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Earth observation satellite (EOS) scheduling is critical for improving the performance of Earth observation system. Most of the existing studies on satellite observation scheduling problems focus on static tasks and real-time dynamic tasks also known as emergency tasks while few attempts have been made for common dynamic tasks yet. The common dynamic tasks are characterized by uncertain arrival times and delayable observations while the emergency tasks require immediate observations. The number of common dynamic tasks is rapidly increasing with the expansion of satellite observation applications, which poses great challenges to EOS observation scheduling. To address this issue, this paper investigates the satellite observation scheduling problem with common dynamic tasks. Firstly, a centralized onboard dynamic scheduling framework based on a periodic-triggered rolling horizontal optimization (RHO) strategy is proposed and a novel two-stage mathematical model is established for the periodic rescheduling problem. Secondly, we propose a low-complexity onboard periodic rescheduling algorithm (OPR), which consists of a greedy-based task allocation algorithm, a pointer network (Ptr-network) based task scheduling algorithm and an iterative local search algorithm. In the greedy-based task allocation algorithm, we define a Task-EOS Fitness Indicator (TEFI) and each task is greedily allocated to the EOS with maximum TEFI. In the Ptr-network based task scheduling algorithm, the allocated task sets of all EOSs are fed into the Ptr-network in parallel to generate the observation scheduling result. Afterward, an iterative local search algorithm is proposed to further improve the quality of the observation scheduling result. Finally, extensive experiments are conducted to demonstrate the superiority of the OPR algorithm for the satellite observation scheduling problem with common dynamic tasks. [ABSTRACT FROM AUTHOR]

The paper considers a process of a controlled attitude motion of a dual-spin nanosatellite. The main goal of control is to achieve a gravitationally stabilized position in a circular orbit in the shortest possible time. The dual-spin nanosatellite contains a gravitational damper and an internal rotor inside a movable unit. The movable unit can fulfill small controlled inclination relative to the main body of the nanosatellite. The mathematical model of the attitude dynamics of the nanosatellite is built and appropriate control laws are developed. Simulation results confirm the performance of the gravitational damper and efficiency of the control algorithm. [ABSTRACT FROM AUTHOR]

• The mathematical model of the reachable domain of the contingency return trajectories. • Reachable domain calculation method of the contingency return trajectories based on interval analysis. • Parameter characteristic analysis of reachable domain. The investigation on reachable domain based on interval analysis is performed, which is aimed for the contingency return trajectories during the circumlunar flight stage in manned lunar landing engineering. First, the issue of contingency return trajectory, which adopts a non-coplanar maneuver during the circumlunar flight phase, is expounded upon. The mathematical model of the reachable domain of contingency return trajectories is established. Second, the contingency return trajectory is designed. An improved interval branch and bound algorithm is introduced and a reachable domain calculation method of the contingency return trajectories is proposed. Third, in numerical simulations, by comparing the reachable domain obtained by the traditional brute force method, the accuracy of the method presented in this paper is verified. It also indicates that this method has a higher calculation efficiency. Finally, numerous simulations are conducted to discuss the parameter characteristic of reachable domain by adopting this method. The study conclusions can serve as an important reference for the selection and decision of contingency return trajectory plans in the future manned lunar landing engineering. [ABSTRACT FROM AUTHOR]

In recent times, origami-inspired deployable structures have received significant interest from the research community as a major area of research in the fields of science and technology. This paper deals with the geometry and the deformation behavior of deployable cones based on the four-fold line origami concept. First, a novel geometric design algorithm is presented to develop axially foldable conical structures based on generalized Miura-ori pattern, which is then utilized to investigate the influence of four design parameters on folding geometry. The foldability of thus obtained origami patterns is verified with the help of physical models. The geometric incompatibilities during the deployment are highlighted using a simple experiment, showing the unfolding sequence of a paper model. The deformations due to incompatibilities are analyzed by adopting the concept of pin-jointed truss modeling of the origami structures. A mathematical model of the deployment problem is formulated to capture the deployment deformations of the structure, on the basis of which an algorithm for deformation analyses is developed. One example is considered to characterize the deformation behavior of the conical origami structures as the design parameters of the folding pattern are varied. The analytical findings demonstrate that the fold line strains of the origami cone are very sensitive to the changes in three design parameters, number of origami units (m), fold angle (α 0), and angle θ 2 ; except the length ratio (l r 0). The variation in design parameters may induce bi-stability in the deployment path of the conical structure. The findings of the analytical investigation are verified numerically, demonstrating that the strain responses obtained from the numerical analyses are completely consistent with the analytical results. [ABSTRACT FROM AUTHOR]

This paper proposes a procedure for managing the risk of reentering space objects and risk assessment methodologies used for the process. The proposed procedure comprises three phases encompassing the whole reentry stages of space objects. Mathematical models for assessing the impact risk of the reentering space objects by utilizing the information available during different risk management phases and the recommended risk analysis results for public communication are presented. The concept of the conditional casualty expectation is proposed as the metric representing the reentry risk and the method to compute its profile is introduced. A case study on the risk management procedure with the dataset on an actual reentry event is conducted to demonstrate the efficacy of the proposed procedure. [ABSTRACT FROM AUTHOR]

In this paper, a fundamental approach to analyzing the maneuverability of spacecraft with mounted control moment gyros is addressed by searching feasible angular momentum. The geometrical array of control moment gyros considered is a roof array also known as a 2-SPEED system . Due to the simplicity of the singularity envelope of the array considered, it is reasonably practical to conduct rotational performance analysis of the spacecraft. This maneuverability analysis technique uses a unique chart developed in this work, which allows a guaranteed maximum torque output and angular momentum at any time without concern about the singularity problem of the control moment gyros. Therefore, the purpose of this paper is to provide a conservative method for maneuverability analysis of a spacecraft with installed control moment gyros by searching allowable maximum angular momentum. This method is demonstrated using an illustrative example. [ABSTRACT FROM AUTHOR]

