4:00 PM - 4:15 PM
[PPS07-18] Numerical simulation of impact crater shapes on a rapidly rotating top-shape body
The top-shape of the near-Earth asteroid (162173) Ryugu is considered to have formed under a rapid rotation close to the past critical angular velocity ωc (the angular velocity when centrifugal force is equivalent to self-gravity at the celestial equator) (Watanabe et al. 2019). It has been suggested that when a celestial collision occurs on a rapidly rotating small body, the orbits of ejecta are bent to the west by the Coriolis force, resulting in an east-west asymmetry that the west side of the crater rim is higher than the east side (Hirata et al. 2019). In the first stage of this study, we investigated the asymmetry of the topographies stabilized by landslide relaxation of a craters formed at the equator on a spherical body rotating rapidly. The results showed that the characteristic asymmetry remains after landslide relaxation, with a wide rim on the east side of the crater and a rim that is locally high just east of the crater. However, the surface of a spherical body rotating rapidly is practically a slope due to effective gravity (net force of self-gravity and centrifugal force), and this tilt angle exceeds the repose angle 30°, making it unstable against landslides. In the second stage of this study, we aimed to perform a similar crater topography analysis assuming a top-shape with surface slopes stable against landslides, and to clarify the asymmetry of the crater topography.
First, from the spherical harmonic function calculated based on Ryugu shape model by Matsumoto et al. (2020), we obtained an axisymmetric top-shaped body. We calculated its gravity field by considering the shape of this body as a superposition of thin disks and obtained its effective gravity under rapid rotation at an angular velocity ω~ (ω~=ω/ωc) close to the critical angular velocity ωc. Second, we calculated the orbit and the landing point of the ejecta on the surface of the body by integrating the equation of motion of the ejecta, containing self-gravity, centrifugal force, and Coriolis force for a top-shaped body, and obtained the thickness distribution of the ejecta in the crater vicinity.
Our calculations of the effective gravity on the top-shaped body show that the surface tilt angles of the body surface due to effective gravity were generally in the range of 30°-35° at ω~=0.95 (~3.5 h in the Ryugu rotation period). This means that the landslide to the equator occurred under the rapid rotation of Ryugu with a rotation period of ~3.5 h and tilt angle became the repose angle and the landslide stopped, resulting in the formation of the top-shape.
We also obtained the thickness distribution of ejecta by varying ω~ for a crater on the equator with rim radius Rr=50 m (on Ryugu, which is assumed to be a sphere with radius 448.2 m). For ω~≧0.8, a region where the ejecta does not land on the east side of the crater was created, and this boundary made a parabola convex to the east. For ω~=0.9, a second thickness peak, different from the rim peak, appeared near the eastern boundary of the landing region, and for ω~=0.95, the double peaks merged into a higher single peak on the east. Thus, even on a top-shaped body, an east-west asymmetry of crater shape was observed for ω~≧0.8.
However, the crater shape formed by the impact excavation depends on the surface topography near the impact point, which changes the volume of ejecta. Therefore, it is necessary to perform an analysis considering the changes of excavated crater shape and ejecta volume depending on the location of the crater. It is also necessary to analyze the relaxation processes considering the asymmetry of the landslide direction due to the slope of the body surface induced by effective gravity. We will report a crater topography analysis method considering these points, and the results of asymmetry of crater topographies.
First, from the spherical harmonic function calculated based on Ryugu shape model by Matsumoto et al. (2020), we obtained an axisymmetric top-shaped body. We calculated its gravity field by considering the shape of this body as a superposition of thin disks and obtained its effective gravity under rapid rotation at an angular velocity ω~ (ω~=ω/ωc) close to the critical angular velocity ωc. Second, we calculated the orbit and the landing point of the ejecta on the surface of the body by integrating the equation of motion of the ejecta, containing self-gravity, centrifugal force, and Coriolis force for a top-shaped body, and obtained the thickness distribution of the ejecta in the crater vicinity.
Our calculations of the effective gravity on the top-shaped body show that the surface tilt angles of the body surface due to effective gravity were generally in the range of 30°-35° at ω~=0.95 (~3.5 h in the Ryugu rotation period). This means that the landslide to the equator occurred under the rapid rotation of Ryugu with a rotation period of ~3.5 h and tilt angle became the repose angle and the landslide stopped, resulting in the formation of the top-shape.
We also obtained the thickness distribution of ejecta by varying ω~ for a crater on the equator with rim radius Rr=50 m (on Ryugu, which is assumed to be a sphere with radius 448.2 m). For ω~≧0.8, a region where the ejecta does not land on the east side of the crater was created, and this boundary made a parabola convex to the east. For ω~=0.9, a second thickness peak, different from the rim peak, appeared near the eastern boundary of the landing region, and for ω~=0.95, the double peaks merged into a higher single peak on the east. Thus, even on a top-shaped body, an east-west asymmetry of crater shape was observed for ω~≧0.8.
However, the crater shape formed by the impact excavation depends on the surface topography near the impact point, which changes the volume of ejecta. Therefore, it is necessary to perform an analysis considering the changes of excavated crater shape and ejecta volume depending on the location of the crater. It is also necessary to analyze the relaxation processes considering the asymmetry of the landslide direction due to the slope of the body surface induced by effective gravity. We will report a crater topography analysis method considering these points, and the results of asymmetry of crater topographies.