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The ground space optical observation system considered as one of the main measurement methods to observe space object in Medium Earth Orbit (MEO), Highly Elliptical Orbit (HEO) and Geostationary Orbit (GEO) faces difficulties in forming high-solution images for objects located in GEO that only appears several light spots with limited pixels due to the impacts of observing distance, resolution ratio, and other atmospheric conditions. The light curve is the time history of an object’s observed brightness obtained from the ground-based optical observation system through light curves, right ascension, and declination of space objects. The characteristic of space objects such as position, velocity, size, shape, and material can be inverted. This paper has analyzed the principles, applications, merits, and demerits of several non-linear filtering methods in detail. Besides, the scientific description of inversion for characteristics of a non-resolved space object from ground photometric measurements and the essence of the non-linear filtering inversion method has also been clarified. A selection principle of the non-linear filtering inversion method for different space object characteristics is then proposed, and the developing direction of such inversion methods is also described in the end.

In modern large aperture optical systems for tracking astronomical objects, the technology of bistatic schemes is widely introduced, in which the laser, the main and auxiliary telescopes are spatially separated. This requires additional measures to be taken when aligning the optical axes of telescopes, especially when tracking LEO space objects. The choice of bistatic schemes in astronomical telescopes is due to the problem of “tilt uncertainty” inherent in monostatic schemes for the formation of a laser reference star. This problem is caused by the difficulty or even the impossibility of determining the tilt of the wavefront when the laser guide star jitters in the image plane. The article discusses a monostatic scheme for constructing ground-based adaptive optoelectronic systems. The monostatic scheme combines the optical axis of the laser, which forms the laser guiding star, and the optical axis of the telescope, which serves to obtain images of space objects by eliminating phase disturbances of the atmosphere due to the radiation of the laser guiding star. The proposed method for determining the tilt of the wavefront in a monostatic scheme is based on the analysis of expressions for the dispersion of the tilt jitter of the images of a laser reference star and a space object for the case when the diameter of the receiving aperture of the telescope is much larger than the diameter of the aperture of the laser forming the laser reference star. This approach is based on the long-elicited strong correlation between the instantaneous values of the tilt of the laser beam and the received beam from a natural star, transmitted towards each other. When observing low-orbit small-sized space objects and laser reference stars, it is assumed that they are in the Fresnel zone of the receiving aperture of the optoelectronic system and within the isoplanatism angle of the atmosphere, determined within the framework of an isotropic and locally homogeneous model of atmospheric turbulence. The proposed solution made it possible to determine the value of the instantaneous tilt angle for the image of an inconspicuous space object in the focal plane of the receiving aperture of the telescope on the basis of measuring the instantaneous tilt angle for the actually observed image of the laser reference star. The results can be used in the development of ground-based adaptive optoelectronic tracking systems for low-orbit small-sized space objects.

There are approximately 2900 active space objects cataloged, and the number will increase continually in future. All these space objects may maneuver for some purpose occasionally, including highly elliptical orbit (HEO) transfer, station-keeping, orbit altitude adjustment, etc. Hence maneuver detection is very important for space situational awareness (SSA). It also plays an important role in the catalog maintenance by correlating the orbits before and after maneuver. In the paper, the maneuver detection methods based on orbital dynamical model are proposed. Firstly, the perturbations before and after maneuver are analyzed. Then two kinds of maneuver models are derived using the relative dynamical equations. Finally, several kinds of maneuver cases are performed to verify the models proposed. It is demonstrated that these two models are feasible and effective for the detection of longitude maneuvers.

This work studies the performance of periodic orbits to observe and conduct space traffic management (STM) in cislunar space, with the aim of finding a preferable trajectory for future missions foc...

