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# Monthly number of objects in the Earth orbit cataloged by the US Space Surveillance Network (SSN), organized by object type. The two step increases in 2007 and 2009 result from fragments from the FY-1C ASAT test and Iridium 33/Cosmos 2251 collisions, respectively [1].

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The number of man-made debris objects orbiting the Earth, or orbital debris, is alarmingly increasing, resulting in the increased probability of degradation, damage, or destruction of operating spacecraft. In part, small objects (<10 cm) in Low Earth Orbit (LEO) are of concern because they are abundant and difficult to track or even to detect on a...

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An orbital debris evolutionary model for geosynchronous Earth region named GEODEEM is upgraded for better understanding. One of keys of this upgrade is that all satellites larger than 10 cm in size are tracked individually. The benefits of this upgrade are: 1) collision accidents can be estimated based upon one-by-one collision probabilities, and 2...

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... The minimum elevation of the ground ε is shown in the figure below. It should be noted that ε should be more than 5° to 10° [11] . According to the triangle sine theorem, we can get: ...

... Then the weight coefficient matrix is: 11 ...

In order to demonstrate the key functionalities of large-scale LEO navigation constellations, this paper investigates the small-scale LEO experimental constellation design problem. The major requirements include achieving quadruple coverage of specific ground target areas. The regional navigation constellation consists of four satellites distributed on two orbit planes. Considering the sustainable regional navigation, it is expected that the orbits of the satellites are regressional such that it takes little effort for the constellation to cover the designated region. In this way, the structure of the optimization problem is set up, which is constrained by the quadruple coverage and accuracy requirements. It takes the maximum task time as the objective function. The differential evolution algorithm (DE) is utilized to solve the optimization problem. The optimal regional navigation constellation design scheme satisfying the constraints is obtained. The simulation results show that the regional navigation constellation designed by this method can meet the predetermined requirements.

... Currently, there is at least one in orbit sensor, the Canadian NEOSSAT (Near Earth Object Surveillance Satellite) (Abbasi et al., 2019;Laurin et al., 2008), Following recommendations of (Englert et al., 2014;Worms et al., 1999), ESA has recently started the project on developing Coincident laser sheet particle monitor (COLA), to study the feasibility of a new orbital sensor . The idea is based on placing one or more thin laser sheet light fields around the satellite, and several fast cameras measuring the precise coordinates and brightness of the flashes caused by bypassing particles. ...

We have developed a scattering model allowing to study interaction of light with particles populating the near-Earth environment: satellite explosion remnants, collisional debris, particles detached from peeling paint surfaces, and ejecta resulting from micrometeorite bombardment. In its present configuration the model accounts for rough needles, grains, and plates as primary shape elements. More complex shapes are built upon combining them.
The model is compared and validated against laboratory measurements. The studied samples include a set of space debris analogue samples obtained from the controlled MIRAD (Microparticle impact related attitude disturbances) experiment that collided solar cell panels with a projectile. The resulting samples are mostly carbon needles and curved aluminium sheets. We have both measured and modelled the scattering of light from a set of these samples.
The model agrees rather well with the measurements. The shape and orientation of the particles are found to be the main contributor in how light is scattered, whereas the material dependence shows a weaker trend. Large amount of data with varying viewing and illumination angles are needed to allow for inversion of the target characteristics.
The experimental results exploited in our study have significantly aided the model development. In the future, this work can be expanded to a real-mode in-orbit scattering model that can be utilised in Earth system and/or astronomical observations and space mission concept designs. Additional measurements with larger variety of samples and their expanded size range are required to extend and solidify the model for the full range of populations representing space particles.

... The amount of space debris is currently increasing at a rate of 5% per year, which suggests that spacecraft in their orbits face the rising threat of debris impact [8,13,24]. The bare electrodynamic tether (EDT) is a tool invented by Sanmartin [33] for deorbiting missions. ...

The electrodynamic tether (EDT) is a type of propulsion system that uses the geomagnetic field and ionospheric plasma and has the potential to conduct a space-debris removal mission without consuming a large amount of propellant. To understand the dynamic properties of the bare EDT system, an orbital dynamic model based on a detailed environmental space model and the real discharge characteristics of a hollow cathode plasma contactor (HCPC) was built. By numerical simulation, the differences in the bare tether performance caused by various orbital conditions and HCPC voltage models (at constant or various voltages) were compared and discussed. The results suggest that dynamic distinctions generated by the two bias voltage models increased as the latitude increased from 0° to 60°.

... Radar systems can sometimes detect such space debris objects, but can at best localize them with lower precision than shortwavelength optical systems. A stand-alone optical system based on the use of a light-sheet illumination and scattering concept [3] for spotting debris within meters of a spacecraft has also been proposed. A second system can localize all three coordinates of an unresolved, scattering debris [7,25] by utilizing either the parallex between two observations, or a pulsed laser ranging system, or a hybrid system. ...

We consider three-dimensional (3D) localization and imaging of space debris from only one two-dimensional (2D) snapshot image. The technique involves an optical imager that exploits off-center image rotation to encode both the lateral and depth coordinates of point sources, with the latter being encoded in the angle of rotation of the PSF. We formulate 3D localization into a large-scale sparse 3D inverse problem in the discretized form. A recently developed penalty called continuous exact l0 (CEL0) is applied in this problem for the Gaussian noise model. Numerical experiments and comparisons illustrate the efficiency of the algorithm.

