# Relativistic Newtonian Dynamics for Objects and Particles

## TL;DR

Relativistic Newtonian Dynamics (RND) extends classical Newtonian mechanics by incorporating potential energy effects on spacetime, accurately predicting phenomena like gravitational time dilation, Mercury's precession, and the Shapiro delay.

## Contribution

The paper refines and extends RND to include motion of objects and particles with non-zero mass under conservative forces, deriving equations that predict key relativistic gravitational effects.

## Key findings

- RND accurately predicts gravitational time dilation.
- RND explains Mercury's perihelion precession.
- RND accounts for the Shapiro time delay.

## Abstract

Relativistic Newtonian Dynamics (RND) was introduced in a series of recent papers by the author, in partial cooperation with J. M. Steiner. RND was capable of describing non-classical behavior of motion under a central attracting force. RND incorporates the influence of potential energy on spacetime in Newtonian dynamics, treating gravity as a force in flat spacetime. It was shown that this dynamics predicts accurately gravitational time dilation, the anomalous precession of Mercury and the periastron advance of any binary. In this paper the model is further refined and extended to describe also the motion of both objects with non-zero mass and massless particles, under a conservative attracting force. It is shown that for any conservative force a properly defined energy is conserved on the trajectories and if this force is central, the angular momentum is also preserved. An RND equation of motion is derived for motion under a conservative force. As an application, it is shown that RND predicts accurately also the Shapiro time delay - the fourth test of GR.