17:15 〜 19:15
[MZZ40-P04] 改良Z-modelを用いた運動量輸送効率の推定: 楕円標的へのモデル拡張
キーワード：宇宙防災、高速度衝突、運動量輸送、軌道変更
The Asteroid Impact and Deflection Assessment (AIDA) project, which is a collaboration between NASA’s Double Asteroid Redirection Test (DART) and ESA’s HERA, is currently on-going. AIDA is an in-space experiment to investigate the efficiency of momentum transfer from a kinetic impactor to an asteroid. The orbit of the asteroid Dimorphos has indeed changed after the DART impact. The degree of orbital change is evaluated using the momentum transport efficiency beta. This is calculated as the ratio of the momentum transport before and after the collision, assuming that the momentum transport in the case of a perfectly inelastic collision is unity. When a large amount of ejecta carries momentum to the opposite side of the impact direction, and the target object is further accelerated by the recoil. Detailed observations show that beta in the DART impact is >2, and the main cause of the orbital change is the acceleration of the target object due to the recoil of the ejecta. The detailed investigation of the origin of such a large beta value has been studied with three-dimensional shock physics modeling. In general, however, impact simulations require numerical integration at a time interval determined by the speed of sound of the material (a few kilometers per second) and the spatial resolution, namely, the CFL condition. Numerical calculations for ejecta moving at the escape velocity (e.g., ~10 cm per second for the DART impact) under microgravity conditions on small bodies are computationally expensive.
We have previously constructed a model that introduces the absolute value of the kinetic energy of the streamlines of an excavation flow into the Z model of Maxwell. Because the Z model contains geometric information, it can also be applied to targets with curvature. This model also requires numerical integration in two dimensions, but the time step is independent of the CFL condition. It would serve as a quick-look tool under a variety of impact conditions. In this study, we further extended the model to an ellipsoidal target.
We employed the equation of an ellipse in 2D polar coordinates in our previous model and included include the length of the major and minor axes. We calculated beta values after an impact at the north pole of three types of celestial bodies, including oblate, spheroid, and prolate, based on the three-axis length information of Dimorphos. We also assumed that the formation of the impact crater would occur in the gravity-dominated regime. In the case of prolate bodies that are elongated in the polar direction, beta tends to be small because the ejection angle from the ellipsoidal surface is small. It has been found that the beta value varies between 3 and 4.5 for oblate and prolate bodies. However, it should be noted that this is within the range of uncertainty of the estimated beta value after the DART impact. In the case of the actual Dimorphos, the impact was on the equatorial plane of an oblate object, so it is estimated that the value would be somewhere between the values for oblate and prolate. In addition, the azimuthal anisotropy of the ejecta curtain observed after the DART impact may be explained by the curvature in the latitude and longitude directions.
We have previously constructed a model that introduces the absolute value of the kinetic energy of the streamlines of an excavation flow into the Z model of Maxwell. Because the Z model contains geometric information, it can also be applied to targets with curvature. This model also requires numerical integration in two dimensions, but the time step is independent of the CFL condition. It would serve as a quick-look tool under a variety of impact conditions. In this study, we further extended the model to an ellipsoidal target.
We employed the equation of an ellipse in 2D polar coordinates in our previous model and included include the length of the major and minor axes. We calculated beta values after an impact at the north pole of three types of celestial bodies, including oblate, spheroid, and prolate, based on the three-axis length information of Dimorphos. We also assumed that the formation of the impact crater would occur in the gravity-dominated regime. In the case of prolate bodies that are elongated in the polar direction, beta tends to be small because the ejection angle from the ellipsoidal surface is small. It has been found that the beta value varies between 3 and 4.5 for oblate and prolate bodies. However, it should be noted that this is within the range of uncertainty of the estimated beta value after the DART impact. In the case of the actual Dimorphos, the impact was on the equatorial plane of an oblate object, so it is estimated that the value would be somewhere between the values for oblate and prolate. In addition, the azimuthal anisotropy of the ejecta curtain observed after the DART impact may be explained by the curvature in the latitude and longitude directions.