| The MacCullagh equation (1855) is of key importance in the study of the Earth, describes the
gravity potential outside a bounding sphere of radius R up to the second degree and zeroth
order. It connects the geometrical, and the physical properties of the Earth through the
geodynamical shape factor J2. This second zonal geopotential coefficient is closely
related to the flattening and to the angular spin velocity of the Earth as well as to its
equatorial (A) and polar (C) moments of inertia. Through these moments of inertia the
gravitational potential V is connected to the mass density distribution within the
Earth.
The main target of the present study is to obtain a generalized form of the MacCullagh
equation for even orders n ≈¥ 2 by including the higher order zonal coefficients Jn connected
with the higher (n ≈¥ 2) degree moments of inertia Cn and An. The higher the degree n, the
higher is the weight of the near-surface (i.e. shallow) mass density distribution in Jn. The
second part of this contribution deals with the temporal variations of Jn and dJn/dt . |