Due to high relative velocities, collisions of spacecraft in orbit with Space Debris (SD) or Micrometeoroids (MM) can lead to payload degradation, anomalies as well as failures in spacecraft operation, or even loss of mission. Flux models and impact risk assessment tools, such as MASTER (Meteoroid and Space Debris Terrestrial Environment Reference) or ORDEM (Orbital Debris Engineering Model), and ESABASE2 or BUMPER II are used to analyse mission risk associated with these hazards. Validation of flux models is based on measured data. Currently, as most of the SD and MM objects are too small (millimeter down to micron sized) for ground-based observations (e.g. radar, optical), the only available data for model validation is based upon retrieved hardware investigations e.g. Long Duration Exposure Facility (LDEF), Hubble Space Telescope (HST), European Retrievable Carrier (EURECA). Since existing data sets are insufficient, further in-situ experimental investigation of the SD and MM populations are required. This paper provides an overview and assessment of existing and planned SD and MM impact detectors. The detection area of the described detectors is too small to adequately provide the missing data sets. Therefore an innovative detection concept is proposed that utilises existing spacecraft components for detection purposes. In general, solar panels of a spacecraft provide a large area that can be utilised for in-situ impact detection. By using this method on several spacecraft in different orbits the detection area can be increased significantly and allow the detection of SD and MM objects with diameters as low as 100 μm. The design of the detector is based on damage equations from HST and EURECA solar panels. An extensive investigation of those panels was performed by ESA and is summarized within this paper. Furthermore, an estimate of the expected sensitivity of the patented detector concept as well as examples for its implementation into large and small spacecraft are presented. [ABSTRACT FROM AUTHOR]

WAM is realized making use of the plasma density data collected via the retarding potential analyser on board the Dynamics Explorer 2 spacecraft, capable to model the scintillation climatology over the northern hemisphere high latitude ionosphere. More recently, WAM has been tuned to model the ionospheric scintillations also over the equatorial latitudes. The effort has been done to support the CIGALA (Concept for Ionospheric Scintillation Mitigation for Professional GNSS in Latin America) project in the assessment of the scintillations climatology over Latin America. The concept of the new release of WAM is the same already adopted for the high latitudes: the in situ measurements, supplemented with an ionospheric model and with the irregularity anisotropy model, are treated to describe the morphology of scintillation, provided a suitable propagation model is used. Significant differences have been included in the low latitudes release to account for the anisotropy of the irregularities and for strong scattering regime. The paper describes the new WAM formulation and presents comparisons of the model predictions with the actual measurements collected in Brazil. [ABSTRACT FROM AUTHOR]

In a geodetic radio frequency observing system the phase center offsets and phase center variations of ground antennae are a fundamental component of mathematical models of the system observables. In this paper we describe work aimed at improving the DORIS Starec ground antenna phase center definition model. Seven antennas were analyzed in the Compact Antenna Test Range (CATR), a dedicated CNES facility. With respect to the manufacturer specified phase center offset, the measured antennae varied between −6 mm and +4 mm due to manufacturing variations. To solve this problem, discussions were held with the manufacturer, leading to an improvement of the manufacturing process. This work results in a reduction in the scatter to ±1 mm. The phase center position has been kept unchanged and associated phase law has been updated and provided to users of the International DORIS Service (IDS). This phase law is applicable to all Starec antennas (before and after manufacturing process consolidation) and is azimuth independent. An error budget taking into account these updated characteristics has been established for the antenna alone: ±2 mm on the horizontal plane and ±3 mm on the up component, maximum error values for antennas named type C (Saunier et al., 2016) produced with consolidated manufacturing process. Finally the impact of this updated characterization on positioning results has been analyzed and shows a scale offset only of the order of +12 mm for the Terrestrial Reference Frame. [ABSTRACT FROM AUTHOR]

With the impact of the Global Navigation Satellite System (GNSS), dual-GNSS constellations are playing an increasingly significant role in positioning, navigation and timing (PNT) applications. Aiming at improving from the existing method, i.e., linearization, of solving the single-point positioning problem under a dual-GNSS, this paper develops a closed-form method for solving PNT problems in the case of six satellites. This method reduces the positioning problem to a simple mathematical problem of finding solutions to a quadratic equation, thereby needing only one receiver clock bias (RCB) as variable. By solving the RCB, the positioning information in three dimensions is obtained by utilizing a linear equation. Compared with the existing method, the closed-form method requires no initial position or iterations. This method thus provides a direct solution to single-point positioning. Further, how to check the uniqueness and the validity of the solutions is also derived. Experimental results verify the validity, applicability and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Using total electron content (TEC) data over one and a half solar cycles (1999–2015) provided by the Center for Orbit Determination in Europe (CODE), this paper proposes a new empirical TEC model for northeast China (40–50N, 120–130E). The model, called TECM-NEC, involves the multiplication of four separable components, including diurnal variation, seasonal variation, geomagnetic field dependency, and solar dependency. Diurnal variation is composed of three parts: the typical daily variation of TEC; corrections of Mid-latitude Summer Nighttime Anomaly (MSNA) that depend on geographic location, season, and local time; and corrections of day-to-night ratio under different seasons and solar activities. Four sub-harmonics of the year with annual, semiannual, four-, and three-month periods are used to describe seasonal variations. For geomagnetic variation, geomagnetic latitude is based on the latest International Geomagnetic Reference Field (IGRF12) model. Compared with similar empirical models, the solar proxy index F10.7P = (F10.7 + F10.7A)/2, where F10.7A is the 81-day running mean of daily F10.7, is chosen as having linear relationship with TEC for the model. This model has 43 coefficients, which are determined by nonlinear least squares fitting (NLSF) technique. The TECM-NEC model fits with the TEC/CODE input data with a bias of 0.03TECU and a RMS deviation of 2.76TECU. The proposed TECM-NEC model can reproduce the MSNA and nighttime TEC enhancements phenomenon over northeast China. [ABSTRACT FROM AUTHOR]

The time-consuming experimental method for handling qualities assessment cannot meet the increasing fast design requirements for the manned space flight. As a tool for the aircraft handling qualities research, the model-predictive-control structured inverse simulation (MPC-IS) has potential applications in the aerospace field to guide the astronauts’ operations and evaluate the handling qualities more effectively. Therefore, this paper establishes MPC-IS for the manual-controlled rendezvous and docking (RVD) and proposes a novel artificial neural network inverse simulation system (ANN-IS) to further decrease the computational cost. The novel system was obtained by replacing the inverse model of MPC-IS with the artificial neural network. The optimal neural network was trained by the genetic Levenberg–Marquardt algorithm, and finally determined by the Levenberg–Marquardt algorithm. In order to validate MPC-IS and ANN-IS, the manual-controlled RVD experiments on the simulator were carried out. The comparisons between simulation results and experimental data demonstrated the validity of two systems and the high computational efficiency of ANN-IS. [ABSTRACT FROM AUTHOR]

