  Geodesic orbit equations in the Schwarzschild geometry of general relativity
reduce to ordinary conic sections of Newtonian mechanics and gravity for
material particles in the non-relativistic limit. On the contrary, geodesic
orbit equations for a proper spatial submanifold of Schwarzschild metric at any
given coordinate-time correspond to an unphysical gravitational repulsion in
the non-relativistic limit. This demonstrates at a basic level the centrality
and critical role of relativistic time and its intimate pseudo-Riemannian
connection with space. Correspondingly, a commonly popularized depiction of
geodesic orbits of planets as resulting from the curvature of space produced by
the sun, represented as a rubber sheet dipped in the middle by the weighing of
that massive body, is mistaken and misleading for the essence of relativity,
even in the non-relativistic limit.
