The shape of Planet Earth
Professor Etienne Ghys of the Unité de Mathématiques Pures et Appliquées de l'E.N.S. de Lyon gave a presentation in October 2006 to an audience of geologists on the historical mathematical approaches to determining the theoretical shape of the Earth. Professor Ghys and myself collaborated to produce the graphics for this presentation. The page below is a result of this collaboration.
All images and films copyright Jos Leys/Etienne Ghys. Films and images were made using Povray.
This page is also available in Romanian/Pagina aceasta de asemenea este disponibilă în limba română..
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1. Introduction
The shape of the Earth has intrigued scientists throughout history. The general acceptance of the fact that the Earth is round came about in the first century A.D., although Pythagoras had already postulated a spherical Earth 600 years earlier. The flat Earth concept resurfaced now and again in the Middle Ages, sometimes on religous grounds, but it is safe to say that mankind has known for 2000 years that we live on a sphere.
We know also that it is not a perfect sphere: the diameter from pole to pole is shorter than the diameter at the equator. The difference is small: the equatorial diameter is about 12,700 kilometers, and the pole to pole diameter is only about 40 km shorter.
The reason for this difference is the Earth's rotation, wich creates a centrifugal force perpendicular to the rotation axis. If the Earth consisted of solid material, then there would be no effect on the shape. Suppose the Earth was like a solid billiard ball. The rotation would put a strain on the material but there would be no deformation. Our Earth has a molten interior, it has tectonic plates on the thin crust that can move slowly, and so it is certainly not a solid ball. The Earth is "viscous" and this accounts for the slight flattening at the poles.
Because of the rotation, the Earth has an angular momentum, L. One can look at the Earth as a huge flywheel. The energy stored in a rotating mass is L*ω/2, where ω is the rotation speed of 2π radians per day. The value for L is 5.86.1033 kJoule.sec. To put this in perspective: if we could harness the rotational energy of the Earth, then it would take 5.108 years to use it all up. (at the current worldwide energy use of 10,000 million tonnes of oil equivalent per year). The snag is that in 500 million years, the Earth would stand still!
We will be discussing what happens if the value of L changes, so keep in mind the colossal scale of the energy associated with the Earth's rotation.
The theoretical shape of the Earth has been studied by mathematicians over the past 4 centuries (although the interest has waned the last 40 years or so). The list of people who have contributed to this topic sounds like an all-time hall of fame of mathematicians: Newton (1689), Huygens (1690), Cassini (1701), Maupertuis (1732), Clairaut (1733), Euler (1740), MacLaurin (1742), D'Alembert (1756), Lagrange (1759), Laplace (1772), Legendre (1784), Monge (1787), Poisson (1811), Gauss (1813), Cauchy (1815), Jacobi (1834), Dirichlet (1857), Dedekind (1860), Riemann (1860), Poincaré (1885), Darwin (1906, the son of Charles Darwin), Jeans (1917), Cartan (1924), Chandrasekhar (1960), and others.
It was Isaac Newton who first claimed that the Earth is not spherical, but "oval". Newton imagined two wells going down to the center of the Earth: one drilled from the North Pole, and one drilled from the equator, both filled with water. The water in the equatorial well is subject to the centrifugal force, and the water in the Polar well is not. For the two columns of water to be in equilibrium, it follows that the equatorial well must be longer..
In what follows we will discuss the theoretical shapes the Earth could take at a higher angular momentum, through the milestone discoveries of Colin MacLaurin, Carl Jacobi, and Henri Poincaré.
Clicking the image above will bring up a film of the Earth as we all know it, only it turns about 800 times faster than it does in reality (otherwise the film would have to last for 24 hours for one full turn). In all the films on this page, rotation speed is the only item that has been scaled. The dimensions have been calculated with exact formulas.
This is a small part of a very big Article.
This article, pictures, Video are copy right protected, please don’t copy or Alter anything of this. Our attempt is to discuss on the subject, we will keep discussing in the light of Quran. We repeat, we are here to discuss on Article, our intention in any way not to copy. This Scientific huge article is located here:
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[Holy Quran, 020:053]
"He Who has, made for you the earth like a carpet spread out; has enabled you to go about therein by roads (and channels); and has sent down water from the sky." With it have We produced diverse pairs of plants each separate from the others.
[Holy Quran, 79 : 30] And the earth, moreover, hath He extended (to a wide expanse);
Transliteration : Waalarda baAAda thalika dahaha
Allah Almighty used the word "dahaha" in Noble Verse 79:30, it's because the word is the most precise out of all. It describes the roundness and the flatness of the earth at once.
FROM THE ABOVE ARTICLE:
Our Earth has a molten interior, it has tectonic plates on the thin crust that can move slowly, and so it is CERTAINLY NOT a solid ball. The Earth is "viscous" and this accounts for the slight FLATTENING at the poles.
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Mrs.Omairah Mohammed Altao
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