Evolution of periodic orbits near the Lagrangian point L2

A study of the evolution of the periodic and the quasi-periodic orbits near the Lagrangian point L₂, which is located to the right of the smaller primary on the line joining the primaries and whose distance from the more massive primary is greater than the distance between the primaries, in the framework of restricted three-body problem for the Sun–Jupiter, Earth–Moon (relatively large mass ratio) and Saturn–Titan (relatively small mass ratio) systems is made. Two families of periodic orbits around the smaller primary are identified using the Poincaré surface of section method – family I (initially elliptical, gradually becomes egg-shaped with the increase in the Jacobi constant C and elongated towards the more massive primary) and family II (initially egg-shaped orbits elongated towards L₂ and gradually becomes elliptical with the increase in C). The family I in the Sun–Jupiter and Saturn–Titan systems contains two separatrix caused by third-order and fourth-order resonances, while the Earth–Moon system has only one separatrix which is caused by third-order resonances. Also in the Sun–Jupiter and the Saturn–Titan systems, family I merge with family II, around Jacobian constant 3.0393 and 3.0163, respectively, while in the Earth–Moon system, family II evolves separately from two different branches. The two branches merge at C = 3.184515. In the Earth–Moon system, the family II contains a separatrix due to third-order resonances which is absent in the other two systems.     

Variability of foE in the equatorial ionosphere with solar activity

This research examined the variability of f_oE in the equatorial ionosphere with solar activity within the equatorial ionospheric anomaly region. Ionosonde data recorded at Ouagadougou (lat. 12.4°N, long. 1.5°W and magnetic dip 1.43°N) were engaged to study the transient variations of the critical frequency of the E-layer (f_oE) and its dependence on solar activity. The study revealed that f_oE increases with the increase in solar intensity of the sun. The variability of the f_oE decreases with increases in the solar activity. The maximum value of the f_oE is at local noon when the ionosphere is stable; the variability at this local time is minimal. The minimum value of the f_oE is at sunrise and sunset, at this period on local time the equatorial ionosphere recorded its maxima variability. Irrespective of the degree of solar activity, f_oE is observed to be maximum in June solstice, followed by the equinoxes and minimum in December solstice. Equinoctial asymmetry occurred in the variation of the relative standard deviation of f_oE with maximum in September/March equinox for low/high solar activity.     

Two-dimensional phase plane structure and the stability of the orbital motion for space debris in the geosynchronous ring

Based on the orbital resonance model, we study the two-dimensional phase plane structure of the motion of space debris orbiting the geosynchronous ring under the combined effects of the tesseral harmonics J₂₂, J₃₁ and J₃₃ of the Earth’s gravitational field. We present the main characteristic parameters of the two-dimensional phase plane structure. We also analyze the stability of the two-dimensional phase plane structure with numerical method. Our main findings indicate that the combined effects of the tesseral harmonics J₂₂, J₃₁ and J₃₃ fully determine the two-dimensional phase plane structure of the space debris, and it remains robust under the effect of the Earth’s actual gravitational field, the luni-solar perturbations and the solar radiation pressure with the normal area-to-mass ratios.     

强不规则天体引力场中的动力学研究进展

小行星探测与彗星探测是深空探测的重要方面。一般来说,小行星和彗星因质量都不足以使得万有引力克服应力达到流体静力学平衡,而具有强不规则的外形。研究强不规则天体引力场中的动力学行为及其内在机制,是探测器被不规则天体捕获并对其形成近距离探测轨道的基础。从引力场模型和动力学行为两个方面综述了强不规则天体引力场中动力学的研究进展,在引力场模型的研究方面介绍了强不规则天体引力场建模的球谐函数摄动展开模型、简单特殊体模型及多面体模型的研究现状,在动力学机制的研究方面介绍了强不规则天体引力场中的周期轨道和拟周期轨道、平衡点、流形、分岔与共振以及混沌运动的研究现状,指出了这些方面研究的重点与难点。分析了强不规则体引力场中动力学的研究趋势。     

