  Using Fisher information matrices, we forecast the uncertainties $\sigma_M$
on the measurement of a "Planet X" at heliocentric distance $d_X$ via its tidal
gravitational field's action on the known planets. Using planetary measurements
currently in hand, including ranging from the Juno, Cassini, and Mars-orbiting
spacecraft, we forecast a median uncertainty (over all possible sky positions)
of $\sigma_M=0.22M_\oplus (d_x/400\,\textrm{AU})^3.$ A definitive $(5\sigma)$
detection of a $5M_\oplus$ Planet X at $d_X=400$ AU should be possible over the
full sky but over only 5% of the sky at $d_X=800$ AU. The gravity of an
undiscovered Earth- or Mars-mass object should be detectable over 90% of the
sky to a distance of 260 or 120 AU, respectively. Upcoming Mars ranging
improves these limits only slightly. We also investigate the power of
high-precision astrometry of $\approx8000$ Jovian Trojans over the 2023--2035
period from the upcoming Legacy Survey of Space and Time (LSST). We find that
the dominant systematic errors in optical Trojan astrometry (photocenter
motion, non-gravitational forces, and differential chromatic refraction) can be
solved internally with minimal loss of information. The Trojan data allow
useful cross-checks with Juno/Cassini/Mars ranging, but do not significantly
improve the best-achievable $\sigma_M$ values until they are $\gtrsim10\times$
more accurate than expected from LSST. The ultimate limiting factor in searches
for a Planet X tidal field is confusion with the tidal field created by the
fluctuating quadrupole moment of the Kuiper Belt as its members orbit. This
background will not, however, become the dominant source of Planet X
uncertainty until the data get substantially better than they are today.
