The inclination of the planetary system relative to the solar equator may be explained by the presence of planet 9
Open accessAbstract
We evaluate the effects of a distant planet, commonly known as planet 9, on the dynamics of the giant planets of the solar system. We find that the dynamics of the giant planets can be decomposed into a classic Lagrange–Laplace dynamics relative to their own invariant plane and a slow precession of said plane relative to the total angular momentum vector of the solar system, including planet 9. Under specific configurations for planet 9, this precession can explain the current tilt of ∼6° between the invariant plane of the giant planets and the solar equator. An analytical model is developed to map the evolution of the inclination of the inner giant planets’ invariant plane as a function of the planet 9's mass and orbital elements, and numerical simulations of the equations of motion are performed to validate our analytical approach. The longitude of the ascending node of planet 9 is found to be linked to the longitude of the ascending node of the giant planets’ invariant plane, which also constrains the longitude of the node of planet 9 on the ecliptic. Some of the planet 9 configurations that allow the explanation of the current solar tilt are compatible with those proposed to explain the orbital confinement of distant Kuiper Belt objects. This work gives an elegant explanation for the current tilt between the invariant plane of the inner giant planets and the solar equator and also adds new constraints to the orbital elements of planet 9.
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The secular gravitational torque exerted by P9 upon the canonical giant planets would slowly perturb the orbital plane of the planets away from its initial state, exciting a spin-orbit misalignment between the total angular momentum vector of the canonical giant planets and the spin-axis of the sun.
“Shortly after the initial formulation of the Planet Nine hypothesis, it was pointed out by Bailey et al. (2016); Gomes et al. (2016); Lai (2016) that the secular gravitational torque exerted by P9 upon the canonical giant planets would slowly perturb the orbital plane of the planets away from its initial state, thereby exciting a spin-orbit misalignment between the total angular momentum vector of”
From The planet nine hypothesis (2019) · cites this paper as Gomes et al. (2016)
Cites
Evidence for a Distant Giant Planet in the Solar System
Batygin, K., & Brown, M. E. (2016) · The Astronomical Journal · doi:10.3847/0004-6256/151/2/22 · Cited by 432 · cited 20× · see citing works
“For example, the standard pl9 in Batygin & Brown (2016) with = Åm M109 and = I 309 has =a 700 au9 and e9=0.6.”
BackgroundMethodResultInfluentialA Sedna-like body with a perihelion of 80 astronomical units
Trujillo, C. A., & Sheppard, S. S. (2014) · Nature · doi:10.1038/nature13156 · Cited by 303 · see citing works
Observational constraints on the orbit and location of Planet Nine in the outer solar system
Brown, M. E., & Batygin, K. (2016) · The Astrophysical Journal Letters · doi:10.3847/2041-8205/824/2/l23 · Cited by 112 · cited 6× · see citing works
“ajor axis. For example, the standard pl9 in Batygin and Brown (2016) with m9 = 10M⊕ and I9 = 30◦ has a9 = 700 au and e9 = 0.6. In our case, for the same m9, I9 and a9 the eccentricity must be 0.8. In Brown and Batygin (2016) the best pl9 for I9 = 30◦ and m9 = 10M⊕ has a9 = 600 au and e9 = 0.5. In our analysis for the…”
BackgroundResultInfluentialA distant planetary-mass solar companion may have produced distant detached objects
GOMES, R., MATESE, J., & LISSAUER, J. (2006) · Icarus · doi:10.1016/j.icarus.2006.05.026 · Cited by 70 · cited 1× · see citing works
“According to Gomes et al. (2006), the averaged effect can be computed assuming that the perturber is on a circular orbit of radius b, where = -b a e19 9 9 2 is the semi-minor axis of the real perturber’s orbit.”
BackgroundSelf-citationGomes, R. S., Soares, J. S., & Brasser, R. (2015) · Icarus · doi:10.1016/j.icarus.2015.06.020 · Cited by 49 · see citing works
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Batygin, K., Adams, F. C., Brown, M. E., & Becker, J. C. (2019) · Physics Reports · doi:10.1016/j.physrep.2019.01.009 · Cited by 181 · see citing works
“Finally, numerical experiments that fully resolve the dynamics of the entire outer solar system have also been performed (Batygin and Brown, 2016b; Sheppard and Trujillo, 2016; Gomes et al., 2016; Bailey et al., 2016; Becker et al., 2018; Sheppard et al., 2018).”
BackgroundOrigin and Evolution of Short-period Comets
Nesvorný, D., Vokrouhlický, D., Dones, L., Levison, H. F., Kaib, N., & Morbidelli, A. (2017) · The Astrophysical Journal · doi:10.3847/1538-4357/aa7cf6 · Cited by 163 · see citing works
Self-citationTesting the Isotropy of the Dark Energy Survey’s Extreme Trans-Neptunian Objects
Bernardinelli, P. H., Bernstein, G. M., Sako, M., Hamilton, S., Gerdes, D. W., Adams, F. C., Saunders, W. R., Aguena, M., Allam, S., Avila, S., et al. (2020) · The Planetary Science Journal · doi:10.3847/psj/ab9d80 · Cited by 39 · see citing works
New constraints on the location of P9 obtained with the INPOP19a planetary ephemeris
Fienga, A., Di Ruscio, A., Bernus, L., Deram, P., Durante, D., Laskar, J., & Iess, L. (2020) · Astronomy & Astrophysics · doi:10.1051/0004-6361/202037919 · Cited by 32 · see citing works
Has Kronos Devoured Planet Nine and Its Epigones?
Iorio, L. (2026) · Universe · doi:10.3390/universe12020042
“On the other hand, we can try to reconcile the observational data with the acceleration of the Universe through modifications of the theory of gravity.”
- Authors
- Gomes, R., Deienno, R., & Morbidelli, A.
- Affiliations
- National Observatory (BR)
- Centre National de la Recherche Scientifique (FR)
- Corresponding author
- Gomes, Rodney
- Venue
- The Astronomical Journal
- Publisher
- American Astronomical Society
- Published
- 2016-12-22
- Volume
- 153
- Issue
- 1
- Pages
- 27
- ISSN
- 0004-6256 (ISSN-L)
- 1538-3881
- OpenAlex
- W2500073897
- Cited by
- 49
- References
- 5
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 2 · 2023: 4 · 2022: 3 · 2021: 1 · 2020: 11 · 2019: 9 · 2018: 9 · 2017: 7 · 2016: 1
- FWCI
- 4.14
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- The Astronomical Journal (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Biblioteca Digital da Memória Científica do INPE (National Institute for Space Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Astro and Planetary Science
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Stellar, planetary, and galactic studies
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › History and Developments in Astronomy
- Keywords
- Planet Nine, giant planets, invariant plane, precession, solar equator, longitude of ascending node, Kuiper belt objects, orbital elements
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