If there is a Planet Nine out there, I assume we’ll find it soon. That would be a welcome development, in that it would imply the Solar System isn’t quite as odd as it sometimes seems to be. We see super-Earths – and current thinking seems to be that this is what Planet Nine must be – in other stellar systems, in great numbers in fact. So it would stand to reason that early in its evolution our system produced a super-Earth, one that was presumably nudged into a distant, eccentric orbit by gravitational interactions.

The gap in size between Earth and the next planet up in scale is wide. Neptune is 17 times more massive than our planet, and four times its radius. Gas giant migration surely played a role in the outcome, and when considering stellar system architectures, it’s noteworthy as well that all that real estate between Mars and Jupiter seems to demand something more than asteroidal debris. To make sense of such issues, Stephen Kane (University of California, Riverside) has run a suite of dynamical simulations that implies we are better off without a super-Earth anywhere near the inner system.

Image: Artist’s concept of Kepler-62f, a super-Earth-size planet orbiting a star smaller and cooler than the sun, about 1,200 light-years from Earth. What effect would such a planet have in our own Solar System? Image credit: NASA Ames/JPL-Caltech/Tim Pyle.

Supposing a super-Earth did exist between Mars and Jupiter, Kane’s simulations demonstrated the outcomes for a range of different masses, the results presented in a new paper in the Planetary Science Journal. The heavyweight of our system, Jupiter’s 318 Earth masses carry profound gravitational significance for the rest of the planets. Disturb Jupiter, these results suggest, and in some scenarios the inner planets, including our own, are ejected from the Solar System. Even Uranus and Neptune can be affected and perhaps ejected as well depending on the super-Earth’s location.

As the paper notes, the range of possibilities is wide:

…several thousand simulations were conducted, producing a vast variety of dynamical outcomes for the solar system planets. The inner solar system planets are particularly vulnerable to the addition of the super-Earth planet, resulting in numerous regions of substantial system instability. The broad region of 2–4 au contains many locations of MMRs [Mean Motion Resonances] with the inner planets that further amplify the chaotic evolution of the inner solar system. There are also important MMR locations with the outer planets within the 2–4 au region, with potential significant consequences for the ice giants.

Let’s look at one possible outcome. The figure below shows the evolution in the eccentricity of the orbits of the inner planets in our Solar System, assuming a super-Earth with a mass of 7 times Earth’s and a semi-major axis of 2 AU. The simulation covers 107 years.

Image: This is Figure 2 from the paper. Caption: Eccentricity evolution of the solar system terrestrial planets (top four panels) for a 107 yr simulation, where the additional planet (bottom panel) has a mass and semimajor axis of 7.0 M? and 2.00 au, respectively. Credit: Stephen Kane.

The results show the devastating disruption this scenario produces. The orbits of the four inner planets become unstable over time, removing all of them from the system before the simulation concludes. Mars gets knocked out halfway through the simulation period, while Mercury is ejected early due to interactions with Venus and the Earth. The latter two planets see a gradual increase in their eccentricities. The semimajor axis of Venus increases as it decreases for Earth, creating close encounters and removing both worlds from the system 8 to 9 Myr after the simulation starts.

Different things happen, of course, as Kane manipulates the variables. Assuming a super-Earth with a mass eight times the Earth’s at 3.7 AU, the surprising result (surprising to me, at least) is that Mars remains largely unaffected, while it’s the super-Earth whose interactions with the outer planets become intense. The orbits of Venus and Earth begin to become more eccentric, with perturbations to the orbit of Mercury that eventually remove it from the system entirely. It’s fascinating to work through this paper to examine the various scenarios. Take a look at yet another possibility:

Image: This is Figure 8. Caption: Eccentricity evolution of the solar system outer planets (top four panels) for a 107 yr simulation, where the additional planet (bottom panel) has a mass and semimajor axis of 7.0 M? and 3.80 au, respectively. Credit: Stephen Kane.

Here we get Mean Motion Resonances with Jupiter and Saturn after about two million years, increasing the eccentricity of both, with the super-Earth ultimately being ejected from the system. Uranus is lost after about 4 million years and Neptune undergoes significant changes to its eccentricity. As Kane notes, the simulations show changes to system dynamics that are hugely sensitive to initial conditions, and in cases where significant interactions occur in the outer system, the orbits of the inner planets tend to become unstable as well. In the case of Figure 8, Mars is eventually ejected.

And this may have some bearing on our search for Planet Nine:

…the initial orbit for the additional planet was coplanar with Earth. Mutual inclinations between planetary orbits plays a role in overall system stability (Laskar 1989; Chambers et al. 1996), particularly for large inclinations (Veras & Armitage 2004; Correia et al. 2011), and may provide solutions to otherwise unstable architectures (Kane 2016; Masuda et al. 2020). It is therefore possible that there are orbital inclinations for the super-Earth that may reveal further locations of long-term stability, or else enhance unstable scenarios…

The paper implies, as the author adds in his conclusion, the “dynamical fragility” of the Solar System we have, with applications for the study of exoplanetary system architectures. How systems manage to work out sharing arrangements with super-Earths will doubtless become a key question for research as we move further into the era of space-based astrometry and learn more about how systems evolve.

The paper is Kane, “The Dynamical Consequences of a Super-Earth in the Solar System,” Planetary Science Journal Vol. 4, No. 2 (28 February 2023) 38 (full text).