A different method to update monthly median hmF2 values

The height, h_mF2, and the electron density, N_mF2, of the F2 peak are key model parameters to characterize the actual state of the ionosphere. These parameters, or alternatively the propagation factor, M3000F2, and the critical frequency, f_oF2, of the F2 peak, which are related to h_mF2 and N_mF2, are used to anchor the electron density vertical profile computed with different models such as the International Reference Ionosphere ( Bilitza, 2002), as well as for radio propagation forecast purposes. Long time series of these parameters only exist in an inhomogeneous distribution of points over the surface of Earth, where dedicated instruments (typically ionosondes) have been working for many years. A commonly used procedure for representing median values of the aforementioned parameters all over the globe is the one recommended by the ITU-R ( ITU-R, 1997). This procedure, known as the Jones and Gallet mapping technique, was based on ionosondes measurements gathered from 1954 to 1958 by a global network of around 150 ionospheric stations (  and ). Even though several decades have passed since the development of that innovative work, only few efforts have been dedicated to establish a new mapping technique for computing h_mF2 and N_mF2 median values at global scale or to improve the old method using the increased observational database. Therefore, in this work three different procedures to describe the daily and global behavior of the height of the F2 peak are presented. All of them represent a different and simplified method to estimate h_mF2 and are based on different mathematical expressions. The advantages and disadvantages of these three techniques are analyzed, leading to the conclusion that the recommended procedure to represent h_mF2 is best characterized by a Spherical Harmonics expansion of degree and order equal to 15, since the differences between the h_mF2 values obtained with the Jones and Gallet technique and those obtained using the abovementioned procedure are of only 1%.     

Comparing IRI and a regional model with ionosonde measurements in Pakistan

We have used the technique of expansion in Empirical Orthogonal Functions (EOFs) to develop regional models of the critical frequencies of E and F₂ layers (f_oE, f_oF₂), peak height (h_mF₂), and semi-thickness of F₂ layer (Y_mF₂) over Pakistan. In the present study levels of solar activity specified by Smoothed Sunspot Number (R) from 10 to 200 are taken into account. The magnetic dip angle for the model ranges from 30° to 60°. We have compared the regional model and the International Reference Ionosphere (IRI) with measurements of three ionosondes in Pakistan. The model parameters f_oE and f_oF₂ are found overall comparable to the observed hourly median values during daytime at Karachi (geographic latitude = 24.95°N, longitude = 67.13°E, magnetic inclination = 37°), Multan (30.18°N, 71.48°E, 45°) and Islamabad (33.75°N, 73.13°E, 51.5°) during the years 1988, 1996 and 2000. For h_mF₂ the computed values by regional and IRI model for the year 1995 are found close to each other. However, for Y_mF₂the results are better during daytime as compared to nighttime.     

A deformation model of flexible,HAMR objects for accurate propagation under perturbations and the self-shadowing effects

A new type of space debris in near geosynchronous orbit (GEO) was recently discovered and later identified as exhibiting unique characteristics associated with high area-to-mass ratio (HAMR) objects, such as high rotation rates and high reflection properties. Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that its motion depends on the actual effective area, orientation of that effective area, reflection properties and the area-to-mass ratio of the object is not stable over time. Previous investigations have modelled this type of debris as rigid bodies (constant area-to-mass ratios) or discrete deformed body; however, these simplifications will lead to inaccurate long term orbital predictions. This paper proposes a simple yet reliable model of a thin, deformable membrane based on multibody dynamics. The membrane is modelled as a series of flat plates, connected through joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account through lump masses at the joints. The attitude and orbital motion of this flexible membrane model is then propagated near GEO to predict its orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field (J₂), third body gravitational fields (the Sun and Moon) and self-shadowing. These results are then compared to those obtained for two rigid body models (cannonball and flat rigid plate). In addition, Monte Carlo simulations of the flexible model by varying initial attitude and deformation angle (different shape) are investigated and compared with the two rigid models (cannonball and flat rigid plate) over a period of 100?days. The numerical results demonstrate that cannonball and rigid flat plate are not appropriate to capture the true dynamical evolution of these objects, at the cost of increased computational time.     

Rotational constants of linear and/or bent Cn+1H and CnN(n = 1–6): A DFT study

The geometries, dipole moments, and rotational constants for the linear and/or bent cations, C_n+1H⁺ and C_nN⁺(n = 1–6), were studied by the B3LYP method with the modest basis sets. For C_nH⁺(n = odd; 3, 5, 7) and C_nN⁺(n = even; 2, 4, 6), the theoretical rotational constants (B_es) of closed-shell singlet C₃H⁺, C₅H⁺, C₇H⁺, CCN⁺, C₄N⁺, and C₆N⁺ were calculated to be about 11,244, 2420, 885.2, 11,970, 2439, and 880.8 MHz, respectively. By contrast, the triplets are stable than the corresponding singlets for C_nH⁺(n = odd; 2, 4, 6) and C_nN⁺(n = even; 3, 5) except CN⁺.     

