Can the Gravitational Effect of Planet X be Detected in Current-era Tracking of the Known Major and Minor Planets?

Abstract

Using Fisher information matrices, we forecast the uncertainties σ _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 sky positions) of ${\sigma }_{M}=0.22\,{M}_{\oplus }{({d}_{x}/400{\rm{au}})}^{3}.$ A 5 σ detection of a 5 M _⊕ 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 ≈8000 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, nongravitational forces, and differential chromatic refraction) can be solved internally with minimal loss of information. The Trojan data allow cross-checks with Juno/Cassini/Mars ranging, but do not significantly improve the best achievable σ _M values until they are ≳10× 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 uncertainty until the data get substantially better than they are today.

Keywords

• Planetary dynamics
• Fisher’s Information
• Kuiper belt
• Trans-Neptunian objects
• Astrometry
• Gravitation