Timely detection of changes in the characteristics of space hardware objects during their long-term operation is one of the main tasks in the development and study of onboard systems that maintain the efficiency of their operation. This paper presents a statistical method for simulating the motion of space objects (spacecraft and used launch vehicle stages) in the class of autoregressive models. The method allows one to improve the quality of description and prediction of the motion of space objects based on simulating time series of their TLE-elements (two-line orbital element sets). The purpose of this work is to increase the accuracy of mathematical models of the observed motion of space objects in the problems of deorbit time determination, satellite collision prediction, and space debris cataloging. The paper presents a system for simulating the motion of space objects, which allows one to determine an optimal amount of learning samples in simulating time series of TLE elements, determine the order of autoregression and find an optimal model structure for each variable element, identify model parameters in conditions of unequally spaced observations, identify features of the time behavior of the root-mean-square errors of the constructed autoregressive models on the basis of dividing the initial time series of TLE-elements into successive learning intervals, and obtain predictive estimates of the values of variable elements. The proposed statistical method of space object motion simulation can be recommended to describe and predict the motion of spacecraft and used launch vehicle stages represented as time series of TLE-elements (which are publicly available and regularly updated). The application of the proposed statistical method will increase the accuracy of mathematical models of the observed motion of space objects in the problems of deorbit time determination, satellite collision prediction, and space debris cataloging.

We study the machine learning method for classifying the basic shape of space debris in both simulated and observed data experiments, where light curves are used as the input features. In the dataset for training and testing, simulated light curves are derived from four types of debris within different shapes and materials. Observed light curves are extracted from Mini-Mega TORTORA (MMT) database which is a publicly accessible source of space object photometric records. The experiments employ the deep convolutional neural network, make comparisons with other machine learning algorithms, and the results show CNN (Convolutional Neural Network) is better. In simulational experiments, both types of cylinder can be distinguished perfectly, and two other types of satellite have around 90% probability to be classified. Rockets and defunct satellites can achieve 99% success rate in binary classification, but in further sub-classes classifications, the rate becomes relatively lower.

Since nanosatellites are spotlighted as a verification platform for space technology, new studies on on-orbit satellite servicing using nanosatellites are being conducted. This servicing is based on space robotics using vision-based sensors in the rendezvous state with a target satellite. The space environment, such as sunlight and Earth albedo, affects the mission. Simulation of the space environment on the ground is difficult, but the development of robust algorithms which reflect the effect is essential. In particular, missions such as active debris removal require a method for overcoming changes in any known information due to external factors such as collisions. This study proposes a new strategy on nanosatellite for on-orbit space object classification by applying deep learning to sensor-based orbit satellite service activity. When previously known information is changed, a method of online learning on orbit after obtaining additional data at a short relative distance can help determine the final service part. Using the images and point cloud data that simulate the space environment, we apply a convolutional neural network and PointNet to classify the objects. The learning environment is studied using a general desktop and a micro-graphics processing unit (GPU) board that can be mounted on a nanosatellite. For the training, we used self-produced data using 3D models of nanosatellites and asteroids with similar shapes, which are difficult to distinguish with existing algorithms. Consequently, the proposed strategy by the author shows feasibility of using nanosatellite’s micro GPU for on-orbit space object classification, and it is verified that point cloud–based methods are more suitable by utilizing deep learning for nanosatellites. The proposed method with processor of nanosatellite is applicable to satellite service missions in orbit, such as capturing of robotic parts for extending life span or removing space debris.

In the last thirty years, the encounter and approach of Rendezvous Proximity Operations (RPO) of human made space objects have developed. This development indicated by the developments in field of technology. The focus of this study is regarding RPO as a mission that has potential to increase the amount of space debris. This study aims to analyze the RPO activity as a potential hazardous mission in increasing the space debris population. Moreover, this research aims to analyze RPO activity as a potentially vulnerable mission to increase the space debris population. In this study, the method was carried out descriptively, by exploring data and information about RPO. The results of this study indicated that RPO activity still limited to LEO due to the high difficulty level for the GEO orbit. The results of this study indicate that RPO activity is still limited to LEO due to the high difficulty level for the GEO orbit. This is actually because in LEO orbit have more space debris (75%) than GEO orbit and it has a higher risk of falling to Earth. Based on the results obtained, it can be concluded that RPO activities are double-edged and therefore greater supervision needs to be carried out especially to safeguard Indonesia’s interests in space.

Resident space object population in highly elliptical high perigee altitude (> 600 km) orbits is significantly affected by luni-solar gravity. Using regularization, an analytical orbit theory with luni-solar gravity effects as third-body perturbations in terms of Kustaanheimo-Stiefel regular elements is developed. Numerical tests with different cases resulted in good accuracy for both short- and long-term orbit propagations. It is observed that the luni-solar perturbations affect the accuracy of the analytical solution seasonally. The analytical theory is tested with the observed orbital parameters of the few objects in highly elliptical orbits. The analytical evolution of osculating perigee altitude is found to be concurrent with observed data. Solar perturbation, when compared with lunar perturbation, is established to be dominant over such orbits.

