  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.
