The radial acceleration relation (RAR) of disc galaxies is governed by a single acceleration scale, a₀ ≈ 1. 20×10⁻¹⁰ m s⁻², whose origin has long been an open question. We report a two-input closed-form relation for this scale and a corresponding closed-form RAR law. From the two late-time cosmological parameters (H₀, Ω_Λ) alone we obtain a₀ = c H₀ / (2π Ω_Λ^3/8) = 1. 20055×10⁻¹⁰ m s⁻² at Planck-2018 central values, with no galaxy-level fit parameter; the bare Hubble-temperature scale c H₀/ (2π) undershoots the empirical value by about 13%, and the Ω_Λ^−3/8 factor supplies the missing normalisation. Built on this scale, the closed-form law gₒbs² = gbar² + a₀ gbar · (1 + √ (3/2) ·√ (gbar/a₀) ) · exp −e gbar / (2π Ω_Λ^3/8 a₀) has the correct deep-MOND and Newtonian limits and, with no parameter fitted to galaxy kinematics, matches the SPARC RAR at a level comparable to the standard empirical interpolation under the same fixed baryonic model. On the full SPARC Q=1 sample (93 galaxies, N=2060 radial points, no outlier rejection) it is comparable to the McGaugh interpolation (χ²/N = 44. 84 versus 45. 48 under a common relative-scoring prescription, the difference interpreted descriptively rather than as a calibrated likelihood significance), while a one-parameter free-a₀ fit returns a₀ (free) = 1. 1999×10⁻¹⁰ m s⁻², in 0. 05% agreement with the cosmological prediction. We present these as empirical, falsifiable closed-form relations; the microscopic mechanism behind the Ω_Λ^−3/8, √ (3/2), and e factors is developed in a companion manuscript.
Yunbeom Yi (Sun,) studied this question.
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