分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Aims. An asymmetric dust cloud was detected around the Moon by the Lunar Dust Experiment on board the Lunar Atmosphere and Dust Environment Explorer mission. We investigate the dynamics of the grains that escape the Moon and their configuration in the Earth-Moon system. Methods. We use a plausible initial ejecta distribution and mass production rate for the ejected dust. Various forces, including the solar radiation pressure and the gravity of the Moon, Earth, and Sun, are considered in the dynamical model, and direct numerical integrations of trajectories of dust particles are performed. The final states, the average life spans, and the fraction of retrograde grains as functions of particle size are computed. The number density distribution in the Earth-Moon system is obtained through long-term simulations. Results. The average life spans depend on the size of dust particles and show a rapid increase in the size range between $1\, \mathrm{\mu m}$ and $10\, \mathrm{\mu m}$. About ${3.6\times10^{-3}\,\mathrm{kg/s}}$ ($\sim2\%$) particles ejected from the lunar surface escape the gravity of the Moon, and they form an asymmetric torus between the Earth and the Moon in the range $[10\,R_\mathrm{E},50\,R_\mathrm{E}]$, which is offset toward the direction of the Sun. A considerable number of retrograde particles occur in the Earth-Moon system.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： It is expected since the early 1970s that tenuous dust rings are formed by grains ejected from the Martian moons Phobos and Deimos by impacts of hypervelocity interplanetary projectiles. In this paper, we perform direct numerical integrations of a large number of dust particles originating from Phobos and Deimos. In the numerical simulations, the most relevant forces acting on dust are included: Martian gravity with spherical harmonics up to 5th degree and 5th order, gravitational perturbations from the Sun, Phobos, and Deimos, solar radiation pressure, as well as the Poynting-Robertson drag. In order to obtain the ring configuration, simulation results of various grain sizes ranging from submicron to 100 microns are averaged over a specified initial mass distribution of ejecta. We find that for the Phobos ring grains smaller than about 2 microns are dominant; while the Deimos ring is dominated by dust in the size range of about 5-20 microns. The asymmetries, number densities and geometrical optical depths of the rings are quantified from simulations. The results are compared with the upper limits of the optical depth inferred from Hubble observations. We compare to previous work and discuss the uncertainties of the models.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Lunar dust particles are generated by hypervelocity impacts of interplanetary micron-meteoroids onto the surface of the Moon, which seriously threatens the security of explorations. Studying the lunar dust dynamics helps to understand the origin and migration mechanism of lunar dust, and to provide the theoretical guidelines for the orbital design of lunar space missions. This paper reviews previous research on the lunar dust dynamics, including the interplanetary impactor environment at the Earth-Moon system, the mass production rate, the initial mass, speed and ejecta angle distributions, the related space exploration missions, the dynamical model and spatial distribution of dust particles originating from the lunar surface in the whole Earth-Moon system.
分类： 数学 >> 计算数学 分类： 数学 >> 应用数学 提交时间： 2017-08-22
摘要： Many numerical methods have been proposed in the last 30 years for inverse problems. While very successful in many cases, progress has lagged in other areas of applications which are forced to rely on {\em limited-aperture} measurements. In this paper, we introduce some techniques to retrieve the other data that can not be measured directly. We consider the inverse acoustic scattering of time harmonic plane waves and take the scattering amplitude to be the measurements. Assume that the scattering amplitude can only be measured with observation directions restricted in $S^{n-1}_0$, which is compactly supported in the unit sphere. Based on the reciprocity relation of the scattering amplitude, we prove a special symmetric structure of the corresponding multi-static response matrix. This will also be verified by numerical examples. Combining this, with the help of the Green's formula for the scattered field, we introduce an iterative scheme to retrieve approximate {\em full-aperture} scattering amplitude. As an application, using a recently proposed direct sampling method [28], we consider the fast and robust sampling methods with {\em limited-aperture} measurements. Some numerical simulations are conducted with noisy data, and the results will further verify the effectiveness and robustness of the proposed data retrieval method and of the sampling method for inverse acoustic scattering problems.
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