that all noncircular bound orbits in the Schwarzschild spacetime have ’the relativistic pericentre advance’, that is $\Delta\varphi>0$. In contrast, in Fig. \[fig2\] we plot the shape of orbits possessing the same apocentre radius as the orbit in Fig. \[fig1\]; one of them (in the middle panel) has, in addition, the same pericentre radius. In all three cases, the angles of precession are negative and sufficiently large in magnitude. The shape of an orbit depends on the specific angular momentum $J$ and the specific energy $E$ of a test particle. Numerical simulations show that the number of oscillations per revolution decreases with increasing $J$ when the value of $E$ is fixed, as well as with decreasing $E$ when the value of $J$ is fixed; both these dependences appear to be true in general, not only for the family (\[xi\]).

Fig. \[fig3\] represents comparable orbits around SFNSs and around the corresponding Schwarzschild black hole with the same mass $m_{\scriptscriptstyle Sch}=m_{\scriptscriptstyle NS}=1$. For the SFNS with $a=2.5$, an orbit which looks like a Keplerian orbit, whose pericentre and apocentre are not shifting during one revolution of a test particle and thus $\Delta\varphi=0$, is represented in the left panel. In the Schwarzschild spacetime, the 