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The Minkowski metrics relativistic factor and the Schwarzschild metric rescaling factor for the affine Minkowski metric are set in octonian coordinates 0,1,...,7 to a stereographic projection using a projective homogeneous norming and to a nonlinear rescaling of a gravitational compass needle from a barycenter B to a system Q in spiralic rotational motion with an orthogonal projection. The two projection geometries for this can come in both versions using for the rescaling. Most statements of this kind are in this article my contribution coming from nuclear geometry considerations. It stresses the geometrical nuclear reasons for the existence of the two metrics. Einstein makes for gravity GR a curved Riemannian metric computation from which I don’t compute newly for instance the Schwarzschild radius Rs of a mass system in the universe. In mathematics his metric is proved by analysis and an energy momentum tensor computation. It is not coming from an octonian geometry for particles as described here.