| Abstract: |
| We consider the planar elliptic restricted four-body problem as a model for the motion of Hektor`s moonlet Skamandrios relative to the Sun, Jupiter and the Trojan asteroid Hektor. We derive the corresponding elliptic Hill four-body problem, representing the limiting case when the mass of the asteroid tends to zero. The resulting system can be viewed as a small perturbation of the circular Hill four-body problem, with the perturbation parameter being the eccentricity of Jupiter`s orbit. We show that the effect of the perturbation can accumulate and yield some orbits whose energy undergoes significant changes over time. Consequently, it is possible that the moonlet can be ejected or crash onto the asteroid. |
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