Newton’s law of universal gravitation in ocean dynamics

Oceanographers simplify the Newton’s law of universal gravitation, treat the solid Earth as a point mass located at the Earth’s center, and call it the “gravitational force”. Combination of such defined “gravitational force” with the centrifugal force leads to the effective gravity ( g eff ). This simplification is not feasible because the mass distribution inside the solid Earth is nonuniform. The solid Earth cannot be treated as a point mass. The true gravitational force is the volume integration over all the point masses inside the solid Earth on the point mass in oceans. It leads to the true gravity g . The gravity disturbance vector, δ g  =  g – g eff , is a major variable in geodesy and quantified by gravity models with observations. On the contrary, δ g is totally neglected in oceanography. After replacement of g eff by g (i.e., including δ g ) in ocean dynamics, new hydrostatic balance, geostrophic balance, thermal wind relation, 1½ layer model with rigid lid, and combined Sverdrup-Stommel-Munk equation are obtained in the effective-geopotential coordinates. Depth dependent nondimensional D -number and depth independent ( B , F 1 , F 2 ) numbers are defined to identify the importance of gravity disturbance vector versus the traditional forcing terms in the thermal wind relation, 1½ layer model, and combined Sverdrup-Stommel-Munk equation, and calculated from three publicly available datasets in climatological, geodetic, and oceanographic communities. Their evidently non-small values demonstrate the urgency to replace g eff by g in ocean dynamics.