Zero,minimum and maximum relative radial acceleration for planar formation flight dynamics near triangular libration points in the Earth–Moon system

Assume a constellation of satellites is flying near a given nominal trajectory around _L4$L_4$ or _L5$L_5$ in the Earth–Moon system in such a way that there is some freedom in the selection of the geometry of the constellation. We are interested in avoiding large variations of the mutual distances between spacecraft. In this case, the existence of regions of zero and minimum relative radial acceleration with respect to the nominal trajectory will prevent from the expansion or contraction of the constellation. In the other case, the existence of regions of maximum relative radial acceleration with respect to the nominal trajectory will produce a larger expansion and contraction of the constellation. The goal of this paper is to study these regions in the scenario of the Circular Restricted Three Body Problem by means of a linearization of the equations of motion relative to the periodic orbits around _L4$L_4$ or _L5$L_5$. This study corresponds to a preliminar planar formation flight dynamics about triangular libration points in the Earth–Moon system. Additionally, the cost estimate to maintain the constellation in the regions of zero and minimum relative radial acceleration or keeping a rigid configuration is computed with the use of the residual acceleration concept. At the end, the results are compared with the dynamical behavior of the deviation of the constellation from a periodic orbit.     

Experimental investigation on deformation behavior of TJ-1 lunar soil simulant subjected to principal stress rotation

The knowledge of mechanical properties of lunar soil is of fundamental importance for the coming exploration of the Moon. This paper aims to investigate the fundamental deformation behavior of lunar soil and the effects of the intermediate principal stress coefficient, deviatoric stress ratio, and mean stress during the principal stress rotation. First, an improved technique was proposed to generate homogeneous samples based on the Multi-layer Undercompaction Method. Second, three series of tests on TJ-1 lunar soil simulant under the principal stress rotation were performed with a hollow cylinder apparatus at Tongji University, China. In each series of tests, only one value of the three variables mentioned above was changed while the others were kept constant. The test results demonstrate that the rotation of principal stress can result in significant plastic deformation, volumetric strain, and non-coaxiality (non-coincidence of the increment direction of principal plastic strain with the principal stress direction) of TJ-1 lunar soil simulant. In addition, it is found that the intermediate principal stress coefficient, deviatoric stress ratio, and mean stress have different influences on the four strain components, i.e. _εz,_εr,_εθ${\epsilon }_z\text{,}{\epsilon }_{\text{r}}\text{,}{\epsilon }_{\theta }$ and _γzθ${\gamma }_{z\theta }$, volumetric strain, and non-coaxiality during the principal stress rotation. The influence of deviatoric stress ratio is relatively stronger than the others. Therefore, the influence of principal stress rotation on the deformation behavior of lunar soil should be taken into account carefully in the design and construction of facilities on the lunar surface in the future.     

Calculation of fast neutron removal cross sections for different lunar soils

The interaction of galactic cosmic rays (GCRs) and solar energetic particles (SEPs) with the lunar surface produces secondary radiations as neutrons. The study of the production and attenuation of these neutrons in the lunar soil is very important to estimate the annual ambient dose equivalent on the lunar surface and for lunar nuclear spectroscopy. Also, understanding the attenuation of fast neutrons in lunar soils can help in measuring of the lunar neutron density profile and to measure the neutron flux on the lunar surface. In this paper, the attenuation of fast neutrons in different lunar soils is investigated. The macroscopic effective removal cross section (_ΣR)$({\mathrm{\Sigma }}_R)$ of fast neutrons was theoretically calculated from the mass removal cross-section values (_ΣR/ρ)$({\mathrm{\Sigma }}_R/\rho )$ for various elements in soils. The obtained values of (_ΣR)$({\mathrm{\Sigma }}_R)$ were discussed according to the density. The results show that the attenuation of fast neutrons is more important in the landing sites of Apollo 12 and Luna 16 than the other landing sites of Apollo and Luna missions.     

Titanium estimates of the central peaks of lunar craters: Implications for sub-surface lithology of moon

Central peaks of 24 lunar craters, having mafic rocks, were studied to estimate their average titanium content and infer the nature of the subsurface lithologies. Titanium contents were derived from Clementine UV–Vis data (415, 750 nm) following the approach of Lucey et al. [Lucey, P.G., Blewett, D.T. and Jolliff, B.L., Lunar iron and titanium abundance algorithms based on final processing of Clementine ultraviolet–visible images, J. Geophys. Res.106 (E8), 20297–20,305, 2000]. _TiO2${\mathrm{TiO}}_2$ content exceeding 1 wt% suggests presence of mantle derived mafic sub-surface rock types (plutonic/volcanic) within the central peaks. Even though, the algorithm used for deriving titanium content is susceptible to variation in topography and sun angle, especially at higher latitudes, careful selection and analyses of data for regions within the central peaks revealed compositional heterogeneities. The results indicate a preponderance of mafic lithologies with low _TiO2${\mathrm{TiO}}_2$ content (<1 wt%) in the central peaks of lunar craters populating the equatorial region. Average titanium content of central peaks can serve as a useful tracer for distinguishing mantle derived mafic subsurface lithologies from those formed during global magma ocean episode.     

