Can the gravitational effect of Planet X be detected in current-era tracking of the known major and minor planets?

TL;DR

This study forecasts the ability of current and upcoming planetary tracking methods to detect or constrain the gravitational influence of a hypothetical Planet X at various distances, highlighting the potential and limitations of existing data.

Contribution

It provides quantitative forecasts of Planet X detection capabilities using Fisher matrices and assesses the impact of different observational data sources and systematic errors.

Findings

A 5 Earth-mass Planet X at 400 AU could be detected with 5σ significance.

Detection of Earth- or Mars-mass objects is possible within 260 and 120 AU, respectively.

Trojan astrometry offers cross-checks but does not significantly improve detection limits.

Abstract

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.