Identification of known space objects is a critical step in maintaining accurate catalogs for space situational awareness activities. With increasing numbers of objects in orbit, optical measurements of space objects become more populated with detections, stressing the algorithms used to track and identify these objects. Traditional algorithms used for identifying space objects, such as elliptical gating, suffer from ambiguous or incorrect classifications as gates tend to overlap in dense detection environments. An algorithm is developed that couples elliptical gating with a star pattern recognition algorithm called the planar triangle method to overcome the difficulties found in spatially dense observations. Unlike star catalogs, cataloged resident space objects often contain considerable uncertainty, further challenging the identification of objects in a cluttered field-of-view. The proposed approach leverages uncertainties of the catalog as well as the optical measurement sensor uncertainty to support the space object identification. Simulation results using the gating-assisted planar triangle method show a significant improvement in robust identification of space objects as compared to traditional elliptical gating methods when faced with highly cluttered observations.

In this paper, a composite weighted average consensus filtering (CWACF) algorithm is proposed for space object tracking by combining two distributed heterogeneous nonlinear filters. In light of the sensors' different sensing accuracy and computational capability, extended Kalman filter (EKF) and sparse-grid quadrature filter (SGQF) are compositely adopted on different sensors as local filters. Then, estimates from neighbours are fused based on the weighted average consensus framework to attain better estimation performance. Moreover, it is proved that the estimation error is exponentially bounded in mean square. The performances of the proposed algorithm, the distributed extended Kalman filtering (DEKF) and the distributed sparse-grid quadrature filter (DSGQF) are compared in a space object tracking problem.

Limited by the conditions and performance of ground-based optical observations, it is difficult for us to obtain a plethora of optical cross section (OCS) data for some space objects (SOs). Unevenly distributed OCS data and unclear labels will affect the performance of SOs recognition based on neural networks. Furthermore, when we need to identify a new SO or SO category using deep neural network, the trained network model may no longer be applicable. We need to retrain the network with new training data. In order to alleviate these problems and improve the generalization and training convergence speed of SOs recognition networks, a novel, to the best of our knowledge, neural network model, ARSRNet, is proposed in this paper. The ARSRNet can identify SOs and their attitude accurately using only a small quantity of training OCS data and without clear labels. And the proposed network is able to adapt to new recognition tasks. Meanwhile, we propose an AdamRprop network optimization algorithm to accelerate network training and improve recognition accuracy. Experimental results show that the recognition accuracy of ARSRNet reaches 90.60% on the test OCS dataset. Compared with mainstream network optimization algorithms, the proposed AdamRprop is more appropriate for ARSRNet and can accelerate the convergence of ARSRNet.

Orbital error provides a strict accuracy description of the space object’s state in a perturbing environment and plays a vital role in space situation awareness (SSA) related tasks like space conjunction analysis. However, challenge occurs for hundreds of thousands of space debris that how efficiently and accurately can the orbital error be propagated in a way that agrees well with the nonlinear orbit dynamics system (ODS). In this paper, the problem is addressed by propagating the orbital error in the semi-analytic ODS (SODS). By applying the multiscaling technique to separate out the effects of a perturbation acting on an orbit in short-periodic and long-term time scales, the developed SODS allows the long-term error component to be propagated by numerically integrating the mean equations with 1-day step, while the short-periodic error component is analytically recovered. Performance of the error propagation in the SODS is verified using statistical state moments of 104 samples of two low-Earth-orbit (LEO) satellites. Experimental results from the Monte Carlo simulation demonstrate that the SODS is capable of propagating orbital error that can well capture the statistical characteristics of predicted states in terms of the error magnitude. More importantly, the computational efficiency of the SODS against the high-fidelity ODS is improved by nearly 95%, making it attractive for the error propagation of numerous debris.