The relation between the Black hole mass and the Bulge mass for low redshift AGNs. Part I: Ground-based observations

Using the bulge data from AGN image decomposition with ground-based observations, we calculate the ratios of the central supermassive black hole mass(SMBH) to the Bulge mass (_Mbh/_Mbulge$M_{\text{bh}}/M_{\text{bulge}}$) in a sample of X-ray selected AGNs, including 15 Narrow-line Seyfert 1 galaxies (NLS1s) and 18 broad-line Seyfert 1 galaxies (BLS1s). We found that the mean value of log(_Mbh/_Mbulge)$\log (M_{\text{bh}}/M_{\text{bulge}})$ is -3.81±0.11$-3.81\pm 0.11$ for 15 NLS1s, and -2.91±0.13$-2.91\pm 0.13$ for 18 BLS1s, showing the lower _Mbh/_Mbulge$M_{\text{bh}}/M_{\text{bulge}}$ in NLS1s relative to BLS1s. The calculation shows that the Bulge mass from the host image decomposition in NLS1s is statistically smaller than that from Hubble-type correction method, and a linear mass relation is suggested for NLS1s and a nonlinear mass relation for BLS1s. The studying of host galaxies with ground-based observations strongly limited by the atmospheric seeing. We need to do the decomposition of host images for NLS1s with Hubble Space Telescope observation in the future.     

Semi-empirical model of the maximum electron concentration in the ionosphere: Comparison with data from Toluca (México)

A simple semi-empirical model to determine the maximum electron concentration in the ionosphere (_NmF2$N_m{F}_2$) for South American locations is used to calculate _NmF2$N_m{F}_2$ for a northern hemisphere station in the same longitude sector. _NmF2$N_m{F}_2$ is determined as the sum of two terms, one related to photochemical and diffusive processes and the other one to transport mechanisms. The model gives diurnal variations of _NmF2$N_m{F}_2$ representative for winter, summer and equinox conditions, during intervals of high and low solar activity. Model _NmF2$N_m{F}_2$ results are compared with ionosonde observations made at Toluca-México (19.3°N; 260°E). Differences between model results and observations are similar to those corresponding to comparisons with South American observations. It seems that further improvement of the model could be made by refining the latitude dependencies of coefficients used for the transport term.     

Gravitationally bound geoengineering dust shade at the inner Lagrange point

This paper presents a novel method of space-based geoengineering which uses the mass of a captured near Earth asteroid to gravitationally anchor a cloud of unprocessed dust in the vicinity of the _L1${\mathrm{L}}_1$ position to reduce the level of solar insolation at Earth. It has subsequently been shown that a cloud contained within the zero-velocity curve of the largest near Earth asteroid, Ganymed, can lead to an insolation reduction of 6.58% on Earth, which is significantly larger than the 1.7% required to offset a 2 °C increase in mean global temperature. The masses of the next largest near Earth asteroids are found to be too small to achieve the required level of insolation reduction, however, they are significant enough to be used as part of a portfolio of geoengineering schemes.     

Comparison of the magnetic field before the subsolar magnetopause with the magnetic field in the solar wind before the bow shock

Crossings of the magnetopause near the subsolar point are analyzed using data of THEMIS mission. Variations of the magnetic field near magnetopause measured by one of THEMIS satellites are studied and compared with simultaneous measurements in the solar wind by another THEMIS satellite. The time delay of the solar wind arrival at the subsolar point of the magnetopause is taken into account. 30 and 90 s averaging of the magnetic field in the magnetosheath is produced. The results of averaging are compared with the results of measurements in the solar wind before the bow shock and foreshock. It is shown, that _Bx$B_x$ component of the magnetic field near magnetopause is near to zero, which supports the possibility to consider the magnetopause as the tangential discontinuity. Comparatively good correlation of _By$B_y$ component in the solar wind and near the magnetopause is observed. The correlation of _Bz$B_z$ component near the magnetopause and IMF is practically absent, the sign of the _Bz$B_z$ near the subsolar point does not coincide with the sign of IMF _Bz$B_z$ in ∼$\sim$30% cases.     

Nonlinear electromagnetic perturbations in a degenerate electron–positron plasma

Nonlinear propagation of fast and slow magnetosonic perturbation modes in an ultra-cold, degenerate (extremely dense) electron–positron (EP) plasma (containing non-relativistic, ultra-cold, degenerate electron and positron fluids) has been investigated by the reductive perturbation method. It is shown that due to the property of being equal mass of the plasma species (_me=_mp$m_e=m_p$, where _me$m_e$ and _mp$m_p$ are electron and positron mass, respectively), the degenerate EP plasma system supports the K-dV solitons which are associated with either fast or slow magnetosonic perturbation modes. It is also found that the basic features of the electromagnetic solitary structures, which are found to exist in such a degenerate EP plasma, are significantly modified by the effects of degenerate electron and positron pressures. The applications of the results in an EP plasma medium, which occurs in compact astrophysical objects, particularly in white dwarfs, have been briefly discussed.     

