  We study the Nordstr\"om-Vlasov system which describes the dynamics of a
self-gravitating ensemble of collisionless particles in the framework of the
Nordstr\"om scalar theory of gravitation. If the speed of light $c$ is
considered as a parameter, it is known that in the Newtonian limit $c\to\infty$
the Vlasov-Poisson system is obtained. In this paper we determine a higher
approximation and establish a pointwise error estimate of order $O(c^{-4})$.
Such an approximation is usually called a 1.5 post-Newtonian approximation.