Two line element (TLE) released by the North American Aerospace Defense Command (NORAD) is widely used by aerospace workers, and the matched SGP4/SDP4 (Simplified General Perturbation Version 4/Simplified Deep-space Perturbation Version 4) model is used to propagate it. Nevertheless, no corresponding information about its accuracy and covariance is clearly given, thus the application of the TLE data is greatly restricted. In this paper, the determined and predicted orbits are compared to generate the orbit error data, based on the historical TLE data obtained from the Space-Track website and the SGP4/SDP4 model. By dividing different time bins, the fitting coefficients of the variation of orbit prediction error with time are given for each space object, and the characteristics of the error evolution are further discussed for the different types of orbits. The mean analytic model of the orbit prediction error evolution with time is given respectively for the four orbit types of space objects, which provides a valuable reference for extending the application of the TLE data.

Space Surveillance and Tracking (SST) is the ability to detect and predict the movement of space debris in orbit around the Earth. SPOOK (SPace Object Observations and Kalman filtering) is a versatile and highly configurable software tool developed by Airbus, for the detection, cataloguing and orbit prediction analysis of Earth orbiting objects. It provides an integrated framework for all the activities related with SST sensor architecture simulation. Throughout this paper, the functionalities of the tool are described and examples of different simulation scenarios are provided.

The cannonball assumption of three-degree-of-freedom (3DOF) space object state prediction can lead to large inaccuracies if the sphericity assumption is violated, while numerical propagation of bot...

Surveillance of artificial space objects must be performed, especially for re-entry objects that have the potential to fall into Indonesian territory. This system requires a database that contains the orbital parameter information of every artificial object orbiting the earth. The purpose of this paper is to design a database model by applying the DBLC method for the artificial space object surveillance system. Data sources are from a satellite catalog and bulk-TLE of all active and decayed objects derived from the Space-Track. Those data are aiming as input for the real-time surveillance system of re-entry artificial space objects and the web-based informative catalog of all artificial space objects with their properties. The result of the design is a relational database consisting of 7 tables and 6 relations. Hopefully, this design can assist in developing a surveillance system of artificial space objects and the orbital database information system for all objects registered in NORAD.

Space activities are technically sophisticated and challenging endeavors involving high risk. Notwithstanding precautionary measures that are taken by commercial operators, damage may be caused during space objects’ launching, passing through air space, in-orbit maneuvering and operating, and de-orbiting. The rules and procedures aimed at ensuring the prompt payment of a full and equitable compensation for such damage constitute the international liability regime, which is of crucial importance in space law. The first reference to international liability for damage caused by space objects and their component parts on Earth, in air space, or in outer space can be traced back to the very beginning of the space era. In 1963, just a few years after the first ever artificial satellite was launched, international liability was declared by the United Nations General Assembly as one of the legal principles governing the activities of states in the exploration and use of outer space. It was later made legally binding by inclusion in the 1967 Outer Space Treaty and received further development in the 1972 Liability Convention. The latter is generally referred to as lex specialis when the interrelation between the two international treaties is described and introduces several provisions that treat liability for damage caused in specific circumstances somewhat differently. International space law imputes liability on states that launch or procure launchings of space objects and states from whose territory or facility space objects are launched. This does not, however, exclude liability for damage caused by space objects that are operated by private entities. Still, international liability for accidents involving commercial operators stays with the so-called launching states, as this term is defined by the Liability Convention for the same states that are listed in the Outer Space Treaty as internationally liable. Insurance is well known to address damages and liability issues, including those arising from commercial launches; however, it is not always mandatory. Frequently, space-related accidents involve nonfunctional space objects and their component parts, which are usually referred to as “space debris.” This may include spent rocket stages and defunct satellites, as well as fragments from their disintegration. Since the nonfunctional state of a space object does not change its legal status, the relevant provisions of international space law that are applicable to space objects continue to apply to what is called space debris. This means, in particular, that launching states are internationally liable for damage caused by space debris, including cases where such debris was generated by private spacecraft. The probability of liability becomes even higher when it comes to active space debris removal. Such space activities, which are extensively developed by private companies, are inextricably linked to potential damage. Yet, practical problems arise with identification of space debris and, consequently, an efficient implementation of the liability regime.

Accurate orbit information plays an important role in space and national defense security, such as space object prediction, maneuver detection, collision prevention and so on. Therefore, it is highly necessary to master the characteristics of orbital elements of space objects. In this paper, the Fourier series fitting method is proposed, in which the TLE orbit data is used to analyze the orbit elements of GEO, LEO and HEO. According to the orbit elements of different types of targets, the orbit elements variation rule is approximated by using the fitting method, and the resulting variation function can be used for predictions. The experimental results show that the predictions of this method is promising.