Abstract: Period of October–November 2003 provides a wide range of geomagnetic conditions. This paper looks at three intervals: a moderate magnetic disturbance (13–16.10.2003) and two intense magnetic storms (29–31.10 and 20–21.11). One purpose of this paper is to define the behavior of the two parameters of the ionosphere, foF2 (or NmF2) and TEC, in this period. Data of foF2 of European ionosondes and TEC values of global maps for the corresponding coordinates are used. The emphasis is on the study of the synchrony of these parameters, which determine the behavior of the proportionality factor τ(obs) between the TEC and NmF2. The second objective is to compare two methods of determining foF2 during the disturbances, using: (i) the STORM-factor of the IRI model, (ii) the median equivalent slab thickness τ(med), together with the global TEC maps. It is shown that synchrony of variations of TEC and NmF2 does not always exist, which leads to unpredictable behavior of τ(obs). Acceptable option of the calculation of foF2 from TEC is to use τ(med), ensuring compliance with the experimental data better than 0.5MHz in the case of synchrony, and 1.5MHz when it does not exist. The relationship between τ(obs) and the plasmaspheric part of the TEC of the IRI-Plas model is considered. A comprehensive investigation of this relationship in cases where no synchrony may contribute to the development of model of τ(obs) during the disturbances. [Copyright &y& Elsevier]

Abstract: The probability of occurrence of spread-F can be modeled and predicted using neural networks (NNs). This paper presents a feasibility study into the development of a NN based model for the prediction of the probability of occurrence of spread-F over selected equatorial stations within the Brazilian sector. The input space included the day number (seasonal variation), hour (diurnal variation), sunspot number (measure of the solar activity), magnetic index (measure of the magnetic activity) and magnetic position. Twelve years of spread-F data from Brazil (covering the period 1978–1989) measured at the equatorial site Fortaleza (3.9°S, 38.45°W) and low latitude site Cachoeira Paulista (22.6°S, 45.0°W) are used in the development of an input space and NN architecture for the model. Spread-F data that is believed to be related to plasma bubble developments (range spread-F) was used in the development of the model. The model results show the probability of spread-F occurrence as a function of local time, season and latitude. Results from the Brazilian Sector NN (BSNN) based model are presented in this paper, as well as a comparative analysis with a Brazilian model developed for the same purpose. [Copyright &y& Elsevier]

Abstract: A new neural network (NN) based global empirical model for the foF2 parameter, which represents the peak ionospheric electron density, has been developed using extended temporal and spatial geophysical relevant inputs. It has been proposed that this new model be considered as a suitable replacement for the International Union of Radio Science (URSI) and International Radio Consultative Committee (CCIR) model options currently used within the International Reference Ionosphere (IRI) model for the purpose of F2 peak electron density predictions. The most recent version of the model has incorporated data from 135 global ionospheric stations including a number of equatorial stations. This paper concentrates on the ability of this new model to predict foF2 for the equatorial sector, an area that has been identified as problematic within the current IRI peak prediction setup. The improvement in the predictions of the foF2 parameter by the new model as compared to the URSI and CCIR model options of the IRI is demonstrated and the requirement for additional foF2 data from the equatorial zone for the purpose of global modeling of foF2 is highlighted in this paper. [Copyright &y& Elsevier]

The transient dynamic behaviour of supersonic disk-gap-band parachutes in a Mars entry environment involving fluid structure interactions is studied. Based on the multi-material Arbitrary Lagrange–Euler method, the coupling dynamic model between a viscous compressible fluid and a flexible large deformation structure of the parachute is solved. The inflation performance of a parachute with a fixed forebody under different flow conditions is analysed. The decelerating parameters of the parachute, including drag area, opening loads, and coefficients, are obtained from the supersonic wind tunnel test data from NASA. Meanwhile, the evolution of the three-dimensional shape of the disk-gap-band parachute during supersonic inflation is presented, and the structural dynamic behaviour of the parachute is predicted. Then, the influence of the presence of the capsule on the flow field of the parachute is investigated, and the wake of unsteady fluid and the distribution of shock wave around the supersonic parachute are presented. Finally, the structural dynamic response of the canopy fabric under high-pressure conditions is comparatively analysed. The results show that the disk-gap-band parachute is well inflated without serious collapse. As the Mach numbers increase from 2.0 to 2.5, the drag coefficients gradually decrease, along with a small decrease in inflation time, which corresponds with test results, and proves the validity of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

The thermal subsystem of spacecrafts and payloads is always designed with the help of Thermal Mathematical Models. In the case of the Thermal Lumped Parameter (TLP) method, the non-linear system of equations that is created is solved to calculate the temperature distribution and the heat power that goes between nodes. The accuracy of the results depends largely on the appropriate calculation of the conductive and radiative conductances. Several established methods for the determination of conductive conductances exist but they present some limitations for complex geometries. Two new methods are proposed in this paper to calculate accurately these conductive conductances: The Extended Far Field method and the Mid-Section method. Both are based on a finite element calculation but while the Extended Far Field method uses the calculation of node mean temperatures, the Mid-Section method is based on assuming specific temperature values. They are compared with traditionally used methods showing the advantages of these two new methods. [ABSTRACT FROM AUTHOR]

This paper uses surrogate models to reduce the computational cost associated with spacecraft mission design in three-body dynamical systems. Sampling-based least squares regression is used to project the system response onto a set of orthogonal bases, providing a representation of the Δ V required for rendezvous as a reduced-order surrogate model. Models are presented for mid-field rendezvous of spacecraft in orbits in the Earth–Moon circular restricted three-body problem, including a halo orbit about the Earth–Moon L 2 libration point (EML-2) and a distant retrograde orbit (DRO) about the Moon. In each case, the initial position of the spacecraft, the time of flight, and the separation between the chaser and the target vehicles are all considered as design inputs. The results show that sample sizes on the order of 10 2 are sufficient to produce accurate surrogates, with RMS errors reaching 0.2 m/s for the halo orbit and falling below 0.01 m/s for the DRO. A single function call to the resulting surrogate is up to two orders of magnitude faster than computing the same solution using full fidelity propagators. The expansion coefficients solved for in the surrogates are then used to conduct a global sensitivity analysis of the Δ V on each of the input parameters, which identifies the separation between the spacecraft as the primary contributor to the Δ V cost. Finally, the models are demonstrated to be useful for cheap evaluation of the cost function in constrained optimization problems seeking to minimize the Δ V required for rendezvous. These surrogate models show significant advantages for mission design in three-body systems, in terms of both computational cost and capabilities, over traditional Monte Carlo methods. [ABSTRACT FROM AUTHOR]