... As of January 2019, more than 128 million bits of debris which are less than 1cm were estimated (D Mahrholz, 2002) [2]. Space debris is extended over 160km to 36000km above the Earth's surface (Christoph R Englert, 2014) [3]. The tracking and cataloguing of space debris are efficiently done by the US Space surveillance Network. ...

... A stand-alone optical system based on the use of a light-sheet illumination and scattering concept [1] for spotting debris within meters of a spacecraft has been proposed. A second system can localize all three coordinates of an unresolved, scattering debris [2,3] by utilizing either parallex between two observatories or a pulsed laser ranging system or a hybrid system. ...

An optical imager that exploits off-center image rotation to encode both the lateral and depth coordinates of point sources in a single snapshot can perform 3D localization and tracking of space debris. When actively illuminated, unresolved space debris, which can be regarded as a swarm of point sources, can scatter a fraction of laser irradiance back into the imaging sensor. Determining the source locations and fluxes is a large-scale sparse 3D inverse problem, for which we have developed efficient and effective algorithms based on sparse recovery using non-convex optimization. Numerical simulations illustrate the efficiency and stability of the algorithms.

... American Institute of Aeronautics and Astronautics 8 For a given material and given required change in velocity, Equation 1 [23] helps in calculating the drag force due to magnetic field on a spherical body of diameter 10cm. This gives approximate results at high velocities also: [24] The number of artificial man-made objects orbiting earth is increasing at alarming rates. The large objects can be tracked by ground based observatories. ...

... Since these debris particles can't be tracked from existing earth based tracking mechanisms, a real-time debris tracking approach needs to be adopted. The Optical Orbital Debris Spotter [24] is one such mechanism which can be used for tracking debris as small as 0.01cm in the vicinity of the satellite. The concept of this system is to create a light sheet using a collimated source and a conic mirror [24] . ...

... The Optical Orbital Debris Spotter [24] is one such mechanism which can be used for tracking debris as small as 0.01cm in the vicinity of the satellite. The concept of this system is to create a light sheet using a collimated source and a conic mirror [24] . When the orbit trajectory of a debris object intersects the light sheet, the object will scatter, reflect, transmit and/or absorb some amount of light. ...

... A stand-alone optical system based on the use of a light-sheet illumination and scattering concept [8] for spotting debris within meters of a spacecraft has been proposed. A second system can localize all three coordinates of an unresolved, scattering debris [10,39] by utilizing either parallex between two observatories or a pulsed laser ranging system or a hybrid system. ...

We consider the high-resolution imaging problem of 3D point source image recovery from 2D data using a method based on point spread function (PSF) engineering. The method involves a new technique, recently proposed by S.~Prasad, based on the use of a rotating PSF with a single lobe to obtain depth from defocus. The amount of rotation of the PSF encodes the depth position of the point source. Applications include high-resolution single molecule localization microscopy as well as the problem addressed in this paper on localization of space debris using a space-based telescope. The localization problem is discretized on a cubical lattice where the coordinates of nonzero entries represent the 3D locations and the values of these entries the fluxes of the point sources. Finding the locations and fluxes of the point sources is a large-scale sparse 3D inverse problem. A new nonconvex regularization method with a data-fitting term based on Kullback-Leibler (KL) divergence is proposed for 3D localization for the Poisson noise model. In addition, we propose a new scheme of estimation of the source fluxes from the KL data-fitting term. Numerical experiments illustrate the efficiency and stability of the algorithms that are trained on a random subset of image data before being applied to other images. Our 3D localization algorithms can be readily applied to other kinds of depth-encoding PSFs as well.

... In spite of the high costs of space debris detection, it is very important given the large investment made by various space actors, since the largest concentration of space debris is in LEO (ISS orbit). As reported by Englert et al. [26] and Andrade [22], there is no expressive number of space debris in GEO. ...

The lack of technologies for space debris removal and explicit rules for the use of space are jeopardizing the future of space activities. Thus, the objective of this work was to analyse the current scientific research for space debris mitigation, prevention, monitoring and removal. We used bibliometric and patent analyses from the following databases: Space-track; Celestrack; Derwent; Web of Science.
In this work, the scientific, technological and political actions oriented to space debris mitigation were divided into (1) prevention policies, (2) monitoring and (3) capture. We observed great interest, mainly by the major spacefaring nations, in the development of technologies for detection and removal of space debris from low earth orbit. This increasing interest to develop feasible technologies and effective policies includes governments, space agencies, universities, institutes and private companies, especially from the main spacefaring nations.

... The number of space debris objects has been continu- ously increasing in the last few decades (Englert et al., 2014). In addition to approx. ...

We successfully demonstrate Stare & Chase: Space debris laser ranging to uncooperative targets has been achieved without a priori knowledge of any orbital information. An analogue astronomy CCD with a standard objective, piggyback mounted on our 50 cm Graz SLR receive telescope, ’stares’ into the sky in a fixed direction. The CCD records the stellar background within a field of view of approx. 7°. From the stellar X/Y positions on the sensor a plate solving algorithm determines the pointing data of the image center with an accuracy of approx. 15 arc seconds. If a sunlit target passes through this field of view, its equatorial coordinates are calculated, stored and a Consolidated Prediction Format (CPF) file is created in near real time. The derived CPF data is used to start laser ranging (’chase’ the object) within the same pass to retrieve highly accurate distance information. A comparison of Stare & Chase CPFs with standard TLE predictions shows the possibilities and limits of this method.