The perihelion of Mercury advance and the light bending calculated in (enhanced) Newton's theory

TL;DR

This paper demonstrates that Newton's gravitational theory, when interpreted with curved space geometry, can accurately predict Mercury's perihelion advance and light bending, aligning with observed phenomena.

Contribution

It introduces an enhanced Newtonian framework incorporating space curvature via an additional equation linking Ricci scalar and matter density.

Findings

Newtonian predictions match observed Mercury perihelion shift.

Light bending calculations align with empirical data.

Enhanced Newtonian theory reproduces key relativistic effects.

Abstract

We show that results of a simple dynamical gedanken experiment interpreted according to standard Newton's gravitational theory, may reveal that three-dimensional space is curved. The experiment may be used to reconstruct the curved geometry of space, i.e. its non-Euclidean metric. The perihelion of Mercury advance and the light bending calculated from the Poisson equation and the equation of motion in the curved geometry have the correct (observed) values. Independently, we also show that Newtonian gravity theory may be enhanced to incorporate the curvature of three dimensional space by adding an extra equation which links the Ricci scalar with the density of matter. Like in Einstein's general relativity, matter is the source of curvature. In the spherically symmetric (vacuum) case, the metric of space 3gik that follows from this extra equation agrees, to the expected accuracy, with the metric measured by the Newtonian gedanken experiment mentioned above.