No need. Celestial mechanics works remarkably well using Newtonian gravity. Including for orbiting Earth satellites residing in an r/R regime where your idea of how to add elemental contributions, predicts strong departure from strictly 1/r^2 gravity. Overwhelming evidence is 1/r^2 Newtonian gravity accounts very well for all such orbital motions. For all values of r/R > 1. In agreement with shell theorem. Can you cite a single article where some appreciable discrepancy has ever been reported? Don't you think NASA or ESA etc. would have discovered any such many decades ago? This has started to go in circles. Either you are prepared to accept the basic maths leading inevitably to the shell theorem and it's corroboration in every space program and more, or you will continue holding to a pov that never gains any traction.