What question did this study set out to answer?

Derive the MOND interpolation function ν(x) using the minimum-energy displacement approach from Verlinde's model.

June 21, 2026Open Access

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.

Abstract

Derives the MOND interpolation function ν (x) from Verlinde's (2016) elastic medium (Section 4) using the minimum-energy displacement ansatz uᵣ (r) = (u₀/2) (r/rM + rM/r). The entropic force chain yields ν (x) = 1/2 + √ (1/4+1/x). Confronted with the RAR on 175 SPARC galaxies. Addresses two open questions from Papers VI–VIII.

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Cite This Study

Jean Pedinielli (Fri,) studied this question.

synapsesocial.com/papers/6a37813124f042ddf4c5b13f https://doi.org/https://doi.org/10.5281/zenodo.20766318

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