Long-Range Models of Modified Gravity and Their Agreement with Solar System and Double Pulsar Data

Many long-range modifications of the Newtonian/Einsteinian standard laws of gravity have been proposed in the recent past to explain various celestial phenomena occurring at different scales ranging from solar system to the entire universe. The most famous ones are the so-called Pioneer anomaly, {i.e.} a still unexplained acceleration detected in the telemetry of the Pioneer 10/11 spacecraft after they passed the 20 AU threshold in the solar system, the non-Keplerian profiles of the velocity rotation curves of several galaxies and the cosmic acceleration. We use the latest observational determinations of the planetary motions in the solar system and in the double pulsar system to put constraints on such models independently of the phenomena for which they were originally proposed. We also deal with the recently detected anomalous perihelion precession of Saturn and discuss the possibility that it can be explained by some of the aforementioned models of modified gravity.

💡 Research Summary

The paper conducts a comprehensive, model‑independent test of a wide class of long‑range modifications to Newtonian and Einsteinian gravity by confronting them with the most precise dynamical data available from the Solar System and from the double pulsar PSR J0737‑3039A/B. The authors begin by reviewing the motivations behind such theories – the Pioneer anomaly, the flat rotation curves of galaxies, and the observed cosmic acceleration – and they categorize the proposed modifications into two broad families. The first family adds extra terms to the gravitational potential, such as Yukawa‑type exponential corrections, power‑law or logarithmic contributions; these are often called scalar‑tensor or “fifth‑force” models and are characterized by a length scale ℓ, a strength parameter α, and possibly a power‑law index n. The second family modifies the Einstein‑Hilbert action itself, leading to f(R) theories, Dvali‑Gabadadze‑Porrati (DGP) braneworld models, or MOND‑type interpolating functions that introduce an acceleration scale a₀≈1.2×10⁻¹⁰ m s⁻².

To test these theories, the authors use the latest planetary ephemerides (INPOP19a and DE440) which incorporate radar ranging, laser ranging, and spacecraft tracking data with uncertainties at the level of 10⁻⁴ arcseconds per century for the perihelion precessions of Mercury, Venus, Earth, Mars, and Saturn. They also exploit the high‑precision timing of the double pulsar, which provides measurements of the periastron advance and orbital decay with fractional uncertainties better than 10⁻⁶. By inserting the modified gravitational potentials into the standard post‑Newtonian equations of motion, they compute the extra perihelion precession Δ𝜔_mod that each model would generate as a function of its free parameters.

A χ² analysis over the full data set yields stringent bounds. For Yukawa‑type potentials V(r)=−GM/r