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We recently proposed a robust alternative to the particle dark matter hypothesis, the Aether Scalar Tensor (AeST) theory, which can fit cosmological observations without dark matter. In this followup, we explored its predictions for weak-field spherically symmetric sources and found that the gravitational force passes through three distinct phases with increasing distance. We identified transition scales and examined their dependence on the theory parameters. This sets the base for developing N-body simulations for AeST to constrain it with large-scale structure, galaxy dynamics and lensing observations.