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.The shell theorem could only be proven in a Cavendish setup experiment using identical outer diameter and same weight source masses , one setup with high density material and largest possible spherical hole in source mass and second setup with low density solid source of same weight .( The same diameters and weights solely to "destabilize" calculation handicapped mainstream scientists .

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.The "elliptic" shapes of celestial bodies do not concern me , their diameter and rotation absorb the "sun" given potential energy so orbit (speed and radi ) is diminished ( again in miniscule but calculable amount)

Here an rather old estimation of earth gravitation. Mass ruohgly estimated, disregarding the three body problem ) , next will include sun that after all have a 200 times stronger field on earth than the moon (6*10^-3 to 3*10^5 m/s^2)

Hope capping do not mean banning , just ignore me if the alternative theory is too alternative .