Orbits Of Objects Research Articles

Energetically Optimal Control of the Convergence of the Spacecraft in Non-Central Gravitational Field of the Earth on the far Guidance Stage

The article is devoted to the development of algorithms for calculating energy-optimal programs for controlling the approach of a spacecraft to an orbital object at the long-range guidance stage using the maximum principle L.S. Pontryagin. It is assumed that the spacecraft is equipped with a longitudinal propulsion system running on chemical fuel. The programs of optimal change in the second fuel consumption and the vector of cosine guides, which determine the orientation of the thrust force of the propulsion system, should be determined. As a criterion for optimal control, we consider a functional that determines the minimum consumption of the working fluid. The optimal control problem is solved in a limited region of the state space, which is determined by the range of variation of the angular range of the spacecraft within one revolution. The full equations of the boundary value problem of the maximum principle are given using the model of the object's motion in the normal gravitational field of the Earth, the boundary conditions, and also the analytical dependencies that determine the control structure in the optimal mode. The boundary optimization problem is solved with the Newton method. To determine the initial approximation of conjugate variables, an analytical solution is given to the problem of energy-optimal approach control in a uniform central field. The results of numerical studies of energy-optimal programs to control the interception in the normal gravitational field of the Earth with the final pitch at the stage of long-range guidance are presented. In general, the use of optimal approach control algorithms in the airborne and ground complex allows to reduce fuel costs when performing the maneuver, reduce time, and expand the reachability area of the target objects. In addition, the optimal solution can be considered as a reference, with which it is necessary to compare various variants of approximate control algorithms, evaluate their quality and make informed decisions on their practical use.

Near earth space object detection using parallax as multi-hypothesis test criterion.

The US Strategic Command (USSTRATCOM) operated Space Surveillance Network (SSN) is tasked with Space Situational Awareness (SSA) for the U.S. military. This system is made up of Electro-Optic sensors, such as the Ground-based Electro-Optical Deep Space Surveillance (GEODSS) and RADAR based sensors, such as the Space Fence Gaps. They remain in the tracking of Resident Space Objects (RSO's) in Geosynchronous Orbits (GEO), due to limitations of SST and GEODSS system implementation. This research explores a reliable, ground-based technique used to quickly determine an RSO's altitude from a single or limited set of observations. Implementation of such sensors into the SSN would mitigate GEO SSA performance gaps. The research entails a method used to distinguish between the point spread function (PSF) observed by a star and the PSF observed from an RSO by using Multi-Hypothesis Testing with parallax as a test criterion. Parallax is the effect that an observed object will appear to shift when viewed from different positions. This effect is explored by generating PSFs from telescope observations of space objects at different baselines. The research has shown the PSF of an RSO can be distinguished from that of a star using single, simultaneous observations from reference and parallax sensing telescopes. This report validates these techniques with both simulations and experimental data from the SST and Naval Observatory sensors.

A Novel Space-Based Orbit Determination Method Based on Distribution Regression and Its Sparse Solution

There is an inherent need to track and catalog space debris (objects) in geosynchronous earth orbits (GEO) based on space-based surveillance networks and a large amount of observation data. However, for objects in GEO, angle-only measurements containing noises have been regarded as difficult for short-arc orbit determination (OD) when pursuing high accuracy. In this paper, from a data-driven perspective, we propose a novel method for space-based OD based on distribution regression (DR), which is called the weighting distribution-regression OD (WDR-OD) method. The OD is treated as a regression process, which is learned from abundant observation data and the corresponding orbits of known objects. First, we propose the structure of space-based OD samples, wherein the feature variables with a weighting matrix are introduced to enhance prediction accuracy. Second, a two-stage sampled learning theory is employed to learn the mapping from measurements to objects' orbit through kernel mean embedding. The proposed method is experimentally compared with the improved Laplace method and shows greater robustness in measurements with white Gaussian noise (WGN) and colored noise. The positional RMSE reaches 0.8793 km with WGN and 1.6972 km with colored noise, which are significantly smaller than the corresponding Laplace method's 5.0804 km and 14.8132 km. Furthermore, we propose a RIP-based ROMP algorithm to provide the theoretical bound of sparsity and then to pursue a sparse solution. Although the positional RMSE increases to 1.6554 km in the sparse method, it shrinks the 90% to 93% nonzero elements of the coefficients matrix to zero, which is helpful in reducing the computing load, and it meaningfully extends the application domain of the WDR-OD method.

