Has Kronos devoured Planet Nine and its epigones?

TL;DR

The paper investigates whether distant unseen planets such as Planet Nine and its proposed epigones can be constrained through Saturn's measured orbital precessions. It derives secular quadrupolar perturbations from a distant pointlike perturber and compares the predicted rates of Saturnian orbital elements to observational uncertainties, using a conservative tenfold rescaling to account for systematics. The findings tentatively rule out Planet X, largely constrain Planet Y to aphelion-like configurations for Mercury-mass, and keep Planet Nine viable near aphelion for certain masses, with the allowed regions shrinking under stricter coordinate-frame constraints. The work highlights that improved Uranus data or a dedicated deep-space probe could substantially sharpen these constraints and offers a practical pathway to testing these speculative planets.

Abstract

The Planet Nine hypothesis encompasses a body of about 5-8 Earth's masses whose orbital plane would be inclined to the ecliptic by one or two tens of degrees and whose perihelion distance would be as large as about 240-385 astronomical units. Recently, a couple of his epigones have appeared: Planet X and Planet Y. The former is a sort of minor version of Planet Nine in that all its physical and orbital parameters would be smaller. Instead, the latter would have a mass ranging from that of Mercury to the Earth's one and semimajor axis within 100-200 astronomical units. By using realistic upper bounds for the orbital precessions of Saturn, one can get insights on their position which, for Planet Nine, appears approximately confined around its aphelion. Planet Y can be just a Mercury-sized object at no less than about 125 astronomical units, while Planet X appears to be ruled out. Dedicated data reductions by modeling such perturber(s) are required to check the present conclusions, to be intended as hints of what might be detectable should planetary ephemerides include them. A probe on the same route of Voyager 1 would be perturbed by Planet Nine by about 20-40 km after some decades.

Figures (5)

• Figure 1: Allowed regions in the $\left\{f_\mathrm{Y},\Omega_\mathrm{Y},\omega_\mathrm{Y}\right\}$ parameter space for an elliptical orbit of a Mercury-mass Planet Y characterized by $e_\mathrm{Y}=0.2$ and different values of the semimajor axis $a_\mathrm{Y}$ (125 au, 150 au and 200 au) and the inclination $I_\mathrm{Y}$ (10$^\circ$ and 25$^\circ$) to the ecliptic. They were inferred by imposing that the theoretical rates of change of $e,I,\Omega,\varpi$ of Saturn due to Planet Y, calculated with Equations (\ref{['dadt']})--(\ref{['dvarpidt']}), simultaneously fulfil the condition of Equation (\ref{['condiz']}) by using the uncertainties in Table \ref{['Tab:1']} rescaled by a factor of ten.
• Figure 2: Allowed regions in the $\left\{f_9,\Omega_9,\omega_9\right\}$ parameter space for an elliptical orbit of a $5\,m_\oplus$ Planet Nine characterized by $a_9=520\,\mathrm{au}$ and different values of the eccentricity $e_9$ (0.259 and 0.538) and the inclination $I_9$ (11$^\circ$ and 21$^\circ$) to the ecliptic. They were inferred by imposing that the theoretical rates of change of $e,I,\Omega,\varpi$ of Saturn due to Planet Nine, calculated with Equations (\ref{['dadt']})--(\ref{['dvarpidt']}), simultaneously fulfil the condition of Equation (\ref{['condiz']}) by using the uncertainties in Table \ref{['Tab:1']} rescaled by a factor of ten.
• Figure 3: Allowed regions in the $\left\{f_9,\Omega_9,\omega_9\right\}$ parameter space for an elliptical orbit of a $8.4\,m_\oplus$ Planet Nine characterized by $a_9=520\,\mathrm{au}, e_9=0.538$ and different values of the inclination $I_9$ (11$^\circ$ and 21$^\circ$) to the ecliptic. They were inferred by imposing that the theoretical rates of change of $e,I,\Omega,\varpi$ of Saturn due to Planet Nine, calculated with Equations (\ref{['dadt']})--(\ref{['dvarpidt']}), simultaneously fulfil the condition of Equation (\ref{['condiz']}) by using the uncertainties in Table \ref{['Tab:1']} rescaled by a factor of ten.
• Figure 4: Allowed regions in the $\left\{r_9,\alpha_9,\delta_9\right\}$ parameter space for an elliptical orbit of Planet Nine characterized by different values of its mass $m_9$ ($4.9\,m_\oplus$ and $8.4\,m_\oplus$). They were inferred by imposing that the theoretical Kronian rates of change of $e,I,\Omega,\varpi$, referred to the International Celestial Reference Frame (ICRF), due to Planet Nine, calculated with Equations (\ref{['dadt']})--(\ref{['dvarpidt']}), simultaneously fulfil the condition of Equation (\ref{['condiz']}) by using the uncertainties in Table \ref{['Tab:1']} rescaled by a factor of ten. The ranges of variation for the heliocentric distance $r_9$ and the astrometric angles $\alpha_9,\delta_9$ of P9 are retrieved from 2021AJ....162..219B (upper row) and 2016AJ....152...94H (middle row), while the lower row shows the allowed regions without assuming any a priori bounds for $\alpha_9,\delta_9$.
• Figure 5: Numerically produced time series $\Delta\rho(t),\Delta\alpha(t),\Delta\delta(t)$ of the signatures induced on the range $\rho$, RA and decl. of Voyager 1 from March 1986 to today by a P9 with $m_9=4.9\,m_\oplus$ (lef column) and $m_9=8.4\,m_\oplus$ (right column). They were obtained by integrating the barycentric equations of motion of the probe and of all the eight known planets of the solar system with respect to the ICRF with and without P9. Both runs shared the gravitational pulls of the solar system's planets from Mercury to Neptune and the same initial conditions for both the probe and the planets themselves retrieved from the WEB interface of the HORIZONS program maintained by the JPL, NASA.