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I've just read here that:
How correct is that information and what exactly are Equatorial radius and Polar radius with diagram if possible? |
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As to, how do we know? Originally we sent teams of (mostly French) madmen to measure the distance on the ground between two distant mountain tops near the equator, in the jungles of south America, and then the same thing between places in the arctic. They then measured the angular distance between the points by making astronomical measurements of star positions. By comparing the circumference (ground distance) and the arc (angle distance) you get the radius of the Earth at that point. These expeditions took many years and generally because of the difficulties of making the precise distance measurements - were inconclusive. Now we just use gps and radio telescopes to make amazingly accurate geoid maps. |
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The shape of the earth is called a Geoid.
Read here: http://www.esri.com/news/arcuser/0703/geoid1of3.html |
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Most interesting question, since it can be discussed from several different points of view which are fascinating in themselves. If you know actual shape of Earth that you need only to measure parameters which define the geometrical figure. For perfect sphere there is the only parameter - the radius. In principle you can drill a hole into Earth and measure how deep it is, but neglecting the practical difficulties (the deepest drill has some 12 kilometers) how can you be sure you hit the center of the sphere? In practice you would measure circumference of the globe and then compute the radius. Less direct approach (chosen by Eratoshtenes and others) is to measure part of a meridian. This brings another problem - how you know which part of the entire circumference you measured, solved by measurements of geographical latitude. This relies on astronomical measurements - in principle you measure distance of stars from zenith. Since zenith is defined by direction of local gravitational force the results depend also on distribution of mass in the sphere, not only on its shape. If you release the condition of the perfect shere the next shape is a flattened ellipsoid (Earth is reasonably supposed to be flattened by its rotation). Than you don't have polar or equatorial radius but semiaxes but still you can go along a meridian and the equator and measure their length or length of their parts. In fact the shape of Earth is more complicated. General shape of the solid surface (or equipotential surfaces given by distribution of mass and amount of rotation) can be derived from observation made by external observer (a satellite) or - in principle - by measurements made only within the 2D surface along recipes given by Gauss and Riemann in other context. Strictly speaking (to a non euclidean geometer) there are no parallels on Earth. In fact I am little confused that non euclidean geometry - given that spherical Earth was on our mental eyes so long - was first discovered for hyperbolic surfaces. |
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