Effects of UV-B radiation on photosynthesis activity of Wolffia arrhiza as probed by chlorophyll fluorescence transients

The higher plant Wolffia arrhiza is regarded to be well suited concerning the provision of photosynthetic products in the cycle of matter of a Controlled Ecological Life Support System (CELSS) to be established in the context of extraterrestrial, human-based colonization and long-term space flight. Since UV radiation is one major extraterrestrial environmental stress for growth of any plant, effects of UV-B radiation on W. arrhiza were assessed in the present study. We found that UV-B radiation significantly inhibited photosynthetic CO₂ assimilation activity, and the contents of chlorophyll a, chlorophyll b (Chl a, Chl b) and carotenoids considerably decreased when plants were exposed to UV-B radiation for 12 h. High UV-B radiation also declined the quantum yield of primary photochemistry (φ_po), the quantum yield for electron transport (φ_Eo) and the efficiency per trapped excitation (Ψ_o) in W. arrhiza simultaneously, while the amount of active PSII reaction centers per excited cross section (RC/CS) and the total number of active reaction centers per absorption (RC/ABS) had comparative changes. These results indicate that the effects of UV-B radiation on photosynthesis of W. arrhiza is due to an inhibition of the electron transport and via inactivation of reaction centers, but the inhibition may take place at more than one site in the photosynthetic apparatus.     

Precursory signature of several major earthquakes studied using 40 kHz low frequency signal

To investigate the precursory signature of earthquakes on low frequency (LF) signal propagation, six earthquakes, having magnitude greater than equal to 6.5 and depth less than equal to 30 km, are being studied. The base line level of 40 kHz signal, transmitted from JJY station, Japan, is analysed with respect to V_d statistical parameter. Results show that the V_d parameter values starts fluctuating from its ambient levels before and during the days of the earthquakes, with significant variation starting 1–3 days prior to the earthquake concerned. This present study is an approach for identifying the precursory signatures of earthquakes on LF signal propagation using a new methodology with V_d parameter.     

High precision dynamic model and control considering J2 perturbation for spacecraft hovering in low orbit

For spacecraft hovering in low orbit, a high precision spacecraft relative dynamics model without any simplification and considering J₂ perturbation is established in this paper. Using the derived model, open-loop control and closed-loop control are proposed respectively. Gauss's variation equations and the coordinate transformation method are combined to deal with the relative J₂ perturbation between the two spacecraft. The sliding mode controller is adopted as the closed-loop controller for spacecraft hovering. To improve the control accuracy, the relative J₂ perturbation is regarded as a known parameter term in the closed-loop controller. The external uncertainty perturbations except J₂ perturbation are estimated by numerical difference method, and the boundary layer method is used to weaken the impact of chattering on the sliding mode controller. The open-loop control of spacecraft hovering with the relative J₂ perturbation and without the relative J₂ perturbation are simulated and compared, and the results prove that the accuracy of open-loop control with relative J₂ perturbation has been significantly improved. Similarly, the simulation of the closed-loop control are presented to validate the effectiveness of the designed sliding mode controller, and the results demonstrate that the designed sliding mode controller including the derived relative J₂ perturbation can guarantee the high accuracy and robustness of spacecraft hovering in long-term mission.     

Antioxidant capacity reduced in scallions grown under elevated CO2 independent of assayed light intensity

Long-duration manned space missions mandate the development of a sustainable life support system and effective countermeasures against damaging space radiation. To mitigate the risk of inevitable exposure to space radiation, cultivation of fresh fruits and vegetables rich in antioxidants is an attractive alternative to pharmacological agents. However it has yet to be established whether antioxidant properties of crops can be preserved or enhanced in a space environment where environmental conditions differ from that which plants have acclimated to on earth. Scallion (Allium fistulosum) rich in antioxidant vitamins C and A, and flavonoids was used as a model plant to study the impact of a range of CO₂ concentrations and light intensities that are likely encountered in a space habitat on food quality traits. Scallions were hydroponically grown in controlled environmental chambers under a combination of 3 CO₂ concentrations of 400, 1200 and 4000 μmol mol⁻¹ and 3 light intensity levels of 150, 300, 450 μmol m⁻² s⁻¹. Total antioxidant activity (TAA) of scallion extracts was determined using a radical cation scavenging assay. Both elevated CO₂ and increasing light intensity enhanced biomass accumulation, but effects on TAA (based on dry weight) differed. TAA was reduced for plants grown under elevated CO₂, but remained unchanged with increases in light intensity. Elevated CO₂ stimulated greater biomass production than antioxidants, while an increase in photosynthetic photo flux promoted the synthesis of antioxidant compounds at a rate similar to that of biomass. Consequently light is a more effective stimulus than CO₂ for antioxidant production.     

