The New Horizons space probe led the first close flyby of one of the most primordial and distant objects left over from the formation of the solar system, the contact binary Kuiper Belt object (486958) Arrokoth, which is composed of two progenitors, the lobes nicknamed Ultima and Thule. In the current work, we investigated Arrokoths surface in detail to identify the location of equilibrium points and also explore each lobes individual dynamic features. We assume Arrokoths irregular shape as a homogeneous polyhedra contact binary. We numerically explore its dynamic characteristics by computing its irregular binary geopotential to study its quantities, such as geometric height, oblateness, ellipticity, and zero-power curves. The stability of Arrokoth Hill was also explored through zero-velocity curves. Arrokoths external equilibrium points have no radial symmetry due to its highly irregular shape. We identified even equilibrium points concerning its shape and spin rate: i.e., four unstable external equilibrium points and three inner equilibrium points, where two points are linearly stable, with an unstable central point that has a slight offset from its centroid. Moreover, the large and small lobes each have five equilibrium points with different topological structures from those found in Arrokoth. Our results also indicate that the equatorial region of Arrokoths lobes is an unstable area due to the high rotation period, while its polar locations are stable resting sites for surface particles. Finally, the zero-power curves indicate the locations around Arrokoth where massless particles experience enhancing and receding orbital energy.
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