Searching for a Black Hole in the Outer Solar System

There are hints of a novel object (Planet 9) with a mass $5-10$ $M_\oplus$ in the outer Solar System, at a distance of order 500 AU. If it is a relatively conventional planet, it can be found in telescopic searches. Alternatively, it has been suggested that this body might be a primordial black hole (PBH). In that case, conventional searches will fail. A possible alternative is to probe the gravitational field of this object using small, laser-launched spacecraft, like the ones envisioned in the Breakthrough Starshot project. With a velocity of order $.001~c$, such spacecraft can reach Planet 9 roughly a decade after launch and can discover it if they can report timing measurements accurate to $10^{-5}$ seconds back to Earth.