A dynamical study of Hilda asteroids in the Circular and Elliptic RTBP

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Abstract
The Hilda group is a set of asteroids whose mean motion is in a 3:2 orbital resonance with Jupiter. In this paper, we use the planar Circular Restricted Three-Body Problem (CRTBP) as a dynamical model and we show that there exists a family of stable periodic orbits that are surrounded by islands of quasi-periodic motions. We have computed the frequencies of these quasi-periodic motions and we have shown how the Hilda family fits inside these islands. We have compared these results with the ones obtained using the Elliptic Restricted Three-Body Problem and they are similar, showing the suitability of the CRTBP model. It turns out that, to decide if a given asteroid belongs to the Hilda class, it is much better to look at its frequencies in the planar CRTBP rather than to use two-body orbital elements as it is commonly done today.
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Funding Information
  • Agencia Estatal de Investigación (PID2021-125535NB-I00)
  • Agencia Estatal de Investigación (PID2021-123968NB-I00)
  • Agència de Gestió d'Ajuts Universitaris i de Recerca (2021 SGR 01072)
  • Agencia Estatal de Investigación (CEX2020-001084-M)

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