2020/04/14 by Jian Li, Zhihong Jeff Xia
Mathematics · Physics and Astronomy · #Aerospace engineering #Astro and Planetary Science #Astronomy #Astrophysics #Binary number #Context (archaeology) #Geology #Geometry #Mathematics #Orbit (dynamics) #Orbital inclination #Orbital plane #Paleontology #Physics #Plane (geometry) #Planet #Planetary Science and Exploration #Stellar, planetary, and galactic studies #astro-ph.EP
paper · pdf · doi:10.1051/0004-6361/202037728
published as A&A 637, A87 (2020) · 7 pages, 9 figures, Accepted for publication on Astronomy and Astrophysics
openalex publication_date 2020/04/14 · arxiv created 2020/04/15 · arxiv updated 2020/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Context. A recent observational census of Kuiper belt objects (KBOs) has unveiled anomalous orbital structures. This has led to the hypothesis that an additional ∼5 − 10 m ⊕ planet exists. This planet, known as Planet 9, occupies an eccentric and inclined orbit at hundreds of astronomical units. However, the KBOs under consideration have the largest known semimajor axes at a > 250 AU; thus they are very difficult to detect. Aims. In the context of the proposed Planet 9, we aim to measure the mean plane of the Kuiper belt at a > 50 AU. In a comparison of the expected and observed mean planes, some constraints would be put on the mass and orbit of this undiscovered planet. Methods. We adopted and developed the theoretical approach of Volk & Malhotra (2017, AJ, 154, 62) to the relative angle δ between the expected mean plane of the Kuiper belt and the invariable plane determined by the eight known planets. Numerical simulations were constructed to validate our theoretical approach. Then similar to Volk & Malhotra (2017, AJ, 154, 62), we derived the angle δ for the real observed KBOs with 100 < a < 200 AU, and the measurement uncertainties were also estimated. Finally, for comparison, maps of the theoretically expected δ were created for different combinations of possible Planet 9 parameters. Results. The expected mean plane of the Kuiper belt nearly coincides with the said invariable plane interior to a = 90 AU. But these two planes deviate noticeably from each other at a > 100 AU owing to the presence of Planet 9 because the relative angle δ could be as large as ∼10°. Using the 1 σ upper limit of δ < 5° deduced from real KBO samples as a constraint, we present the most probable parameters of Planet 9: for mass m 9 = 10 m ⊕ , orbits with inclinations i 9 = 30°, 20°, and 15° should have semimajor axes a 9 > 530 AU, 450 AU, and 400 AU, respectively; for m 9 = 5 m ⊕ , the orbit is i 9 = 30° and a 9 > 440 AU, or i 9 < 20° and a 9 > 400 AU. In this work, the minimum a 9 increases with the eccentricity e 9 (∈[0.2, 0.6]) but not significantly.