Universal Emergent Gravity (Paper IX): Derivation of ν(x) from the Radial Minimum-Energy Ansatz and Confrontation with the Radial Acceleration Relation

Key Points

• Derive the MOND interpolation function ν(x) using the minimum-energy displacement approach from Verlinde's model.
• Utilized the minimum-energy displacement ansatz for radial displacement.
• Derived ν(x) from entropic force principles.
• Confronted findings with the radial acceleration relation (RAR) on 175 SPARC galaxies.
• Derived ν(x) = 1/2 + √(1/4+1/x) from the proposed approach.
• Successfully tested against the RAR for 175 SPARC galaxies, aligning with observed galaxy dynamics.