Audit: Solar System Consistency of ISL Gravity

Date: January 5, 2026
Subject: Compliance of ISL Gravitational Correction with Planetary Ephemeris.

1. The Correction Model

The ISL potential is defined as:

$\Phi_{ISL}(r) = -\frac{GM}{r} + \frac{GM}{r_{mod}} \ln\left(\frac{r}{r_0}\right)$

This leads to a radial acceleration:

$a_{ISL}(r) = \frac{GM}{r^2} \left( 1 + \frac{r}{r_{mod}} \right) = a_N + \delta a$

where $\delta a = \frac{GM}{r \cdot r_{mod}}$ .

2. Evaluation at Solar System Scales

We use the fitted value for the Universal Modularity Radius: $r_{mod} \approx 13.27$ kpc $\approx 4.09 \times 10^{17}$ meters.

2.1 Saturn (r ≈ 9.5 AU)

$r \approx 1.4 \times 10^{12}$ m

$\delta a / a_N \approx r/r_{mod} \approx 3.4 \times 10^{-6}$

Absolute correction $\delta a \approx 2 \times 10^{-14}$ m/s².

2.2 Pluto (r ≈ 40 AU)

$r \approx 6 \times 10^{12}$ m

$\delta a / a_N \approx 1.4 \times 10^{-5}$

Absolute correction $\delta a \approx 5.5 \times 10^{-14}$ m/s².

3. Comparison with Observational Thresholds

Pioneer Anomaly: $a_P \approx (8.74 \pm 1.33) \times 10^{-10}$ m/s².

Ephemeris Precision (INPOP/EPM): Sensitivities to anomalous accelerations are currently at the $\sim 10^{-11}$ to $10^{-12}$ m/s² level.

Conclusion: The ISL correction at solar system scales is 3 to 4 orders of magnitude smaller than current detection thresholds. The theory is perfectly compatible with all known solar system gravitational tests.

4. PPN Parameter Equivalence

While ISL is not a metric theory in the traditional GR sense, the logarithmic term translates to a formal deviation in the $\gamma$ parameter at the level of $\sim 10^{-9}$ at 1 AU, well below the Cassini limit of $\gamma - 1 < 2 \times 10^{-5}$ .