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A hypothetical gravitating body in the outer solar system, the so-calledPlanet 9, was proposed to explain the unexpected clustering of the Kuiper BeltObjects. As it has not been observed via telescopes, it was conjectured to be aprimordial black hole (of the size of a quince) that could be gravitationallydetected by laser-launching many 1-gram mass satellites. Here, we study variousaspects that will affect such a search for Planet 9. Our basic observable isthe angular displacement in the trajectory of a sub-relativistic spacecraftwhich will be mainly affected by the gravity of Planet 9, augmented withseveral other 3-body, non-gravitational, and post-Newtonian forces. First, wecalculate the effect of the Sun in the framework of the circular restrictedthree-body problem of the Sun-Planet 9 spacecraft for the two particularinitial conditions. Then, we study the effects of non-gravitationalperturbations such as magnetic and drag forces exerted by the interstellarmedium; and the solar radiation pressure. In addition, we investigate thepost-Newtonian general relativistic effects such as the frame-dragging,Schwarzschild effect, and geodetic precession on the spacecraft trajectory. Weshow that the leading order angular displacement is due to the solar radiationpressure which makes the detection of Planet 9 difficult. Among the generalrelativistic effects, the frame-dragging has the smallest effect; and theSchwarzschild effect due to Sun has the largest effect. However, none of thegeneral relativistic effects produces a meaningful contribution to thedetection.

A Search for Planet 9 with a Sub-Relativistic Spacecraft: three-body, post-Newtonian and non-gravitational effects