Medium resolution near-infrared spectra of the host galaxies of nearby quasars

We present medium resolution near-infrared host galaxy spectra of low redshift quasars, PG 0844+349$0844+349$ (z = 0.064), PG 1226+023$1226+023$ (z = 0.158), and PG 1426+015$1426+015$ (z = 0.086). The observations were done by using the Infrared Camera and Spectrograph (IRCS) at the Subaru 8.2 m telescope. The full width at half maximum of the point spread function was about 0.3 arcsec by operations of an adaptive optics system, which can effectively resolve the quasar spectra from the host galaxy spectra. We spent up to several hours per target and developed data reduction methods to reduce the systematic noises of the telluric emissions and absorptions. From the obtained spectra, we identified absorption features of Mg I (1.503 μm), Si I (1.589 μm) and CO (6-3) (1.619 μm), and measured the velocity dispersions of PG 0844+349$0844+349$ to be 132 ± 110 km s⁻¹ and PG 1426+015$1426+015$ to be 264 ± 215 km s⁻¹. By using an _MBH–σ$M_{\text{BH}}''–''\sigma$ relation of elliptical galaxies, we derived the black hole (BH) mass of PG 0844+349$0844+349$, log(_MBH/_M⊙)=7.7±5.5$\log (M_{\text{BH}}/M_{\odot })=7.7\pm 5.5$ and PG 1426+015,log(_MBH/_M⊙)=9.0±7.5$1426+015\text{,}\log (M_{\text{BH}}/M_{\odot })=9.0\pm 7.5$. These values are consistent with the BH mass values from broad emission lines with an assumption of a virial factor of 5.5.     

Dynamics of the plasma sheet in the magnetotail: Interrelation of turbulent flows and thin current sheet structures

Dynamics of the magnetotail involves elementary processes of magnetic field merging (reconnection layer formation) occurring on medium spatial scales. Every such process features two different stages, a fast one and a subsequent slower one. The corresponding short time scale _T1$T_1$ is associated with disturbances propagating in the tail lobes. The longer time scale _T2$T_2$ is associated with plasma motions in the plasma sheet. A disturbance appearing in the magnetotail on the time scale _T1$T_1$ results in a loss of equilibrium in the plasma sheet. By means of theoretical argument and numerical simulation, it is shown that the relaxation process which follows on the time scale _T2$T_2$, produces extremely thin embedded current sheets, along with generation of fast plasma flows. The process provides an effective mechanism for transformation of magnetic energy accumulated in the magnetotail, into energy of plasma flows. The fast flows may drive turbulent motions on shorter spatial scales. In their turn, those motions can locally produce very thin current sheets; after that, nonlinear tearing process leads to generation of neutral lines, and reconnection. The latter produces new fast disturbances on the time scale _T1$T_1$ closing the feedback loop.     

On the effects of each term of the geopotential perturbation along the time I: Quasi-circular orbits

This paper provides a useful new method to determine minimum and maximum range of values for the degree and order of the geopotential coefficients required for simulations of orbits of satellites around the Earth. The method consists in a time integration of the perturbing acceleration coming from each harmonic of the geopotential during a time interval T. More precisely, this integral represents the total velocity contribution of a specific harmonic during the period T  . Therefore, for a pre-fixed minimum contribution, for instance 1×10^-8$1\times {10}^{-8}$ m/s during the period of time T, any harmonic whose contribution is below this value can, safely, be neglected. This fact includes some constraints in the degree and order of the terms which are present in the geopotential formula, saving computational efforts compared to the integration of the full model. The advantage of this method is the consideration of other perturbations in the dynamics (we consider the perturbations of the Sun, the Moon, and the direct solar radiation pressure with eclipses), since these forces affect the value of the perturbation of the geopotential, because these perturbations depend on the trajectory of the spacecraft, that is dependent on the dynamical model used. In this paper, we work with quasi-circular orbits and we present several simulations showing the bounds for the maximum degree and order (M) that should be used in the geopotential for different situations, e. g., for a satellite near 500 km of altitude (like the GRACE satellites at the beginning of their mission) we found 35?M?198$35?M?198$ for T=1$T=1$ day. We analyzed the individual contribution of the second order harmonic (_J2$J_2$) and we use its behavior as a parameter to determine the lower limit of the number of terms of the geopotential model. In order to test the accuracy of our truncated model, we calculate the mean squared error between this truncated model and the “full” model, using the CBERS (China-Brazil Earth Resources Satellite) satellite in this test.