(130) Elektra Delta — on the stability of the new third moonlet. (arXiv:2304.14967v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Valvano_G/0/1/0/all/0/1">Giulia Valvano</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Oliveira_R/0/1/0/all/0/1">Rai Machado Oliveira</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Winter_O/0/1/0/all/0/1">Othon Cabo Winter</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Sfair_R/0/1/0/all/0/1">Rafael Sfair</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Borderes_Motta_G/0/1/0/all/0/1">Gabriel Borderes-Motta</a>
The aim of this work is to verify the stability of the proposed orbital
solutions for the third moonlet (Delta) taking into account a realistic
gravitational potential for the central body of the quadruple system (Alpha).
We also aim to estimate the location and size of a stability region inside the
orbit of Gamma. First, we created a set of test particles with intervals of
semi-major axis, eccentricities, and inclinations that covers the region
interior to the orbit of Gamma, including the proposed orbit of Delta and a
wide region around it. We considered three different models for the
gravitational potential of Alpha: irregular polyhedron, ellipsoidal body and
oblate body. For a second scenario, Delta was considered a massive spherical
body and Alpha an irregular polyhedron. Beta and Gamma were assumed as
spherical massive bodies in both scenarios. The simulations showed that a large
region of space is almost fully stable only when Alpha was modeled as simply as
an oblate body. For the scenario with Delta as a massive body, the results did
not change from those as massless particles. Beta and Gamma do not play any
relevant role in the dynamics of particles interior to the orbit of Gamma.
Delta’s predicted orbital elements are fully unstable and far from the nearest
stable region. The primary instability source is Alpha’s elongated shape.
Therefore, in the determination of the orbital elements of Delta, it must be
taken into account the gravitational potential of Alpha assuming, at least, an
ellipsoidal shape.
The aim of this work is to verify the stability of the proposed orbital
solutions for the third moonlet (Delta) taking into account a realistic
gravitational potential for the central body of the quadruple system (Alpha).
We also aim to estimate the location and size of a stability region inside the
orbit of Gamma. First, we created a set of test particles with intervals of
semi-major axis, eccentricities, and inclinations that covers the region
interior to the orbit of Gamma, including the proposed orbit of Delta and a
wide region around it. We considered three different models for the
gravitational potential of Alpha: irregular polyhedron, ellipsoidal body and
oblate body. For a second scenario, Delta was considered a massive spherical
body and Alpha an irregular polyhedron. Beta and Gamma were assumed as
spherical massive bodies in both scenarios. The simulations showed that a large
region of space is almost fully stable only when Alpha was modeled as simply as
an oblate body. For the scenario with Delta as a massive body, the results did
not change from those as massless particles. Beta and Gamma do not play any
relevant role in the dynamics of particles interior to the orbit of Gamma.
Delta’s predicted orbital elements are fully unstable and far from the nearest
stable region. The primary instability source is Alpha’s elongated shape.
Therefore, in the determination of the orbital elements of Delta, it must be
taken into account the gravitational potential of Alpha assuming, at least, an
ellipsoidal shape.
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