On an Unknown-Parameter Organization of Reliable Measurements of the Newtonian Gravitational Constant G

The Newtonian gravitational constant G remains the least precisely known of the major fundamental constants. Recent high-quality measurements do not converge within their quoted uncertainties, although laboratories involved are among the most careful in precision metrology. This article explores a hypothesis developed from the comparison of reliable published values: the spread of G is NOT simply correlated with correlated with source-mass atomic number Z, atomic weight A, or proton fraction Z/A. Instead, the data may reflect a hidden experimental state variable X that organizes apparatus-dependent systematic offsets. Using a data set consisting of the 16 CODATA-22 input values plus the 2026 NIST determination by Schlamminger and colleagues, the measurements are first compared against representative source-mass composition parameters and then ranked from the smallest to the biggest measured G values. There was found a quartic empirical curve describing this sequence with R2 = 0.9779. This curve is interpreted as a possible bias landscape: Gmeasured = Gtrue + B(X). The most promising physical candidate for X could be the Gerber´s gravitational potential with the correction based on the radial velocity between the two interacting masses. The article concludes by proposing that future measurements should publish not only a value of G, but also a systematic-state map capable of revealing the hidden architecture of the experiment: the radial speed of the Earth toward the center of the Milky Way Galaxy (the radial velocity relative to the galactic core, Sagittarius A*) fluctuates throughout the year between roughly -21 km/s (moving away) and +41 km/s (moving toward). Gerber proposed in 1898 a velocity-dependent gravitational potential intended to represent the rate of propagation of gravitation and to account for the anomalous perihelion advance of Mercury. The Gerber´s potential has the form of a Newtonian term multiplied by a retardation factor depending on the radial velocity divided by a propagation speed. Its historical importance is that, at leading order, it yields the same perihelion-advance formula later obtained in general relativity.

Keywords: Earth ↔ Sagittarius A* Radial Velocity, Newtonian Gravitational Constant G, Gerber´S Gravitational Potential, Hidden Variable X.