## A NEW PERSPECTIVE FOR PHYSICAL HEIGHTS IN BRAZIL

Abstract The physical heights definition of heights, proposed by Helmert in 1890 is one of the commonly used heights systems in practice. In Helmert’s definition, the mean value of gravity along plumbline is computed by simplifying the topography with a Bouguer shell containing masses with mean density value. Although this approximation might be accurate enough many purposes, a more rigorous definition can be determined by considering the effects of terrain, topographic mass density variation, and masses contained in the geoid the mean gravity value along the plumbline. The purpose of this paper is to compute the corrections for the Helmert’s definition of the orthometric heights to obtain the rigorous orthometric heights in the state of São Paulo and adjacent states and to evaluate these corrections. The heights system used in Brazil (until July 2018) and some South American countries is normal-orthometric heights, therefore the corrections needs to be applied accordingly. Our numerical results show that there are significant differences between the normal-orthometric and rigorous orthometric heights, with maximum values of ~ 0.4 m, minimum of ~ -0.8 m and mean value of ~ -0.32 m. There are larger differences between normal-orthometric and normal height than the ones between normal and rigorous definition of orthometric heights.