Accurate formula expressing the difference between the normal gravity and its radial component

A simple formula is presented giving the value of γ−γ _r to better than 0.001 mgal associated with an arbitrary reference ellipsoid, where γ is the normal gravity and γ _r is its radial component. Further simplifications of this formula are possible, depending on the desired accuracy. Since in the actual field g−g_r equals γ−γ _r to a good approximation, this formula makes it possible to work in terms of g_r rather than in terms of the measured quantity g. Such a choice is attractive mainly because the spherical harmonic expansion of g_r is very simple.