The base of the dynamics characteristic research on the parachute and vehicle system is to establish a dynamics model, during the parachute descent phase, which can accurately display the relationship among the velocity, altitude and attitude angles as well as the variation of time. This paper starts with a new tracking law – ADRC in Mars entry guidance, which affects the initial states of the parachute deployment point and determines precision landing capability. Then, the influence of unsteady resistance to the parachute in Martian air is considered as the added mass, and a 6DOF nonlinear mathematical model of the parachute and vehicle system is established. [ABSTRACT FROM AUTHOR]

In this paper, the Global Ionospheric Maps (GIMs) during 1998–2012 have been adopted as the primary source of data to generate the Galileo-like ionospheric correction parameters. Taking the previous day GIMs as ingested dataset and the current day GIMs as reference, we have computed the cumulative distribution function (CDF) of TEC (Total Electron Content) error less than 5 TECU (TEC Unit, 1TECU = 10 16 electron/m 2 ) or 20% (denoted as zi 20 ) to study the performance of NeQuick 2 in providing global ionospheric correction. The statistical analysis is carried out to study how the performance changes with seasons, solar activities and geographic latitudes. Our studies showed that: (1) in general, the NeQuick 2 model driven by the previous day GIMs agrees well with the current day GIMs, with monthly averaged zi 20 exceeds 60%. (2) The performance of GIMs-driven-NeQuick model varies with geographic latitudes. The model behaves better in mid-latitudes than in low-latitudes, which is more prominent in northern hemisphere. (3) There is a nonlinear relationship between zi 20 and F10.7. When the solar activity level is low or medium, zi 20 tends to decrease with increasing solar activities. However, when F10.7 increases further to exceed a certain threshold, zi 20 generally shows either saturation or an increase for high solar epoch. The zi 20 decreases with F10.7 more sharply in mid-latitudes than in low-latitudes, in the southern hemisphere than in the northern hemisphere. (4) The seasonal behavior of zi 20 in different latitudinal belts are quite different. In the southern hemisphere, zi 20 mainly presents annual variation, and it is largest in winter and smallest in summer. In the northern hemisphere, the semi-annual variation is dominant, and zi 20 is larger in solstice than in equinox. During the High Solar Activity years, the zi 20 is much larger in summer than in winter in the low-latitude regions. [ABSTRACT FROM AUTHOR]

Abstract: A combined energy and attitude control system (CEACS) is a hybrid system that uses flywheels to store energy and provide a simultaneous attitude control in satellites. Previous work appeared in Advances in Space Research (ASR) employing the proportional-derivative (PD) control has proven that CEACS works well and achieves its mission requirement. However, the in-orbit system performance uncertainties present a challenge to the CEACS attitude pointing capability. Thus, this paper complements the previous mentioned work, and focuses on employing the H∞ optimal attitude control solution for the CEACS attitude control enhancement. The mathematical model and numerical treatments for the CEACS H∞ control architecture are presented. Numerical results show that a better attitude pointing accuracy at least up to 0.043° can be achieved with the H∞ control method. [Copyright &y& Elsevier]

Abstract: This paper presents a novel approach for station-keeping control of a stratospheric airship platform in the presence of parametric uncertainty and external disturbance. First, conceptual design of the stratospheric airship platform is introduced, including the target mission, configuration, energy sources, propeller and payload. Second, the dynamics model of the airship platform is presented, and the mathematical model of its horizontal motion is derived. Third, a fuzzy adaptive backstepping control approach is proposed to develop the station-keeping control system for the simplified horizontal motion. The backstepping controller is designed assuming that the airship model is accurately known, and a fuzzy adaptive algorithm is used to approximate the uncertainty of the airship model. The stability of the closed-loop control system is proven via the Lyapunov theorem. Finally, simulation results illustrate the effectiveness and robustness of the proposed control approach. [Copyright &y& Elsevier]

Abstract: Breakup model is the key area of space debris environment modeling. NASA standard breakup model is currently the most widely used for general-purpose. It is a statistical model found based on space surveillance data and a few ground-based test data. NASA model takes the mass, impact velocity magnitude for input and provides the fragment size, area-to-mass ratio, velocity magnitude distributions for output. A more precise approach for spacecraft disintegration fragment analysis is presented in this paper. This approach is based on hypervelocity impact dynamics and takes the shape, material, internal structure and impact location etc. of spacecraft and impactor, which might greatly affect the fragment distribution, into consideration. The approach is a combination of finite element and particle methods, entitled finite element reconstruction (FER). By reconstructing elements from the particle debris cloud, reliable individual fragments are identified. Fragment distribution is generated with undirected graph conversion and connected component analysis. Ground-based test from literature is introduced for verification. In the simulation satellite targets and impactors are modeled in detail including the shape, material, internal structure and so on. FER output includes the total number of fragments and the mass, size and velocity vector of each fragment. The reported fragment distribution of FER shows good agreement with the test, and has good accuracy for small fragments. [Copyright &y& Elsevier]

Abstract: Estimating the magnetic storm effectiveness of solar and associated interplanetary phenomena is of practical importance for space weather modelling and prediction. This article presents results of a qualitative and quantitative analysis of the probable causes of geomagnetic storms during the 11-year period of solar cycle 23: 1996–2006. Potential solar causes of 229 magnetic storms (Dst ⩽−50nT) were investigated with a particular focus on halo coronal mass ejections (CMEs). A 5-day time window prior to the storm onset was considered to track backward the Sun’s eruptions of halo CMEs using the SOHO/LASCO CMEs catalogue list. Solar and interplanetary (IP) properties associated with halo CMEs were investigated and correlated to the resulting geomagnetic storms (GMS). In addition, a comparative analysis between full and partial halo CME-driven storms is established. The results obtained show that about 83% of intense storms (Dst ⩽−100nT) were associated with halo CMEs. For moderate storms (−100nT< Dst ⩽−50nT), only 54% had halo CME background, while the remaining 46% were assumed to be associated with corotating interaction regions (CIRs) or undetected frontside CMEs. It was observed in this study that intense storms were mostly associated with full halo CMEs, while partial halo CMEs were generally followed by moderate storms. This analysis indicates that up to 86% of intense storms were associated with interplanetary coronal mass ejections (ICMEs) at 1AU, as compared to moderate storms with only 44% of ICME association. Many other quantitative results are presented in this paper, providing an estimate of solar and IP precursor properties of GMS within an average 11-year solar activity cycle. The results of this study constitute a key step towards improving space weather modelling and prediction. [Copyright &y& Elsevier]

