Elongated ellipsoid
When prolonged or prolates ellipsoid a special is spheroid called that by rotating an ellipse about its major axis is formed. Its polar axis is therefore longer than its equatorial diameter. An example of this spindle-like shape is the rugby ball .
The elongated ellipsoid is the counterpart to the flattened ellipsoid , which is the regular shape of the earth and all larger planets. Elongated ellipsoids are of little practical importance, but they are interesting for some aspects of equilibrium and potential theory.
Surprisingly, at the beginning of the 18th century, French degree measurements by Picard , Cassini and Lahire showed that the earth figure was such a body elongated to the pole . But Isaac Newton showed through a thought experiment that the centrifugal force of the earth's rotation must cause the equator to widen. The rapidly rotating Jupiter also has a clearly flattened shape. The false conclusion with the pole diameter being 0.9% too long later turned out to be the result of small systematic measurement errors and an anomaly in the earth's crust .
The issue of "flattened or extended" between the London and Paris academies was finally decided in favor of flattening, which resulted in a 1: 304 figure, only after the French expeditions to Peru and Lapland (1735–1741). The true value determined by satellite geodesy is 1: 298.25.
Due to the influence of tidal friction , two celestial bodies orbiting each other would deform minimally into an elongated ellipsoid. Usually, however, the flattening of the body caused by centrifugal force predominates due to its rotation and runs counter to elongation.
See also
literature
- Karl Ledersteger : Astronomical and Physical Geodesy. (= Jordan-Eggert-Kneissl (Hrsg.): Handbuch der Vermessungskunde. Volume V) JB Metzler, Stuttgart 1969, p. 55 f. (§12, important degree measurement work ).
- Wolfgang Torge : Geodesy . de Gruyter, Berlin 2001, chap. 1.3.2 The Ellipsoidal Earth Model , pp. 7-10.