Previous |  Up |  Next


This paper deals with the general derivation of Pizzetti-Somigliana's formula for the decomposition of gravity. The problem of derivation is solved formally geometrically on the equipotential surface $S$ that need not be the oblate ellipsoid of rotation. In individual cases of confocal systems of quadrics, the introduction of hyperbolic and circular functions in the equations of tri-orthogonal system is motivated. It is indicated that the validity of the formula may be formally generalized also to other quadrics of rotation.
[1] C. F. Baeschlin: Lehrbuch der Geodäsie. Zürich 1948. Zbl 0040.38701
[2] H. П. Грушинский: Теория фигуры земли. Москва 1968. Zbl 1171.62301
[3] W. A. Heiskanen H. Moritz: Physical Geodesy. San Francisco and London 1967.
[4] V. Hlavatý: Diferenciální geometrie křivek a ploch. Praha 1937.
[5] E. Kamke: Differentialgleichungen, Lösungsmethoden und Lösungen. Leipzig 1956. Zbl 0073.07802
[6] J. Lense: Kugelfunktionen. Leipzig 1950. MR 0040486 | Zbl 0038.22202
[7] M. С. Молоденский В. Ф. Еремеев M. И. Юркина: Методы изучения внешнего гравитационного поля и фигуры земли. Tp. ЦНИИГАиК, вып. 131, Москва 1960. Zbl 1225.94001
[8] P. Pizzetti: Principi della teoria meccanica della figura dei pieneti. Pisa 1913.
[9] С. Somigliana: Teoria generale del campo gravitazionale dell'ellissoide di rotazione. M. della S. astr 1., Tom 4, 1929.
Partner of
EuDML logo