Optimal H∞ robust output feedback control for satellite formation in arbitrary elliptical reference orbits

A two degree-of-freedom signal-based optimal H_∞ robust output feedback controller is designed for satellite formation in an arbitrary elliptical reference orbit. Based on high-fidelity linearized dynamics of relative motion, uncertainties introduced by non-zero eccentricity and gravitational J2 perturbation are separated to construct a robust control model. Furthermore, a distributed robust control model is derived by modifying the perturbed robust control model of each satellite with the eigenvalues of the Laplacian matrix of the communication graph, which represent uncertainty in the communication topology. A signal-based optimal H_∞ robust controller is then designed primarily. Considering that the uncertainties involved in the distributed robust control model have a completely diagonal structure, the corresponding analyses are made through structured singular value theory to reduce the conservativeness. Based on simulation results, further designs including increasing the degrees of freedom of the controller, modifying the performance and control weighted functions, adding a post high-pass filter according to the dynamic characteristics, and reducing the control model are made to improve the control performance. Nonlinear simulations demonstrate that the resultant optimal H_∞ robust output feedback controller satisfies the robust performance requirements under uncertainties caused by non-zero eccentricity, J2 perturbation, and varying communication topology, and that 5 m accuracy in terms of stable desired formation configuration can be achieved by the presented optimal H_∞ robust controller. In addition to considering the widely discussed uncertainties caused by the orbit of each satellite in a formation, the optimal H_∞ robust output feedback control model presented in the current work considers the uncertainties caused by varying communication topology in the satellite formation that works in a cooperative way. Other new improvements include adopting a new method to more accurately describe and analyze the effects of the higher-order J2 perturbation, combining all the uncertainties into a diagonal structure, and utilizing a structured singular value to synthesize and analyze the controller.     

Global electric circuit modulation of winter cyclone vorticity in the northern high latitudes

Small changes in extended winter (November–March) 500 hPa vorticity area index (VAI) values for the 60–80°N latitude band are shown to be positively correlated with changes in a proxy for the high latitude ionosphere-to-surface current density _Jz$J_z$.     

Effects of in-track maneuver on Sun illumination conditions of near-circular low Earth orbits

By developing approximate analytical models considering the J₂ perturbation, the effects of an in-track maneuver on the orbital Sun illumination conditions of near-circular low Earth orbits are analyzed. First, two approximate models for the variations in orbital sunshine angles are developed, one for variations at a given time and the other for variations at a given argument of latitude. Next, two approximate models for variations in orbital arc in Earth shadow are developed, one considers the small eccentricity and the other uses the zero eccentricity. Finally, the developed approximate models are applied to analyzing the Sun illumination conditions of a typical in-track maneuver mission on a near-circular low Earth orbit. From the results obtained, three major conclusions can be drawn. First, the variations in orbital sunshine angles at a given time may reach tens of degrees when the drifting time reaches hundreds of orbital periods, and the approximate model for that situation cannot effectively approach the numerical results. Second, the variations in orbital sunshine angles for any given argument of latitude are only a couple of degrees even when the drifting time reaches 500 orbital periods, and the approximation model developed can effectively approach the numerical results. Third, for variations in orbital arc in Earth shadow, the approximate model considering the small eccentricity has simple expressions and can effectively approach the numerical results; in contrast, the approximate model using the zero eccentricity has relatively worse precision.     

The iron Kα-line diagnostics of the rotating black hole metric in Seyfert galaxies

Observations of Seyfert galaxies in X-ray region reveal the wide emissive lines in their spectra, which can arise in inner parts of accretion disks, where the effects of General Relativity (GR) must be taken into account. A spectrum of a solitary emission line of a hot spot in Kerr accretion disk is simulated depending on the radial coordinate r and the angular momentum a = J/M of a black hole, under the assumption of equatorial circular motion of a hot spot. It is shown that the characteristic two-peak line profile with the sharp edges arises at a large distance (about r ≈ (3–10) r_g). The inner regions emit the line, which is observed with one maximum and extremely wide red wing. We present results of simulations for the isothermal and Shakura–Sunayev disks.     

