Can Planet Nine Be Detected Gravitationally by a Sub-Relativistic Spacecraft?

Planet 9 was proposed as an explanation for the clustering of orbits for some trans-Neuptunian objects. Recently, the use of a sub-relativistic spacecraft was proposed to indirectly probe Planet 9's gravitational influence. Here we study the effects of the drag and electromagnetic forces exerted on a sub-relativistic spacecraft by the interstellar medium (ISM) and compare these forces with the gravitational force induced by Planet 9. We find that the resulting noise due to density and magnetic fluctuations would dominate over Planet 9's gravitational signal at sub-relativistic speeds, $v\gtrsim 0.001~c$. We then identify the parameter space required to overcome the drag and magnetic noise from the ISM turbulence and enable the detection of Planet 9's gravity. Finally, we discuss practical strategies to mitigate the effect of the drag and electromagnetic forces.