Abstract: This paper presents the results of modeling the ionospheric effect of the seismogenic electrostatic field (SEF) seen at the earth’s surface as a perturbation of the vertical atmospheric electrostatic field in the earthquake preparation zone. The SEF distribution at ionospheric altitudes is obtained as an analytical solution of the continuity equation for the electric current density. It is shown that at night, the horizontally large scale SEF can efficiently penetrate into the ionosphere and produce noticeable changes in the horizontal distribution of the F region electron density. The results suggest that the seismogenic electrostatic field could be a possible source for the ionospheric variations observed over Taiwan before the strong Chi Chi earthquake of September 21, 1999. [Copyright &y& Elsevier]

Abstract: In this paper, the phase asynchrony between coronal index and sunspot numbers is investigated. It is found that, (1) the sunspot numbers begin one month earlier than coronal index, which should mathematically lead to phase asynchrony between them but with a slight effect; (2) the 11-year Schwabe cycle is the only one period with statistical significance for coronal index and sunspot numbers, and the difference between the length of the Schwabe cycle of them should also lead to phase asynchrony between them; (3) although coronal index and sunspot numbers are coherent in low-frequency components corresponding to the 11-year Schwabe cycle, they are asynchronous in phase in high-frequency components; (4) their different definitions and physical meanings may be a major reason why there is a phase asynchrony between them. [Copyright &y& Elsevier]

Abstract: The equatorial electric field plays an important role in low-latitude ionospheric plasma drift and its distribution at both quiet and disturbed periods, which should be involved in low-latitude ionospheric correction and prediction models. In this paper, an empirical model is established and utilized in real-time ionospheric correction, which contains the affiliation between the ionospheric disturbances and their electric field origins. This model is built using the nonlinear relations between ionospheric foF2 data from two low-latitude ionosondes and equatorial disturbance field data from an empirical model during fifty storms. The performance of the model during twelve intense storms is evaluated and compared with another empirical correction model, STORM. The latter relies on that long-lived negative storm effects are induced by neutral composition changes. The results of our model show that some sharp increase of foF2 could be captured, whereas STORM only gives the probable estimations. The averaged correction error is reduced by 17%, comparing with STORM. This indicates that the disturbance of the electric fields are also important in low-latitude storm-time ionospheric corrections. [Copyright &y& Elsevier]

Abstract: In this paper, Bonnor–Ebert gas sphere model of polytropic stars has been investigated through an analytical approach. Two confirmed and well-established methods have been used: the Enhanced Lagrangian Formulation Method ELFM and the Boubaker Polynomials Expansion Scheme BPES. Solutions to the related generalized Lane–Emden equation of the second kind have been expressed and plotted. Results have given evidence to the relevance of the dimensionless Bonnor–Ebert radius, in good agreement with some recently proposed profiles. [Copyright &y& Elsevier]

Abstract: The issue considered in this paper is the dynamic behavior of flexible probe based on space probe-cone docking mechanism in the docking process. The theoretical model of docking impact dynamics based on flexible beam is built according to the Lagrange Analytical Mechanics theory. The contact problem is solved by using Hertz point-surface contact model. Assumed Modes Method is introduced to describe the deformation of flexible beam. Runge–Kutta numerical method is used to solve this theoretical model. Results of the theoretical model show a good agreement with the experimental and MSC.Patran/Dytran simulation results. Moreover, the influence of flexible beam parameter on docking impact process is analyzed based on the theoretical model. [Copyright &y& Elsevier]

Abstract: The Crustal Movement Observation Network of China (CMONOC) is one of the major scientific infrastructures, mainly using Global Positioning System (GPS) measurements, to monitor crustal deformation in the Chinese mainland. In this paper, decade-long coordinate time series of 26 continuous GPS sites of CMONOC are analyzed for their noise content using maximum likelihood estimation (MLE). We study the noise properties of continuous GPS time series of CMONOC for the unfiltered, filtered solutions and also the common mode signals in terms of power law plus white noise model. In the spatial filtering, we remove for every time series a common mode error that was estimated from a modified stacking of position residuals from other sites within ∼1000km of the selected site. We find that the common mode signal in our network has a combination of spatially correlated flicker noise and a common white noise with large spatial extent. We demonstrate that for the unfiltered solutions of CMONOC continuous GPS sites the main colored noise is a flicker process, with a mean spectral index of ∼1. For the filtered solutions, the main colored noise is a general power law process, indicating that a major number of the filtered regional solutions have a combination of noise sources or local effects. The velocity uncertainties from CMONOC continuous GPS coordinate time series may be underestimated by factors of 8–16 if a pure white noise model is assumed. In addition, using a white plus flicker noise model, the median values of velocity errors for the unfiltered solutions are 0.16 (north), 0.17 (east) and 0.58 (vertical)mm/yr, and the median values for the filtered solutions are 0.09 (north), 0.10 (east) and 0.40 (vertical)mm/yr. [Copyright &y& Elsevier]

Abstract: This paper presents an analysis of the Total Electron Content (TEC) derived from the International GNSS Service receiver (formerly IGS) at Malindi (2.9°S,40.1°E), Kenya for the periods 2004–2006 during the declining phase of solar cycle 23. The diurnal, monthly and seasonal variations of the TEC are compared with TEC from the latest International Reference Ionosphere model (IRI-2007). The GPS–TEC exhibits features such as an equatorial noon time dip, semi-annual variations, Equatorial Ionization Anomaly and day-to-day variability. The lowest GPS–TEC values are observed near the June solstice and September equinox whereas largest values are observed near the March equinox and December solstice. The mean GPS–TEC values show a minimum at 03:00 UT and a peak value at about 10:00 UT. These results are compared with the TEC derived from IRI-2007 using the NeQuick option for the topside electron density (IRI–TEC). Seasonal mean hourly averages show that IRI-2007 model TEC values are too high for all the seasons. The high prediction primarily occur during daytime hours till around midnight hours local time for all the seasons, with the highest percentage deviation in TEC of more 90% seen in September equinox and lowest percentage deviation in TEC of less than 20% seen in March equinox. Unlike the GPS–TEC, the IRI–TEC does not respond to geomagnetic storms and does overestimate TEC during the recovery phase of the storm. While the modeled and observed data do correlate so well, we note that IRI-2007 model is strongly overestimating the equatorial ion fountain effect during the descending phase of solar cycle, and this could be the reason for the very high TEC estimations. [Copyright &y& Elsevier]

