Influence of dark matter on light propagation in solar system

We investigated the influence of dark matter on light propagation in the solar system. We assumed the spherical symmetry of spacetime and derived the approximate solution of the Einstein equation, which consists of the gravitational attractions caused by the central celestial body, i.e. the Sun, and the dark matter surrounding it. We expressed the dark matter density in the solar system in the following simple power-law form, ?(t,r)=ρ(t)(?/r)^k$?(t\text{,}r)=\rho (t)(?/r{)}^k$, where t is the coordinate time; r, the radius from the central body; ?, the normalizing factor; k, the exponent characterizing r  -dependence of dark matter density; and ρ(t)$\rho (t)$, the arbitrary function of time t. On the basis of the derived approximate solution, we focused on light propagation and obtained the additional corrections of the gravitational time delay and the relative frequency shift caused by the dark matter. As an application of our results, we considered the secular increase in the astronomical unit reported by Krasinsky and Brumberg (2004) and found that it was difficult to provide an explanation for the observed dAU/dt = 15 ± 4 m/century.     

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.     

Roto-orbital dynamics of a triaxial rigid body around a sphere. Relative equilibria and stability

We study the roto-orbital motion of a triaxial rigid body around a sphere, which is assumed to be much more massive than the triaxial body. The associated dynamics of this system, which consists of a normalized Hamiltonian with respect to the fast angles (partial averaging), is investigated making use of variables referred to the total angular momentum. The first order approximation of this model is integrable. We carry out the analysis of the relative equilibria, which hinges principally in the dihedral angle between the orbital and rotational planes and the ratio among the moments of inertia $\rho =(B-A)/(2C-B-A)$. In particular, the dynamics of the body frame, though formally given by the classical Euler equations, experiences changes of stability in the principal directions related to the roto-orbital coupling. When $\rho =1/3$, we find a family of relative equilibria connected to the unstable equilibria of the free rigid body.     

Collisional excitation of vinylidene (H2CC)

Though H₂CO, H₂CS, H₂CCC, H₂CCCC, H₂CCO have been identified in cool interstellar molecular clouds, identification of H₂CC is still awaited. To analyze its spectrum, collisional rate coefficients are required. We have calculated collisional rate coefficients for rotational transitions between 23 levels of ortho and para H₂CC for kinetic temperatures 10, 20, 30, 40, and 50 K. The scattering problem is analyzed using the computer code MOLSCAT where the colliding partner is He atom. The interaction between H₂CC and He has been calculated with GAUSSIAN 2003. For the interaction potential obtained with GAUSSIAN 2003, MOLSCAT is used to derive the parameters q(L,M,M^′|E)$q(L\text{,}M\text{,}{M}^{\prime }|E)$ as a function of energy E   of the colliding partner. After averaging the parameters q(L,M,M^′|E)$q(L\text{,}M\text{,}{M}^{\prime }|E)$ over a Maxwellian distribution, the parameters Q(L,M,M^′|T)$Q(L\text{,}M\text{,}{M}^{\prime }|T)$ as a function of the kinetic temperature T in the cloud are obtained. Finally, the collisional rate coefficients have been calculated.     

A proposal on the test of general relativity by clock transportation experiments

We propose a test of the gravitational time dilation in general relativity by long term clock comparison between two stations separated in height. The geopotential difference between the two National time keeping centers in China, Lintong (A)$(A)$ and Beijing (B)$(B)$ is around 4000 geopotential unit, which corresponds to the height difference of 400 m. Two clocks _CA$C_A$ and _CB$C_B$ are fixed at stations A and B, respectively, which are synchronized at beginning by a portable clock C in a short time period with go-back synchronization approach. After one month, the clock C is again transported between A and B  , comparing the records of the keeping time by clocks _CA$C_A$ and _CB$C_B$, respectively. Calculations show that, after one month, the difference of the time durations between the clocks _CA$C_A$ and _CB$C_B$ is around 121 ns, if general relativity is correct.     

Velocity shear Kelvin-Helmholtz instability with inhomogeneous DC electric field in the magnetosphere of Saturn

In this paper parallel flow velocity shear Kelvin-Helmholtz instability has been studied in two different extended regions of the inner magnetosphere of Saturn. The method of the characteristic solution and kinetic approach has been used in the mathematical calculation of dispersion relation and growth rate of K-H waves. Effect of magnetic field (B), inhomogeneity (P/a), velocity shear scale length ($A_i$), temperature anisotropy ($T_{\perp }/T_{||}$), electric field (E), ratio of electron to ion temperature ($T_e/T_i$), density gradient (${\epsilon }_n{\rho }_i$) and angle of propagation ($\theta$) on the dimensionless growth rate of K-H waves in the inner magnetosphere of Saturn has been observed with respect to $k_{\perp }{\rho }_i$. Calculations of this theoretical analysis have been done taking the data from the Cassini in the inner magnetosphere of Saturn in the two extended regions of Rs ～4.60–4.01 and Rs ～4.82–5.0. In our study velocity shear, temperature anisotropy and magnitude of the electric field are observed to be the major sources of free energy for the K-H instability in both the regions considered. The inhomogeneity of electric field, electron-ion temperature ratio, and density gradient have been observed playing stabilizing effect on K-H instability. This study also indicates the effect of the vicinity of icy moon Enceladus on the growth of K-H instability.     