Possible utilization of space debris for laser propulsion

Laser propulsion perspectives become more realistic with the development of laser systems as well as the necessity to resolve space junk problem and to perform high specific impulse interplanetary flights. Unlike others, laser thrusters can use virtually any type of fuel by turning it into plasma; this provides great abilities for harvesting working medium in space instead of bringing it from the Earth. This and ability to reuse external laser source intensively could save a lot of money and broaden abilities for thrusterless small satellites (nano- and pico- especially) and constellations of those. For the first time, we considered several options to use space debris objects (including out-of-use satellites, rocket stages) as a fuel for spacecraft with laser thruster. We evaluated possible mass consumption, thrust, velocity and energy efficiency performance, as well as optimal laser impact regimes, demanded velocity increment and time scale for different missions. We have shown that sufficient momentum to make 1 ton low Earth orbit object burn in the atmosphere can be produced by ablation of 10 kg only. Our findings appear to be rather realistic in terms of state-of-art launchable lasers, surface scanning systems and cost effect.

Initial orbit determination using Doppler shift of Fraunhofer lines

Techniques for tracking objects in low Earth orbit include line-of-sight angle measurements and range measurements using RADAR or laser reflection. However, active ranging techniques are less effective for higher orbits because of the greater signal loss from distant targets. In this paper, using computer simulation, we show how incorporating measurements of the Doppler shift of Solar Fraunhofer lines can improve initial orbit determination. Results indicate that for Doppler measurement errors of less than 5 m/s, prediction accuracies for some orbital configurations can exceed Gooding’s angles-only method, while using only two observations of the target.

Monitoring of Space Debris Rotation Based on Photometry

The number of spacecraft and space debris (SD) in orbit has become so great that there is a real threat to flight safety. The task of precision calculation of the upcoming positions of any space objects (SO) in orbit in order to predict dangerous mutual approaches and to solve practical tasks has become topical. For the development of a modern orbit propagation model and the associated unified forecast of the evolution of orientation and rotation of an uncontrolled satellite, it is necessary to rely on long-term series of high-quality measurements and their analysis. At present, the direction of research on determining the state of SO rotation around a center of mass has become more and more developed. In our work, we analyze the results of photometric observations of several large objects of space debris obtained at the Astronomical Observatory of Odessa University using the KT-50 telescope during the last six years or more. The results of the evolution of the rotation rate and orientation of the Topex/Poseidon, Envisat, Oicets, Cosmos-2487 (Kondor-E) and Sich-2 satellites are presented.

Proximity scenario design for geostationary rendezvous with collocated satellite avoidance

Proximity operation is one of the prerequisites for in-orbit service or debris removal. Especially for objects in geostationary orbit (GEO), there are certain challenges in rendezvous and proximity operations, such as perturbed relative dynamics and constraints from collocated satellites. In this study, a novel optimization model is built to design the GEO proximity scenario, including the keeping points and durations of each phase. First, as a prerequisite of proximity scenario design, relative dynamics considering solar radiation pressure effects and the corresponding two-point boundary value problem are analytically solved. Second, the concept of passive safety performance is introduced. The safety constraints from both the target satellite and the collocated satellites are considered. The optimization model is then built, and an improved differential evolution optimization algorithm is employed to seek the solution with minimal velocity increment. The numerical examples indicate that a GEO proximity scenario can be stably and effectively designed by the presented method. Moreover, in the scenarios without a collocated satellite, with a static collocated satellite, and with dynamic collocated satellites, the optimized proximity scenarios remain passively safe. If any impulse in the scenario ceases, the resulting free drift trajectory would diverge from the target and the collocated satellites, maintaining the safety index and satisfying the given threshold.

Optimising filtering of two-line element sets to increase re-entry prediction accuracy for GTO objects

Predicting re-entry epoch of space objects enables managing the risk to ground population. Predictions are particularly difficult for objects in highly-elliptical orbits, and important for objects with components that can survive re-entry, e.g. rocket bodies (R/Bs). This paper presents a methodology to filter two-line element sets (TLEs) to facilitate accurate re-entry prediction of such objects. Difficulties in using TLEs for precise analyses are highlighted and a set of filters that identifies erroneous element sets is developed. The filter settings are optimised using an artificially generated TLE time series. Optimisation results are verified on real TLEs by analysing the automatically found outliers for exemplar R/Bs. Based on a study of 96 historical re-entries, it is shown that TLE filtering is necessary on all orbital elements that are being used in a given analysis in order to avoid considerably inaccurate results.

