The article gives a way to construct the gravity model of the Earth and the geoid. The model is obtained by solving two successive well-posed problems having a unique solution reduced to solving (generalized) Fredholm integral equations of the second kind. The initial data for constructing of the model are the values of the gravity component of the weight force, independent of time, on the surface of a simply connected area containing the Earth body inside itself. The proposed algorithm, unlike most known ones, makes it possible to construct a real geoid, since it automatically takes into account the presence of masses outside of the quasigeoid. The accuracy of the construction of the gravity model in the form of a volumetric Newtonian potential is limited only by the accuracy of field measurements and can be checked at the computation stage, since the values of the density of this potential, corresponding to the values of the average density of the constituent components of the Earth, must be zero outside of the figure of the Earth. The density of atmospheric air is taken into account.