Variability of the upper troposphere and lower stratosphere observed with GPS radio occultation bending angles and temperatures

Recently, Lewis (2009) introduced a new method for the identification of tropopause heights (TPHs) from GPS radio occultation (RO) bending angles (α)$(\alpha )$. The method uses a covariance transform to identify transitions in a ln(α)$\mathit{ln}(\alpha )$ profile. Lewis validates the results with lapse rate tropopause (LRT) heights from one year of FORMOSAT-3/COSMIC data and radiosondes. In this study we apply the new method to the RO data sets from CHAMP/GRACE (2001–2009) and FORMOSAT-3/COSMIC (2006–2009). These results are the basis for TPH trend estimations for the time period between May 2001 and August 2009 (100 months) based on zonal monthly mean GPS RO data from CHAMP (2001–2008), GRACE (since 2006) and FORMOSAT-3/COSMIC (since 2006). Further, we compare the α$\alpha$ based TPH trends with LRT height trends and discuss the differences, which are largest in the subtropical regions (20°–40°) on both the northern and southern hemisphere. A global increase of the TPH between 5 and 9 m/yr is found for both methods and different data sets (CHAMP/GRACE alone and CHAMP/GRACE plus FORMOSAT-3/COSMIC). The results for the TPH trends are linked with bending angle and temperature trends in the upper troposphere and lower stratosphere region. Generally, an upper tropospheric warming (bending angle decrease) and a lower stratospheric cooling (bending angle increase) is noted.     

Ion and electron superdiffusive transport in the interplanetary space

We study the propagation of energetic particles, accelerated by interplanetary shock waves, upstream of the shock. By using the appropriate propagator, we show that in the case of superdiffusive transport, the time profile of particles accelerated at a traveling planar shock is a power-law with slope 0<γ<1$0<\gamma <1$, at variance with the exponential profile obtained for normal diffusion. By analyzing data sets of interplanetary shocks in the solar wind observed by the Ulysses and the Voyager 2 spacecraft, we find that the time profiles of energetic electrons correspond to power-laws, with slopes γ?0.30–0.98$\gamma ?0.30''–''0.98$, implying a mean square displacement 〈Δx²〉∝t^α$〈\mathrm{\Delta }{x}^2〉\propto t^{\alpha }$, with α=2-γ>1$\alpha =2-\gamma >1$, i.e., superdiffusion. In addition, the propagation of ions is also superdiffusive, with α=1.07–1.13$\alpha =1.07''–''1.13$.     

A combination method using evolutionary algorithms in initial orbit determination for too short arc

With the combination of two evolutionary algorithms EDA and DE, a new method of initial orbit determination for satellites based on ground-based too-short-arc is established. Compared with other algorithms, the proposed method focuses on the most densely populated region in the solution space rather than the individual with best fitness value. Both the global information and local information are well fused in the search of optimum. In the method $(a,e,M)$ are treated as variables of the optimization, and the optimization procedure is carried out as a two-stage hierarchical optimization problem which has three variables for each stage. Kernel density estimation is applied to build the probability distribution model without any assumptions of the specified distribution, accompanied by handling semi-major axis and eccentricity as a pair of dependent variables in the construction of the probability for the correlation between them in the practice. Numerical experiments with real ground-based observations show that the proposed method is applicable to too-short-arc with even 3?s, and the result of bias in several kilometers can be achieved with $5^{″}$ error added to angular measurements.     

An estimation of Envisat’s rotational state accounting for the precession of its rotational axis caused by gravity-gradient torque

The rotational state of Envisat is re-estimated using the specular glint times in optical observation data obtained from 2013 to 2015. The model is simplified to a uniaxial symmetric model with the first order variation of its angular momentum subject to a gravity-gradient torque causing precession around the normal of the orbital plane. The sense of Envisat’s rotation can be derived from observational data, and is found to be opposite to the sense of its orbital motion. The rotational period is estimated to be $(120.674\pm 0.068)·\exp \left((4.5095\pm 0.0096)\times {10}^{-4}·t\right)\text{s}$, where t is measured in days from the beginning of 2013. The standard deviation is 0.760?s, making this the best fit obtained for Envisat in the literature to date. The results demonstrate that the angle between the angular momentum vector and the negative normal of the orbital plane librates around a mean value of $8.53°\pm 0.42°$ with an amplitude from about $0.7°$ (in 2013) to $0.5°$ (in 2015), with the libration period equal to the precession period of the angular momentum, from about 4.8?days (in 2013) to 3.4?days (in 2015). The ratio of the minimum to maximum principal moments of inertia is estimated to be $0.0818\pm 0.0011$, and the initial longitude of the angular momentum in the orbital coordinate system is $40.5°\pm 9.3°$. The direction of the rotation axis derived from our results at September 23, 2013, UTC 20:57 is similar to the results obtained from satellite laser ranging data but about $20°$ closer to the negative normal of the orbital plane.