The eccentric case of a fast-rotating, gravity-gradient-perturbed satellite attitude solution

A closed-form first-order perturbation solution for the attitude evolution of a triaxial space object in an elliptical orbit is presented. The solution, derived using the Lie–Deprit method, takes into account gravity-gradient torque and is facilitated by an assumption of fast rotation of the object. The formulation builds on the earlier implementation of Lara and Ferrer, which assumes a circular orbit. The previously presented work—which assumes spin about an object’s axis of maximum inertia—is further extended by the explicit presentation of the transformations required to apply the solution to an object spinning about its axis of minimum inertia. Additionally, several numerical analyses are presented to more completely assess the utility of the solution. These studies (1) validate the elliptical solution, (2) assess the impact of varying the small parameter of the perturbation procedure, (3) analyze the assumption of fast rotation, and (4) apply the solution to the common and important scenario of a tumbling rocket body.

Revisiting the exomoon candidate signal around Kepler-1625 b

Context. Transit photometry of the Jupiter-sized exoplanet candidate Kepler-1625 b has recently been interpreted as showing hints of a moon. This exomoon, the first of its kind, would be as large as Neptune and unlike any moon we know from the solar system. Aims. We aim to clarify whether the exomoon-like signal is indeed caused by a large object in orbit around Kepler-1625 b, or whether it is caused by stellar or instrumental noise or by the data detrending procedure. Methods. To prepare the transit data for model fitting, we explore several detrending procedures using second-, third-, and fourth-order polynomials and an implementation of the Cosine Filtering with Autocorrelation Minimization (CoFiAM). We then supply a light curve simulator with the co-planar orbital dynamics of the system and fit the resulting planet–moon transit light curves to the Kepler data. We employ the Bayesian information criterion (BIC) to assess whether a single planet or a planet–moon system is a more likely interpretation of the light curve variations. We carry out a blind hare-and-hounds exercise using many noise realizations by injecting simulated transits into different out-of-transit parts of the original Kepler-1625 light curve: (1) 100 sequences with three synthetic transits of a Kepler-1625 b-like Jupiter-size planet and (2) 100 sequences with three synthetic transits of a Kepler-1625 b-like planet with a Neptune-sized moon. Results. The statistical significance and characteristics of the exomoon-like signal strongly depend on the detrending method (polynomials versus cosines), the data chosen for detrending, and the treatment of gaps in the light curve. Our injection-retrieval experiment shows evidence of moons in about 10% of those light curves that do not contain an injected moon. Strikingly, many of these false-positive moons resemble the exomoon candidate, that is, a Neptune-sized moon at about 20 Jupiter radii from the planet. We recover between about one third and one half of the injected moons, depending on the detrending method, with radii and orbital distances broadly corresponding to the injected values. Conclusions. A ΔBIC of − 4.9 for the CoFiAM-based detrending is indicative of an exomoon in the three transits of Kepler-1625 b. This solution, however, is only one out of many and we find very different solutions depending on the details of the detrending method. We find it concerning that the detrending is so clearly key to the exomoon interpretation of the available data of Kepler-1625 b. Further high-accuracy transit observations may overcome the effects of red noise but the required amount of additional data might be large.

Investigation of Light Pressure Influence on Dynamics of Near-Earth Objects in Resonant Orbits

The results of an analysis of changes in resonant orbital dynamics of near-Earth objects, which are caused by light pressure, are presented. We describe features of the orbital evolution of the objects subjected to the combined effect of secular resonances and light pressure. It was shown that the transfer of objects to highly elliptical and hyperbolic orbits is possible when the object’s area-to-mass ratio is large.

Results of the First Observations with a New Optical Complex Based on an RC500 Telescope and an Electron-Multiplying Charge-Coupled Device at the Assy-Turgen Observatory in Kazakhstan

The description of an optical complex at the Assy-Turgen Observatory (Kazakhstan) is given. This complex is suited for astrometric and photometric observations of active and passive objects (small-size space debris included) in geostationary orbits. It may be used to reveal, identify, and track potentially hazardous objects (asteroids and comets). The results of test observations are presented.

