  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 Arrokoth's surface in detail to identify the
location of equilibrium points and also explore each lobe's individual dynamic
features. We assume Arrokoth's 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. Arrokoth's
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 Arrokoth's 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.