Abstract: Fiber optic probes coupled to a Fourier Transform Infrared (FTIR) spectrometer allow sample analysis without the need to place the sample directly into the instrument. This is particularly attractive for spacecraft lander/rover applications where the additional mechanics, mass and cost associated with excavating and placing a small sample in a sample bay is not desirable. This paper uses numerical modeling to analyze fiber bundle array configurations and fiber numerical apertures to determine their light gathering efficiency and sample size as a function of probe-to-sample distance. The model was validated against experimental measurements for a selection of off the shelf fiber optic probes. The collection efficiency of a probe can be optimized by using a hexagonal packing method, and by using fibers with high numerical apertures. By increasing the numerical aperture of the fibers used in our model probes from 0.2 to 0.5, we were able to increase the collection efficiency of a seven fiber probe from 4.5% to 9.5%, with the peak collection efficiency corresponding to a spot size of diameter 3mm. [Copyright &y& Elsevier]

Abstract: Diurnal, seasonal and latitudinal variations of Vertical Total Electron Content (VTEC) over the equatorial region of the African continent and a comparison with IRI-2007 derived TEC (IRI-TEC), using all three options (namely; NeQuick, IRI01-corr and IRI-2001), are presented in this paper. The variability and comparison are presented for 2009, a year of low solar activity, using data from thirteen Global Positioning System (GPS) receivers. VTEC values were grouped into four seasons namely March Equinox (February, March, April), June Solstice (May, June, July), September Equinox (August, September, October), and December Solstice (November, December, January). VTEC generally increases from 06h00 LT and reaches its maximum value at approximately 15h00–17h00 LT during all seasons and at all locations. The NeQuick and IRI01-corr options of the IRI model predict reasonably well the observed diurnal and seasonal variation patterns of VTEC values. However, the IRI-2001 option gave a relatively poor prediction when compared with the other options. The post-midnight and post-sunset deviations between modeled and observed VTEC could arise because NmF2 or the shape of the electron density profile, or both, are not well predicted by the model; hence some improvements are still required in order to obtain improved predictions of TEC over the equatorial region of the Africa sector. [Copyright &y& Elsevier]

Abstract: The solar wind fills the heliosphere and is the background medium in which coronal mass ejections propagate. A realistic modelling of the solar wind is therefore essential for space weather research and for reliable predictions. Although the solar wind is highly anisotropic, magnetohydrodynamic (MHD) models are able to reproduce the global, average solar wind characteristics rather well. The modern computer power makes it possible to perform full three dimensional (3D) simulations in domains extending beyond the Earth’s orbit, to include observationally driven boundary conditions, and to implement even more realistic physics in the equations. In general, MHD models for the solar wind often make use of additional source and sink terms in order to mimic the observed solar wind parameters and/or they hide the not-explicitly modelled physical processes in a reduced or variable adiabatic index. Even the models that try to take as much as possible physics into account, still need additional source terms and fine tuning of the parameters in order to produce realistic results. In this paper we present a new and simple polytropic model for the solar wind, incorporating data from the ACE spacecraft to set the model parameters. This approach allows to reproduce the different types of solar wind, where the simulated plasma variables are in good correspondence with the observed solar wind plasma near 1AU. [Copyright &y& Elsevier]

Abstract: The Earth’s gravity field modelling is an ill-posed problem having a sensitive solution to the error of data. Satellite gravity gradiometry (SGG) is a space technique to measure the second-order derivatives of geopotential for modelling this field, but the measurements should be validated prior to use. The existing terrestrial gravity anomalies and Earth gravity models can be used for this purpose. In this paper, the second-order vertical–horizontal (VH) and horizontal–horizontal (HH) derivatives of the extended Stokes formula in the local north-oriented frame are modified using biased, unbiased and optimum types of least-squares modification. These modified integral estimators are used to generate the VH and HH gradients at 250km level for validation purpose of the SGG data. It is shown that, unlike the integral estimator for generating the second-order radial derivative of geopotential, the system of equations from which the modification parameters are obtained is unstable for all types of modification, with large cap size and high degree, and regularization is strongly required for solving the system. Numerical studies in Fennoscandia show that the SGG data can be estimated with an accuracy of 1mE using an integral estimator modified by a biased type least-squares modification. In this case an integration cap size of 2.5° and a degree of modification of 100 for integrating 30′×30′ gravity anomalies are required. [Copyright &y& Elsevier]

Abstract: The events that occurred after 2007 such as Chinese anti-satellite test, explosion of Briz-M upper stage, break up of cosmos-2421 and collision of cosmos-2251 with Iridium-33 satellites have completely changed the spatial density patterns in low earth orbits. This has increased the risk of collision between active satellites and debris created by them. Aftermath, the risk assessment of possible collisions called as conjunction analysis of working satellites from day to day has become more crucial. Spatial density models are useful in understanding the long-term likelihood of a collision in a particular region of space and helpful in pre-launch orbit planning. In this paper we present an algorithmic procedure for automatically estimating exact model parameters corresponding to the peak location and number of peaks using wavelets that will speed up the parameter estimation process for the models with peaks. [Copyright &y& Elsevier]

Abstract: In this paper, we use the modified GSM TIP model to explore how the thermosphere–ionosphere system in the American longitudinal sector responded to the series of geomagnetic storms on September 9–14, 2005. Comparison of modeling results with experimental data at Millstone Hill, USA (42.6°N, 71.5°W), Ramey, Puerto Rico (18.3°N, 66.8°W) and Jicamarca, Peru (11.9°S, 76.9°W) has shown a good agreement of ionospheric disturbances in the F-region maximum height. We examine in detail the formation mechanisms of these disturbances at different latitudes and describe some of the important physical processes affecting the behavior of the F-region. In addition, we consider the propagation of thermospheric wind surge and the formation of additional layers in the low-latitude ionosphere during geomagnetic storms. [Copyright &y& Elsevier]

