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Figure 3: Effect of the gravitomagnetic force on the hyperbolic motion of a test particle around an astronomical rotating body located at the origin of the depicted frame. The body spin $S$ is directed along the positive $z$ axis, that is, outside the figure. Red line: unperturbed hyperbola. Blue dashed line: perturbed orbit. For illustrative purposes, we choose the Earth as central body and rescaled the magnitude of its gravitomagnetic force by ${10}^{10}$ so that $A^{\text{G}\text{M}}/A^{\text{N}}=0.4$ at perigee. We adopted the initial conditions $x_0=0,y_0=p=a(e^2-1),z_0=0,v_{x0}>0,v_{y0}<0,v_{z0}=0$; the particle moves in the equatorial plane of the spinning Earth in such a way that the radius vector rotates in the opposite sense with respect to the Earth, that is, clockwise. We used $a=\mathrm{8,493.326}$ km, $e=1.81$. The perturbed orbit is deflected inward with respect to the unperturbed one.