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### (-) 0004 What is the shape of the Earth ?

`The Earths shape and mass - a Historical summary` `The shape of the Earth` `Pythagoras (6th c  B.C.) was perhaps the first to guess the roundness of the Earth. It could be deduced from the observation of ships sailing over the horizon and Anaximenes (585BC) understood why the shadow of the Earth on the Moon during a Lunar eclipse was circular. Also the elevation of the Pole Star increased when travelling north from the equator and was constant if traveling East to West.` `The Greek astronomer Eratosthenes (ca 250 BC) was perhaps the first to actually calculate an approximate circumference from the length of shadows at places separated in latitude. At Syene the Sun was vertically overhead while at Alexandria it was 7deg 12mins from vertical. This meant that the linear distance between Alexandria and Syene was 1/50 of the circumference of the Earth. By measureing that distance (5,000 stadia) he expressed the Earths diameter as  50×5000 = 250,000 stadia. Unfortunatly, the size of a 'stadia' is unknown, however taking it to be the same as the Hellenic 'stadion' (185 meters or 517ft) this gives 25,000 geographical miles which is surprisingly close to the actual circumference of the Earth of 24,902 miles (40,075.16 km) at the equator.` `The globe rotated` `The rotation of the Earth although assumed, was not proved until 1851 when the French physicist Foucault performed an experiment with a pendulum in the Pantheon at Paris. This rotation is also measurable using an idea of Newton, who suggested that a weight dropped from a great height would fall east of the line of projection because the top of the tower would be moving faster. An experiment based on this principal was performed in a 500 ft mine shaft. An average deviation of 1 inch was in line with prediction. ` `The accurate size of the Earth` `This was determined by triangulation of the surface. The Dutchman W. Snell [Snellius] (1591-1626) was a pioneer of this method.  A line between two points in the meridian great circle was measured by geodetic triangulation from a baseline of known length. The length of the baseline was found by very careful measurement. In 1671 Picard invented a wheel with a mechanical counter similar to a modern odometer.  Determining the latitude of the two points by astronomical observation and knowing their distance apart enabled the number of miles in 1 degree to be found, and hence the circumference and diameter. One of the first determinations of  a “triaxial terrestrial ellipsoid” was made by a Russian geodesist F. Schubert in 1859 (Ref-3). Hayford in 1909 determined the shape to be an oblate spheroid  1/297. ` `The Mass of the Earth` `The Earth’s mass is measured by a comparison of the force between two known masses and those masses with the Earth.  The Earth is the only planet whose mass can be measured in a laboratory using Newton’s formula F=GM1M2/d2. The earliest estimate was the “Mountain method” where the deflection of a plumb ` `bob was compared in the close vicinity of a mountain.  Maskelyne used the peak of Schiehallion in Scotland, but the first accurate determination was made by Henry Cavenish in 1797 using a gravity balance.  Von Jolly used the same method in 1881 and obtained 6 x10e24 Kg.` `Distance and mass of the Moon` `The average distance of the moon is found from triangulation using the Earth’s diameter as a baseline.` `Further reading:` `1) General Astronomy - H Spencer Jones (1951)` `2) Introduction to Astronomy - C.Payne-Kaposchkin (1956)` `3) Fundamental Constants of Astronomy  K.A.Kulikov - 1955 (translated 1964)`

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