On the forced orbital plane of the Hilda asteroids

Hilda-group asteroids librate in Jupiter's interior 3:2 mean motion resonance. We estimate that the Hilda group is observationally complete up to absolute magnitude H≤16.3. This provides a statistically useful sample of thousands of resonant objects, all within a narrow range of semi-major axes, to compare with theoretical expectations of their orbital distribution from dynamical theory. We use von Mises–Fisher statistics to calculate the sample mean planes and mean plane uncertainties for the Hilda group and its Hilda, Schubart, and Potomac collisional subfamilies. Although Laplace–Lagrange linear secular theory is considered inapplicable within mean motion resonances, we find that the Laplace plane and the orbital plane of Jupiter are both statistically indistinguishable from the sample mean plane of the Hildas. In future work, we intend to extend this investigation to resonant populations in the Kuiper belt so as to further test the validity of Laplace–Lagrange linear secular theory for the mean planes of resonant populations.