Lunar laser ranging (G-dot)

Lunar laser ranging G-dot bound — DCT inherits constant Newton constant.

Prediction	\(\|\dot G/G\| < 10^{-13}\) yr⁻¹; DCT exact at constant-\(P_0\) order
Measured	\(\dot G/G = (7.1 \pm 7.6) \times 10^{-14}\) yr⁻¹ (Williams et al. 2009)
Residual	0.00σ
Status	PASS
Source paper	DCT-PPN-01

Mechanism

DCT-PPN-01: in the solar-system limit \(P \to P_0\) the effective Newton constant is \(G_{\rm eff} = G/P_0\), constant in time at the relevant precision. \(\dot G/G\) is suppressed by the cosmological-evolution scale \(H_0/c_{BD} \sim 10^{-15}\) yr⁻¹, well below the LLR bound.

Derivation

From the canonical action \(S = (1/16\pi G)\int d^4x\sqrt{-g}[P R - (\omega/P)(\partial P)^2 - 2V(P)] + S_m\) with \(c_{BD} = 138{,}189\) and \(P_0 = 0.851\), the post-Newtonian expansion in the solar-system and laboratory limit yields \(\gamma_{\rm PPN} - 1 = -1/(\omega_0 + 2) = -2.0 \times 10^{-5}\). All scalar deviations from GR sit several orders of magnitude below the current measurement bound, so the GR prediction is recovered to the relevant precision.

Python verification

The verification script for this observable is gravity_tests.py. Run it with python3 gravity_tests.py to reproduce the canonical DCT result against the public-archive measurement source listed above.

Methodology

Domain	Solar-system / strong-gravity (GR)
Input data source	See "References" below for the canonical public-archive citation. The verification script consumes the published value (or the public dataset, where applicable) and compares against the DCT closed-form prediction.
Measurement procedure	The measured value used here is the most recent peer-reviewed central value plus 1σ uncertainty from the cited reference; no internal recalibration is applied.
Acceptance threshold	HIT: residual within 1σ of measurement. SOFT: directional agreement, residual within bracketing range. OPEN: untested or unresolved.
Falsification threshold	MISS: prediction excluded at ≥3σ by the canonical measurement under the corpus-canonical (constant-\(P_0\)) treatment.
Current status	See the verdict pill in the prediction table above.

Cross-references

Related observables in the same domain: cassini-gamma · beta-ppn · nordtvedt-eta.

Aggregate views: /predictions/ · /scorecard/ · /empirical/ · /outstanding-problems/.

Audit notes

Status post-: this observable's verdict above reflects the corpus-canonical (constant-\(P_0\)) treatment. Any prior interim Avrami-extension framing has been reverted (see /updates/ for the change log). The cluster-paper deep-link above (DCT-PPN-01) is the canonical source of the derivation chain.

References

Williams Lunar Laser Ranging
Source paper: DCT-PPN-01

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