Open AccessThe relative variation of the vertical gravity gradient on the level ellipsoid
Author(s) -
Bocchio Franco
Publication year - 1995
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1995.tb05734.x
Subject(s) - flattening , geopotential , ellipsoid , geodesy , variation (astronomy) , mathematics , geometry , geology , gravitational field , mathematical analysis , physics , classical mechanics , astrophysics , astronomy
Summary The relative variation of the vertical gravity gradient on an equipotential ellipsoid is given as a function of the geometrical flattening f of the ellipsoid and of the rotational parameter m up to the second order in the quantities f and m. General formulae are also obtained for the relative variation of vertical derivatives of the geopotential with differentiation order higher than two; it is seen that particularly simple first‐order formulae are obtained. A possible application of the concept of ‘flattening’ of the vertical derivatives of the geopotential is also suggested.