is organised as follows. In Sect. \[Sec2\] we describe the necessary mathematical background for static, spherically symmetric scalar field configurations, and obtain some general results both for SFBHs and for SFNSs. One of the most important issues is how to distinguish a naked singularity from a black hole using available observational data. On the other hand, our primary purpose is the study of geodesic motion in these asymptotically flat spacetimes, and in Sect. \[Sec3\] we discuss general features of bound orbits of free massive particles, such as the shape of the orbits and the precession of their pericentres. In Sect. \[Sec4\] we consider a simple, fully analytical, one-parameter family of SFNSs and study the shapes of bound orbits in these spacetimes in comparison with the orbits in the corresponding Schwarzschild black hole spacetimes.

In this paper, we use the geometrical system of units with $G=c=1$ and adopt the metric signature $(+\,-\,-\,-)$.

Comparing SFBHs and SFNSs {#Sec2}
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The action with the minimal coupling between curvature and a real scalar field $\phi$ has the form $$\label{action}
    \Sigma=\frac{1}{8\pi}\int\left(-\frac{1}{2}R + \,\langle d\phi,d\phi\rangle-2V(\phi)\right) \sqrt[]{|g|}\,d^{\,4}x\,,$$ where $R$ is the scalar curvature, $V(\phi)$ is a self-interaction potential, and the angle brackets denote the scalar product with 