Abstract: Observations made with the two Voyager spacecraft confirmed that the solar wind decelerates to form the heliospheric termination shock. Voyager 1 crossed this termination shock at ∼94AU in 2004, while Voyager 2 crossed it in 2007 at a different heliolatitude, about 10AU closer to the Sun. These different positions of the termination shock confirm the dynamic and cyclic nature of the shock’s position. Observations from the two Voyager spacecraft inside the heliosheath indicate significant differences between them, suggesting that apart from the dynamic nature caused by changing solar activity there also may exist a global asymmetry in the north–south (polar) dimensions of the heliosphere, in addition to the expected nose–tail asymmetry. This relates to the direction in which the heliosphere is moving in interstellar space and its orientation with respect to the interstellar magnetic field. In this paper we focus on illustrating the effects of this north–south asymmetry on modulation of galactic cosmic ray Carbon, between polar angles of 55° and 125°, using a numerical model which includes all four major modulation processes, the termination shock and the heliosheath. This asymmetry is incorporated in the model by assuming a significant dependence on heliolatitude of the thickness of the heliosheath. When comparing the computed spectra between the two polar angles, we find that at energies E <∼1.0GeV the effects of the assumed asymmetry on the modulated spectra are insignificant up to 60AU from the Sun but become increasingly more significant with larger radial distances to reach a maximum inside the heliosheath. In contrast, with E >∼1.0GeV, these effects remain insignificant throughout the heliosphere even very close to the heliopause. Furthermore, we find that a higher local interstellar spectrum for Carbon enhances the effects of asymmetric modulation between the two polar angles at lower energies (E <∼300MeV). In conclusion, it is found that north–south asymmetrical effects on the modulation of cosmic ray Carbon depend strongly on the extent of the geometrical asymmetry of the heliosheath together with the assumed value of the local interstellar spectrum. [Copyright &y& Elsevier]

Abstract: Based on the author’s experience in ISO TC20/SC14 Working Group 4, this paper discusses the common problems encountered when developing a standard for solar energetic particle (SEP) fluxes. The problem involving the reliability of the distribution function describing the SEP events and the interpolation of this function into the region of not-yet-observed large events are discussed. The problems with describing the fluences of SEPs over a wide range of energy in the form of energetic spectra are analyzed. Requirements for SEP flux models are formulated. The reliability of some SEP flux models is determined by comparing their predictions with the experimental data. [Copyright &y& Elsevier]

Abstract: Since the United States government discontinued Selective Availability (SA) on 1 May 2000, ionospheric effects have been responsible for the largest errors in GPS systems. The standard Differential GPS (DGPS) method is incapable of completely eliminating the ionospheric error. This paper describes a new approach to determine the differential ionospheric error between geographically distributed receiver stations. The ray paths of GPS signals were simulated using a modified Jones 3D ray tracing programme that includes the effect of the geomagnetic field. A Nelder–Mead optimisation algorithm was embedded in the program to precisely determine the satellite-to-station path. A realistic ionospheric model is essential for accurate ray tracing results and for estimates of differential error that are accurate on sub-centimetre scales. Here, the ionospheric model used in the ray tracing programme was developed by fitting realistic ionosphere profiles with a number of exponential functions. Results were compared to the theoretical approach. Results show that the differential delay is about 1–5cm at low elevation angles for a short baseline of 10km, as reported in other literature. This delay is often neglected in DGPS application. The differential delay also shows a pattern similar to that predicted by the Klobuchar model. The method proposed here can be used to improve future GPS applications. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents results from the Storm-Time Ionospheric Correction Model (STORM) validation for selected Northern and Southern Hemisphere middle latitude locations. The created database incorporated 65 strong-to-severe geomagnetic storms, which occurred within the period 1995–2007. This validation included data from some ionospheric stations (e.g., Pruhonice, El Arenosillo) that were not considered in the development or previous validations of the model. Hourly values of the F2 layer critical frequency, foF2, measured for 5–7days during the main and recovery phases of each selected storm were compared with the predicted IRI 2007 foF2 with the STORM model option activated. To perform a detailed comparison between observed values, medians and predicted foF2 values the correlation coefficient, the root-mean-square error (RMSE), and the percentage improvement were calculated. Results of the comparative analysis show that the STORM model captures more effectively the negative phases of the summer ionospheric storms, while electron density enhancement during winter storms and the changeover of the different storm phases is reproduced with less accuracy. The STORM model corrections are less efficient for lower-middle latitudes and severe geomagnetic storms. [Copyright &y& Elsevier]

Abstract: The paper describes the method and initial results of assimilating the auroral peak E-region density (NmE) and the auroral equatorward boundary (EB) into the International Reference Ionosphere (IRI). The NmE and EB are obtained using a FUV based auroral model or FUV measurements in near real-time. Initial results show that the auroral NmE is often significantly larger than the NmE due to the solar EUV. This indicates the importance of including the contribution of precipitating electrons in IRI. The global equatorial boundary helps to improve the specification of the sub-auroral ionosphere trough in IRI. An IDL software package has been developed to interactively display the IRI parameters with assimilated NmE and EB. It can serve as an operational tool for space weather monitoring. [Copyright &y& Elsevier]

Abstract: We present a new technique for improving ionospheric models of nighttime E-region electron densities under geomagnetic storm conditions using TIMED/SABER measurements of broadband 4.3μm limb radiance. The response of E-region electron densities to geomagnetic activity is characterized by SABER-derived NO+(v) 4.3μm Volume Emission Rates (VER). A storm-time E-region electron density correction factor is defined as the ratio of storm-enhanced NO+(v) VER to a quiet-time climatological average NO+(v) VER, which will be fit to a geomagnetic activity index in a future work. The purpose of this paper is to demonstrate the feasibility of our technique in two ways. One, we compare storm-to-quiet ratios of SABER-derived NO+(v) VER with storm-to-quiet ratios of electron densities measured by Incoherent Scatter Radar. Two, we demonstrate that NO+(v) VER can be parameterized by widely available geomagnetic activity indices. The storm-time correction derived from NO+(v) VER is applicable at high-latitudes. [Copyright &y& Elsevier]

Abstract: This paper presents a mathematical model to simulate ionospheric plasma drifts at equatorial low latitude regions by coupling of E- and F-regions. The governing non-linear differential equations (of elliptic and parabolic nature) are solved numerically through finite-difference schemes and obtained neutral winds and electric fields. The temperature and electron density profiles are generated utilizing MSIS-86 atmospheric model. The continuity equation is employed to obtain night-time E-region density profile using measured ionograms at Trivandrum (India). The computed vertical and zonal plasma drifts are comparable with measured Jacamarca plasma drifts with little variations during noon and evening times. The plasma drifts at Trivandrum (8.5° N, 76.5° E, dip 0.5° N) are compared with those of Jicamarca (12° S, 76.9° W, dip 2° N). Neutral wind simulations of present model agree well with those of horizontal wind model (HWM-93). The post-sunset enhancement and its reversal are also discussed. [ABSTRACT FROM AUTHOR]