In order to realize the situational awareness of the free space and strengthen the ability to perceive the random targets in free space, firstly the free space situational awareness could be realized on the foundation of cooperative surveillance. An important problem of the space surveillance system is presented and a relevant compete design project as well as a relevant object function were proposed. Besides, a new system schemes based on tabu genetic algorithm was put forward to improve the cooperative surveillance model. Through a series of theoretical derivation and some corresponding simulation experiments, it is proved that the system schemes is in possession of stronger ability for solving speed and precision, even detect and track the space object more than 1000.

Long-Wave Infrared (LWIR, wavelength > 8 um) polarimetric measurements can be used to characterize space objects under certain conditions. Both visible and LWIR polarimetry have been demonstrated extensively in terrestrial applications for characterization and detection of objects of interest. Visible polarimetry has also been demonstrated for space object detection. A simulation of a camera and telescope for collection of LWIR polarimetric signatures of space objects has been assembled using three software packages: Systems Tool Kit (STK), MATLAB, and FRED. Characterization of space objects is generally possible across a wide range of target surface temperatures and emissivities, and at a sub-pixel level; characterization is reliable in a narrower range. This approach represents an initial step forward in optical systems for space situational awareness in that it offers a wider field of view than equivalently sized visible light collectors, and it can be used both day and night, regardless of target illumination.

A method is proposed that allows determining the type of space object in the air and space by using a radar portrait along the line of sight. The application of this method will allow to expand the scientific and methodological apparatus of recognition, which will lead to an increase in the main indicators of systems for determining the type of objects under study.

The article proposes a model for the formation of reflection spectra according to a linear law depending on the proportional size of the areas of the structural elements of the artificial Earth satellite, which has been experimentally confirmed.

This paper deals with the observability and sensitivity analysis of the lightcurve measurement for use in the estimation of instantaneous pose (orientation) and shape geometry. Since severa...

The apparent magnitude of a complex shaped space object is difficult to calculate since its visible triangular facets are hard to be determined. The most common-used visible facets determination method is to judge the incident and emergent angle, but this method does not apply to a space object which is a combination of convex bodies or has a concave surface. In this paper, a new quadtree-based hidden vertex removal method is presented, and it is composed of four steps: coordinate transformation, hidden vertex removal, quadtree decompositions and visible triangular facets determination. This method can determine visible triangular facets of a space object of any shapes. Once a space object triangular facet model, the observed direction of a telescope and the incident direction of the sunlight are given, the visible triangular facets of the space object can be obtained. Two experiments are carried out to verify the visible triangular facet determination performance of this method qualitatively and quantitatively. Experiment results show the visible triangular facet calculated by the proposed method is accurate and reasonable.

In the optical observation of space objects, multiple measurements often occur in the tracking gate, which brings about the uncertainty of tracking measurement and the reduction of tracking accuracy, causes the instability along the tracking path, and eventually leads to the interruption of tracking and the loss of the target. A new approach, combining the Kalman filter and probabilistic data association, is proposed in this paper for the adaptive tracking of space objects. In this method, the gate of association is predicted by the Kalman filter, while the equivalent measurement obtained from the probabilistic data association is adopted as an effective feed. The experiments show that this technique can effectively improve the tracking accuracy as well as the robustness for the automatic tracking of space objects.

Estimation of the TTX of radars used to monitor space objects is associated with great material and time costs. In this article, the methodological approaches to the assessment of some technical characteristics of the radar (control zone, radar potential, throughput, the rate of issuance of coordinate measurements, minimum tracking time, minimum RCS value of detectable space object) are presented based on the results of a posteriori statistical processing of the received trajectory measurements. The results of the approbation of these methods are given.

The problem of a space object orbit estimation and determination of region with minimum volume, which contains with guarantee orbit state vector, is considered. Measurements are provided by the telescope and estimation of angle measurements errors are limited in absolute value. The significant dependence of the guaranteed area size on the choice of coordinate system for observations is found, the algorithm for determination of the minimum volume area is suggested based on the simplex-method. In addition the comparison analysis of results of created algorithm with known ones based on various methods (guaranteed and probabilistic) is presented. The developed algorithm is able to give more precise results in several cases in comparison with other known algorithms.

