# Gravitational Deflection in Relativistic Newtonian Dynamics

## TL;DR

This paper applies Relativistic Newtonian Dynamics to derive gravitational deflection of objects and light, showing it reproduces Einstein's weak lensing results and offers an alternative force-based gravity model.

## Contribution

It extends RND to calculate gravitational deflection for both massive and massless particles, providing analytical formulas consistent with known experimental results.

## Key findings

- Derived deflection equations for massive and massless particles.
- Reproduced Einstein's weak lensing deflection angle.
- Validated RND as an alternative to General Relativity in gravitational lensing.

## Abstract

In a recent series of papers, the authors introduced a new Relativistic Newtonian Dynamics (RND) and tested its validity by the accurate prediction of the gravitational time dilation, the anomalous precession of Mercury, the periastron advance of any binary and the Shapiro time delay. This dynamics incorporates the influence of potential energy on spacetime in Newtonian dynamics and, unlike Einstein's General Relativity, treats gravity as a force without the need to curve spacetime. In this paper, this dynamics is applied to derive the gravitational deflection of both objects with non-zero mass and of massless particles passing the strong gravitating field of a massive body. Equations for the trajectory and the resulting analytical expressions for the deflection angle, in terms of the distance and velocity at the point of closest approach to the massive object, were derived in both cases. It is shown that with a carefully defined limit, the trajectory of a massless particle is the limiting case of that of an object with non-zero mass. In the "weak" deflection limit, the derived expression for the deflection angle of a massless particle (photon) reproduces the experimentally tested Einstein's formula for weak gravitational lensing of a light ray, thereby providing another test for the validity of the RND.