Equilibrium Points and Surface Dynamics About Comet 67P/Churyumov-Gerasimenko

Small bodies in our Solar System are considered remnants of their early formation. Studying their physical and dynamic properties can provide insights into their evolution, stability, and origin. ESA's Rosetta mission successfully landed and studied comet Churyumov-Gerasimenko (67P) for approximately two years. In this work, the aim is to analyze the surface and orbital dynamics of comet 67P in detail, using a suitable 3-D polyhedral shape model. We applied the polyhedron method to calculate dynamic surface characteristics, including geometric height, surface tilt, surface slopes, geopotential surface, acceleration surface, escape speed, equilibrium points, and zero-velocity curves. The results show that the gravitational potential is predominant on the comet's surface due to its slow rotation. The escape speed has the maximum value in the Hapi region (the comet's neck). The surface slopes were analyzed to predict possible regions of particle motion and accumulation. The results show that most regions of the comet's surface have low slopes. Furthermore, we analyzed the slopes under the effects of Third-Body gravitational and Solar Radiation Pressure perturbations. Our results showed that the effects of Third-Body perturbations do not significantly affect the global behavior of slopes. Meanwhile, the Solar Radiation Pressure does not significantly affect particles across the surface of comet 67P with sizes >10^-3\, cm at apocenter and >10^-1\, cm at pericenter. We also identified four equilibrium points around comet 67P and one equilibrium point inside the body, where points E₂ and E₅ are linearly stable. In addition, we approximated the shape of comet 67P using the simplified Dipole Segment Model to study its dynamics, employing parameters derived from its 3-D polyhedral shape model. We found 12 families of planar symmetric periodic orbits around the body.