This work presented a comprehensive study of the surface and orbital dynamics of comet 67P/Churyumov-Gerasimenko using a detailed 3-D polyhedral shape model. We treated the comet’s nucleus as a surface similar to that of an asteroid, since no drag force was considered in our analysis. Our objective was to investigate the dynamic features of the surface, particularly the slopes, while incorporating Third-Body (TB) and Solar Radiation Pressure (SRP) perturbations. Additionally, we examined the orbital dynamics around the comet using the DS model, with a focus on planar symmetric periodic orbits. We observed that the comet’s surface presents 98.5% of tilts lower than 100◦. The analysis of its geopotential revealed that the gravitational potential predominates over the centrifugal potential, due to the comet’s slow rotation. The big lobe exhibits maximum surface acceleration values. In contrast, the Hapi (comet’s neck) region exhibits intermediate surface acceleration values, indicating a more substantial influence of gravitational potential in the big lobe than in the Hapi region, closer to the comet’s center of mass. We also found that the surface acceleration of comet 67P has its maximum value, ∼2.2×10−7 km s−2, in its big lobe. Comparing our results with previous works, we found that the slopes are particularly noteworthy in the intervals from 20◦to 40◦and 60◦to 90◦. Regarding the escape speed, it is maximum in the Hapi region, a common feature with other slowly rotating bodies. Additionally, the geopotential minimum regions are the areas with the maximum escape speed. Additionally, we examined the impact of Third-Body gravitational effects and Solar Radiation Pressure on slope behavior. Our findings indicate that Third-Body perturbations have minimal influence on the overall behavior of the slopes. Conversely, Solar Radiation Pressure also appears to have a negligible effect on particles on the surface of comet 67P, specifically for sizes greater than approximately 10−3 cm at apocenter and greater than approximately 10−1 cm at pericenter. We identified five equilibrium points considering the current density and rotational period of comet 67P. Different from previous works, we found that the outer equilibrium point E2 and the inner equilibrium point E5 are linearly stable. The other equilibrium points are unstable. In addition, the Roche lobe (teardrop-shaped region, Fig. 7) intersects at the equilibrium point E1. To analyze the orbital evolution around comet 67P, we simplified the irregular shape of the body using the DS model. A topological classification of the orbit families was performed, revealing the dynamics around comet 67P based on the characteristics of the families, without requiring direct visualization of the orbits. We found 12 families of planar symmetric periodic orbits around the body. We also investigated the horizontal and vertical stabilities of these families.

Finally, comparing the DS and polyhedron models, our results suggest that the DS model could be used for the investigation of families of planar symmetric periodic orbits that have distances larger than ∼5 km from comet 67P. For this case, the gravitational potential relative error compared with the polyhedron method is < 5%.