Given partial observation of a space object, the admissible region is defined as the set of all physically acceptable orbits that are consistent with the observation. Given additional constraints o...

When matters of sustainable development and innovation are on the table for discussion in Africa, culture is often sidelined. Designs, shapes and sizes of new technological innovations need to inte...

A space object exploded near the city of Chelyabinsk on February 15, 2013. Meteorite fragments reached the Earth’s surface, and accordingly we may consider this space object to have been a meteorite. However, this event showed a number of features not corresponding to the destruction of a meteorite. The space object began to disintegrate at an altitude of 70 km when pressure (dynamical loads) on its front surface was ~6.7 × 103 N·m-2. The substance from the object’s surface was not blown off by drops, as at ablation, but was dumped by jets over a distance up to 1 km. The trail of this space object visually reminded us of a jet aircraft’s contrail, made up of water. But there is no enough water at altitudes of 30 - 70 km. It may be assumed that the object itself delivered water to these altitudes. The calculation of gas rise over the trail showed that the temperature in some parts of this trail was about 900 K. Heating of large masses of gas can be explained not only by the release of kinetic energy of the space object, but also by combustion processes of its substance. Thus, it was concluded that the meteorite could have been delivered by a comet.

The astronomical observation model, light curve model and solar radiation pressure force model are established to allow estimation of the positions and attitudes of space objects using a fusion of photometric and astronomical data. Existing algorithms for this purpose involve large errors. The proposed method firstly estimates the attitude of the object by using photometric and astronomical data fusion. Secondly, the position of the object is filtered by the estimated attitude. Theory and numerical simulations show the efficiency of the proposed method.

With the increasing number of uncontrolled objects in the space environment surrounding Earth, it has become important to keep track of the orbits of these objects so as to avoid collisions with ac...

The opportunities to study Phobos’ internal structure provided by radio methods are considered in this paper. The necessity of these studies is related to solution of the problem of the origin of the Martian moons. Radiosounding is one of the most efficient methods of analyzing the internal structure of small space objects and, in particular, that of Phobos. The new Boomerang project planned according to the Federal Space Program of Russia for 2016—2025 within the Expedition-M program aimed at the exploration of Phobos and delivery of soil samples from its surface to the Earth, as well as the specifics of a ballistic scenario of this expedition, provide a unique opportunity to carry out radioscopy of this space object to discover the internal structure Phobos and to solve the key problem of its origin. The model of Phobos’ internal structure, radiosounding ballistic conditions, analysis of optimum frequency range of sounding, and key parameters of the device required for the experiment are considered in this paper. The significance of proposed studies and opportunities for their implementation are discussed.

In the article, the authors considered the challenges for space law, which are created by the intensive development of production technologies of unmanned spacecrafts and space drones, as well as their use in the space industry. The authors clarified the term “space object”, which is used in the Space Law. This helped reveal the difference between the terms “unmanned spacecrafts” and “space drones”, which are synonymous in the Air Law. The authors investigated the basics of the space law and proved that in the existing formulations, the space law is not able to regulate the modern space exploration. Based on the study, the authors proposed: (1) to consolidate the influence of public organizations created in the space industry and specializing in the space exploration in the space law; (2) to change approaches to space law; space law should be considered as an effective regulator capable of ensuring the sustainable development of the mankind;. (3) under the space law, to create a holistic concept for using all types of space object on the Low Earth Orbit.

National space legislation constitutes an important source of “state practice”, i.e. how states behave in practice. In this chapter, a comparative analysis of national space legislations will provide an overview of the dispositions of the twenty selected jurisdictions. The objective of the study is to find out how these states have responded to their international obligations and to figure out the general contours of national space legislation. The comparative study is not intended to reflect upon every minutest details and specifics of the respective legislations but rather the comparative study is done on the following parameters: (a) scope and application of the legislation; (b) implementation of authorization and supervision principle that includes authorizing body, authorizing conditions and procedure and means of achieving continuing supervision; (c) implementation of the registration principle; (d) recourse against liability; (e) transfer of the space object and (f) protection of the environment. These parameters have been identified in the analysis of the various national space legislations and also recommended in various model laws. They ascertain a common minimum approach taken towards regulating space activities conducted by non-governmental entities. Some legislation regulates additional matters also. Any such distinction, which is relevant from the perspective of this study, will be discussed under the heading “other aspects”.