Gamma ray bursts: Short vs. long

Short and long GRBs are thought to be two distinct classes based on their different duration and spectrum. Through the spectral analysis of two similarly selected samples of BATSE short and long GRBs, we show that short GRBs are harder than long events, confirming what found from the comparison of their hardness ratio. However, this spectral diversity seems to be due to a harder low energy spectral component of short GRBs, rather than a (slightly higher) peak energy. Interestingly short GRBs have a spectrum which is similar to the spectrum of the emission of the first 1–2 s of long events. We find evidence that short GRBs are inconsistent with the E_peak–E_iso correlation defined by long bursts while they follow the same E_peak–L_iso correlation of long GRBs. These results, coupled to the similar variability timescale of short events and the first seconds of long ones, suggest that a common (or similar) dissipation mechanism could operate in both classes. The difference in the duration would then be due mainly to the central engine lifetime.     

Stability of relative equilibria of the full spacecraft dynamics around an asteroid with orbit–attitude coupling

The full dynamics of spacecraft around an asteroid, in which the spacecraft is considered as a rigid body and the gravitational orbit–attitude coupling is taken into account, is of great value and interest in the precise theories of the motion. The spectral stability of the classical relative equilibria of the full spacecraft dynamics around an asteroid is studied with the method of geometric mechanics. The stability conditions are given explicitly based on the characteristic equation of the linear system matrix. It is found that the linearized system decouples into two entirely independent subsystems, which correspond to the motions within and outside the equatorial plane of the asteroid respectively. The system parameters are divided into three groups that describe the traditional stationary orbit stability, the significance of the orbit–attitude coupling and the mass distribution of the spacecraft respectively. The spectral stability of the relative equilibria is investigated numerically with respect to the three groups of system parameters. The relations between the full spacecraft dynamics and the traditional spacecraft dynamics, as well as the effect of the orbit–attitude coupling, are assessed. We find that when the orbit–attitude coupling is strong, the mass distribution of the spacecraft dominates the stability of the relative equilibria; whereas when the orbit–attitude coupling is weak, both the mass distribution and the traditional stationary orbit stability have significant effects on the stability. We also give a criterion to determine whether the orbit–attitude coupling needs to be considered.     

Study on O2 generation and CO2 absorption capability of four co-cultured salad plants in an enclosed system

The ability to generate O₂ and absorb CO₂ of several co-cultured vegetable plants in an enclosed system was studied to provide theoretical reference for the future man-plant integrated tests. Four kinds of salad plants (Lactuca sativa L. var. Dasusheng, Lactuca sativa L. var. Youmaicai, Gynura bicolor and Cichorium endivia L.) were grown in the CELSS Integration Test Platform (CITP). The environmental factors including O₂ and CO₂ concentration were continuously monitored on-line and the plant biomass was measured at the end of the test. The changing rules of O₂ and CO₂ concentration in the system were basically understood and it was found that the O₂ generated by the plants could satisfy the respiratory needs of 1.75 persons by calculation. It was also found that the plants could absorb the CO₂ breathed out by 2 persons when the light intensity was raised to 550 mmol m⁻² s⁻¹ PPF. The results showed that the co-cultured plants hold good compatibility and excellent O₂-generating and CO₂-absorbing capability. They could also supply some fresh edible vegetable for a 2-person crew.     

Correction of B2bot for NeQuick during low solar activity at Hainan station

This work is a continuation of the previous article and it focuses on low solar activity and modeling effort. NeQuick model uses Epstein layer formalism to model each part of the profile. We study the diurnal and seasonal variations of B2_bot, ΔB2 (B2_best − B2_NeQuick2) and R (B2_best/B2_{NeQuick 2}) at Hainan station during low solar activity. The results show it is possible to improve the B2_bot parameter of the NeQuick model at that region during low solar activity. Then, we use a function ?(t) with LT in different seasons to correct the B2_bot formula of NeQuick 2. The correction shows that (1) By the correction formula, the B2_bot of NeQuick is improved. The maximum standard deviation is improved for 9 km. (2) The correction formula is more effective in summer than in equinox and winter and performs better during early morning hours than during the rest of the day.