9,10;) [1]. For example he explained the apparent motion of heavenly bodies is only an illusion (Gola 9), with the following simile;
- Just as a passenger in a boat moving downstream sees the stationary (trees on the river banks) as traversing upstream, so does an observer on earth see the fixed stars as movin g towards the west at exactly the same speed (at which the earth moves from west to east.
Aryabhatiya also estimates the circumfurence of Earth which is accurate to 1%, which is remarkable. Aryabhata gives the radius of planets in terms of the Earth-Sun distance as essentially their periods of rotation around the Sun. He also gave the correct explanation of lunar and solar eclipses and that the Moon shines by reflecting sunlight [2].
[edit] The Middle Ages
Revising the figures of Posidonius, another Greek philosopher determined 18,000 miles as the earth's circumference. This last figure was promulgated by Ptolemy through his world maps. The maps of Ptolemy strongly influenced the cartographers of the Middle Ages. It is probable that Christopher Columbus, using such maps, was led to believe that Asia was only 3 or 4 thousand miles west of Europe. It was not until the 15th century that his concept of the earth's size was revised. During that period the Flemish cartographer, Mercator, made successive reductions in the size of the Mediterranean Sea and all of Europe which had the effect of increasing the size of the earth.
[edit] Scientific revolution
The invention of the telescope and the theodolite and the development of logarithm tables allowed exact triangulation and grade measurement.
Jean Picard performed the first modern arc measurement. He measured a base line by the aid of wooden rods, used a telescope in his angle measurements, and computed with logarithms. Jacques Cassini later continued Picard's arc northward to Dunkirk and southward to the Spanish boundary. Cassini divided the measured arc into two parts, one northward from Paris, another southward. When he computed the length of a degree from both chains, he found that the length of one degree in the northern part of the chain was shorter than that in the southern part. Figure 2.
This result, if correct, meant that the earth was not a sphere, but an oblong (egg-shaped) ellipsoid -- which contradicted the computations by Isaac Newton and Christiaan Huygens. Newton's theory of gravitation predicted the Earth to be an oblate ellipsoid flattened at the poles to a ratio of 1:230.
The issue could be settled by measuring, for a number of points on earth, the relationship between their distance (in north-south direction) and the angles between their astronomical verticals (the projection of the vertical direction on the sky). On an oblate Earth the distance corresponding to one degree would grow toward the poles.
The French Academy of Sciences dispatched two expeditions. One expedition under Pierre Louis Maupertuis (1736-37) was sent to Lapland (as far North as possible). The second mission under Pierre Bouguer was sent to Peru, near the equator (1735-44).
The measurements conclusively showed that the earth was oblate, with a ratio of 1:210. Thus the next approximation to the true figure of the Earth after the sphere became the oblong ellipsoid of revolution.
In South America Bouguer noticed, as did George Everest in India, that the astronomical vertical tended to be "pulled" in the direction of large mountain ranges, obviously due to the gravitational attraction of these huge piles of rock. As this vertical is everywhere perpendicular to the idealized surface of mean sea level, or the geoid, this means that the figure of the Earth is even more irregular than an ellipsoid of revolution. Thus the study of the "undulations of the geoid" became the next great undertaking in the science of studying the figure of the Earth.
[edit] 19th century
In the late 19th century the Zentralbüro für die Internationale Erdmessung (that is, Central Bureau for International Geodesy) was established by Austria-Hungary and Germany. One of its most important goals was the derivation of an international ellipsoid and a gravity formula which should be optimal not only for Europe but also for the whole world. The Zentralbüro was an early predecessor of the International Association for Geodesy (IAG) and the International Union of Geodesy and Geophysics (IUGG) which was founded in 1919.
Most of the relevant theories were derived by the German geodesist F.R. Helmert in his famous books Die mathematischen und physikalischen Theorien der höheren Geodäsie (1880). Helmert also derived the first global ellipsoid in 1906 with an accuracy of 100 meters (0.002 percent of the Earth's radii). The US geodesist Hayford derived a global ellipsoid in ~1910, based on intercontinental isostasy and an accuracy of 200 m. It was adopted by the IUGG as "international ellipsoid 1924".
[edit] See also
- J.L. Greenberg: The problem of the Earth's shape from Newton to Clairaut: the rise of mathematical science in eighteenth-century Paris and the fall of "normal" science. Cambridge : Cambridge University Press, 1995 ISBN 0-521-38541-5
- M.R. Hoare: Quest for the true figure of the Earth: ideas and expeditions in four centuries of geodesy. Burlington, VT: Ashgate, 2004 ISBN 0-7546-5020-0
[edit] About this article
An early version of this article was taken from the public domain source at http://www.ngs.noaa.gov/PUBS_LIB/Geodesy4Layman/TR80003A.HTM#ZZ4 -- please update as necessary.
The next article in this series is mirrored in figure of the Earth.
