# Earths form

From the 3rd century BC, when the Greek mathematician Eratosthenes made his measurements, during the nineteen centuries it was believed that the Earths form is a ball. Only in the 17th century it became clear that gravity in Cayenne in French Guiana was different from gravity in Paris. And then Newton suggested that the form Earth Not a perfect ball, but a body flattened at the poles. He proposed the following thought experiment. It is necessary to dig two mines: from the pole to the center of the Earth and from the equator to the center of the Earth. These mines are flooded with water. If the Earth has the shape of a sphere, then the depth of the mines is the same. But the water in the equatorial shaft operates centrifugal force, while the water in the polar mine - no. Therefore, to balance the water in both mines, it is necessary that the equatorial shaft be longer. Further development of the theory of the figure of the Earth was due to the work of Huygens, Cassini, Clairaux, McLauren, d'Alembert, Lagrange, Laplace, Legendre, Jacobi, Dirichlet, Poincare, etc. Over the next 300 years systematic geophysical measurements established that each of the poles at 21 km 470 m closer to the center of the Earth than the equator.

Artificial Earth Satellites opened a new era in geodesy. The analysis of the orbit of the second artificial satellite showed that the shape of the Earth (flattening) at the poles was previously overestimated: the equatorial diameter turned out to be greater than the polar diameter by 42 km 770 m, rather than 42 km 940 m, as previously thought. Satellite geodesy has brought a lot of unexpected and surprising discoveries, of which the most sensational is the pear-shaped nature of the Earth. The South Pole was closer to the center than the North Pole, at 44 m 70 cm. The South Pole is located 25 m 80 cm below the surface of the flattened sphere. The North Pole appears like a cut of a pear on 18 m 90 cm. Let us make a reservation: the described form of the Earth, strictly speaking, is a geometric view of the surface of the World Ocean rather than the Earth. Pear-shapedness of the Earth directly affects only the water surface. Therefore, the largest value of the pear-shaped form of the Earth can have for navigation, but the greatest theoretical significance in cosmology.

In geodesy and astronautics, the shape of the Earth is usually described by an ellipsoid of revolution or a geoid. The system of astronomical coordinates is connected with the geoid, with the ellipsoid of rotation - the system of geodetic coordinates. By definition, a geoid is a surface everywhere normal to gravity. If the Earth were completely covered by the ocean and not subjected to tidal influence of other celestial bodies and other similar perturbations, it would have the form of a geoid. In fact, in different places the surface of the Earth can differ significantly from the geoid. For better approximation of the surface, we introduce the notion of a reference ellipsoid, which coincides well with the geoid only at some part of the surface. The geometric parameters of the reference ellipsoids differ from those of the average terrestrial ellipsoid, which describes the earth's surface as a whole. In practice, several different average terrestrial ellipsoids and associated terrestrial coordinate systems are used.