Abstract: Different algorithms have been proposed for the modeling of the ionosphere. The most frequently used method is based on the spherical harmonic functions achieving successful results for global modeling but not for the local and regional applications due to the bounded spherical harmonic representation. Irregular data distribution and data gaps cause also difficulties in the global modeling of the ionosphere. In this paper we propose an efficient algorithm with Multivariate Adaptive Regression Splines (MARS) to represent a new non-parametric approach for regional spatio-temporal mapping of the ionospheric electron density using ground-based GPS observations. MARS can handle very large data sets of observations and is an adaptive and flexible method, which can be applied to both linear and non-linear problems. The basis functions are directly obtained from the observations and have space partitioning property resulting in an adaptive model. This property helps to avoid numerical problems and computational inefficiency caused by the number of coefficients, which has to be increased to detect the local variations of the ionosphere. Since the fitting procedure is additive it does not require gridding and is able to process large amounts of data with large gaps. Additionally the model complexity can be controlled by the user via limiting the maximal number of coefficients and the order of products of the basis functions. In this study the MARS algorithm is applied to real data sets over Europe for regional ionosphere modeling. The results are compared with the results of Bernese GPS Software over the same region. [Copyright &y& Elsevier]

Abstract: DORIS is one of the four space-geodetic techniques participating in the Global Geodetic Observing System (GGOS), particularly to maintain and disseminate the Terrestrial Reference Frame as determined by International Earth rotation and Reference frame Service (IERS). A few years ago, under the umbrella of the International Association of Geodesy, a DORIS International Service (IDS) was created in order to foster international cooperation and to provide new scientific products. This paper addresses the organizational aspects of the IDS and presents some recent DORIS scientific results. It is for the first time that, in preparation of the ITRF2008, seven Analysis Centers (AC’s) contributed to derive long-term time series of DORIS stations positions. These solutions were then combined into a homogeneous time series IDS-2 for which a precision of less than 10mm was obtained. Orbit comparisons between the various AC’s showed an excellent agreement in the radial component, both for the SPOT satellites (e.g. 0.5–2.1cm RMS for SPOT-2) and Envisat (0.9–2.1cm RMS), using different software packages, models, corrections and analysis strategies. There is now a wide international participation within IDS that should lead to future improvements in DORIS analysis strategies and DORIS-derived geodetic products. [Copyright &y& Elsevier]

Abstract: This paper presents the results of the cross-validation of a multivariate logistic regression model using remote sensing data and GIS for landslide hazard analysis on the Penang, Cameron, and Selangor areas in Malaysia. Landslide locations in the study areas were identified by interpreting aerial photographs and satellite images, supported by field surveys. SPOT 5 and Landsat TM satellite imagery were used to map landcover and vegetation index, respectively. Maps of topography, soil type, lineaments and land cover were constructed from the spatial datasets. Ten factors which influence landslide occurrence, i.e., slope, aspect, curvature, distance from drainage, lithology, distance from lineaments, soil type, landcover, rainfall precipitation, and normalized difference vegetation index (ndvi), were extracted from the spatial database and the logistic regression coefficient of each factor was computed. Then the landslide hazard was analysed using the multivariate logistic regression coefficients derived not only from the data for the respective area but also using the logistic regression coefficients calculated from each of the other two areas (nine hazard maps in all) as a cross-validation of the model. For verification of the model, the results of the analyses were then compared with the field-verified landslide locations. Among the three cases of the application of logistic regression coefficient in the same study area, the case of Selangor based on the Selangor logistic regression coefficients showed the highest accuracy (94%), where as Penang based on the Penang coefficients showed the lowest accuracy (86%). Similarly, among the six cases from the cross application of logistic regression coefficient in other two areas, the case of Selangor based on logistic coefficient of Cameron showed highest (90%) prediction accuracy where as the case of Penang based on the Selangor logistic regression coefficients showed the lowest accuracy (79%). Qualitatively, the cross application model yields reasonable results which can be used for preliminary landslide hazard mapping. [Copyright &y& Elsevier]

Abstract: This paper presents an analysis of a set of time series that represent foF2 disturbances during storm conditions, using clustering tools. The time series under study have been drawn from ionospheric observations obtained from eight European middle latitude ionosondes during a significant number of storm-time intervals and they are divided into eight groups according to the latitude (middle to low and middle to high) and the local time of the observation point at storm onset (afternoon, evening, morning, prenoon). The time series in each group have been analyzed using clustering-based methods. Specifically, each time series has been represented using two different ways of representation: the first is the raw representation while the second is through the parameters of the autoregressive (AR) model that best represents it. For each representation a hierarchy of clusterings is produced via the complete link algorithm. The two produced hierarchies are combined to a single one and the final clustering results are extracted from the produced hierarchy. The obtained results are in close agreement with the theoretical formulations concerning ionospheric storm effects at middle latitudes. In addition, they may be proved useful in the development of more accurate ionospheric forecasting methods. [Copyright &y& Elsevier]

Abstract: COST 296 Action refers to the project on Mitigation of Ionospheric Effects on Radio Systems (MIERS) in the framework of European Cooperation in Science and Technology (COST), which is one of the longest-running European instruments supporting cooperation among scientists and researchers across Europe. The main objective of the MIERS project has been to develop an increased knowledge of the effects imposed by the ionosphere on practical radio systems, and for the development and implementation of techniques to mitigate the harmful effects of the ionosphere on such systems. This paper highlights COST 296 Action results that have been achieved during its lifetime period of February 2005–February 2009 with emphasis on space weather ionospheric monitoring and modelling. [Copyright &y& Elsevier]

Abstract: The major problem in the cosmological nucleosynthesis is the evaluation of the reaction rate. The present scenario is that the standard thermonuclear function in the Maxwell–Boltzmann form is evaluated by using various techniques. The Maxwell–Boltzmannian approach to nuclear reaction rate theory is extended to cover Tsallis statistics () and more general cases of distribution functions. The main purpose of this paper is to investigate in some more detail the extended reaction probability integral in the equilibrium thermodynamic argument and in the cut-off case. The extended reaction probability integrals will be evaluated in closed form for all convenient values of the parameter by means of residue calculus. A comparison of the standard reaction probability integrals with the extended reaction probability integrals is also done. [Copyright &y& Elsevier]