Contact dynamics and control of a space robot capturing a tumbling object

Capture of a free-floating space object in orbit is a challenging task especially when the object is tumbling. In this paper, the contact dynamics modeling and control problem for capturing a fast tumbling target object by a space robot are investigated. A generic frictional contact model is developed to represent the contact forces between the robot's end-effector and the target object. The frictional contact formulation is based on the compliance contact force and bristle friction model which can simulate intermittent frictional contact situations involving multiple-point contacts between contact interfaces with complex geometries. A resolved motion admittance control method is designed to realize a good tracking for a tumbling target object while increasing the compliance of the space robot. A simulation example of a 7-joint manipulator capturing a tumbling object in three dimensions is presented. The simulation results revealed that various contact scenarios during the capture process can be well simulated with the developed contact model and a good performance of the designed control method for capturing a fast tumbling target object.

Distinguishing between Kerr and rotating JNW space-times via frame dragging and tidal effects

In this paper, we first investigate some aspects of frame dragging in strong gravity. The computations are carried out for the Kerr black hole and for the rotating Janis-Newman-Winicour solution, that is known to have a naked singularity on a surface at a finite radius. For the Kerr metric, a few interesting possibilities of gyroscope precession frequency, as measured by a Copernican observer outside the ergoregion, are pointed out. It is shown that for certain angular velocities of a stationary observer, this frequency might vanish exactly, close to the ergoregion. Similar computations are repeated for static observers in the naked singularity background, and strong enhancement of the Lense-Thirring precession frequency compared to the black hole case is established. Then, we study the nature of tidal forces in the rotating naked singularity background, in Fermi normal coordinates. Here, physical quantities characterizing tidal disruptions of celestial objects in equatorial circular orbits are computed numerically. Our results here indicate that there might be significant deviations from corresponding Kerr black hole calculations, up to the level of approximation that we consider.

Strategic Implications of the Proliferation of Space Situational Awareness Technology and Information: Lessons Learned from the Remote Sensing Sector

Space situational awareness (SSA) refers to the ability to monitor and understand the state of the space environment, including the ability to track, understand, and predict the location of human-generated and natural objects in orbit around the Earth. This capability is a critical element in attributing and deterring attacks against space assets and in avoiding unintentional collisions. Historically, the United States Department of Defense has operated the most extensive SSA system in the world. Although, in recent years, it has shared data with commercial and foreign users on an ad hoc basis to help avoid collisions, access to the full database is highly restricted. Other nations, including Russia and Europe, have begun to develop or expand independent SSA systems. A number of commercial entities have also begun operating in this area, selling or planning to sell SSA services to satellite operators and governments. There are concerns in the United States about whether this proliferation of SSA technology and information will adversely affect national security, and questions about how the United States should respond to this situation. This article uses the example of remote sensing satellite technology and information, which experienced a similar transition from U.S. and Soviet dominance to participation by a wider range of nations and commercial entities, to identify the key strategic risks and opportunities posed by this trend. I discuss the extent to which these strategic risks and opportunities apply to the proliferation of SSA technology and information, finding that while the same strategic concerns are relevant in this case, typically the risks are lower. There are significant opportunities for the United States to benefit from this proliferation of technology. The article discusses the implications of these findings and offers recommendations that will allow the United States to further decrease the strategic risks associated with this trend, while increasing the benefits.

Effects of Uncertainties in the Atmospheric Density on the Probability of Collision Between Space Objects

AbstractThe rapid increase of the number of objects in orbit around the Earth poses a serious threat to operational spacecraft and astronauts. In order to effectively avoid collisions, mission operators need to assess the risk of collision between the satellite and any other object whose orbit is likely to approach its trajectory. Several algorithms predict the probability of collision but have limitations that impair the accuracy of the prediction. An important limitation is that uncertainties in the atmospheric density are usually not taken into account in the propagation of the covariance matrix from current epoch to closest approach time. The atmosphere between 100 km and 700 km is strongly driven by solar and magnetospheric activity. Therefore, uncertainties in the drivers directly relate to uncertainties in the neutral density, hence in the drag acceleration. This results in important considerations for the prediction of Low Earth Orbits, especially for the determination of the probability of collision. This study shows how uncertainties in the atmospheric density can cause significant differences in the probability of collision and presents an algorithm that takes these uncertainties into account to more accurately assess the risk of collision. As an example, the effects of a geomagnetic storm on the probability of collision are illustrated.

Satellite Cluster Close Approaches Determination for Collision Avoidance

As the number of space objects in orbit about the Earth increases, it is extremely important to determine the close approaches between them. In this paper the close approaches is determined for the satellite cluster using a simulation tool STK for the following (i) satellites of interest within a cluster (ii) a satellites of interest in a cluster and the space objects as listed in the space catalog and the close approach reports are analyzed. The results have indicated that the details of intruder satellites and the duration of close approaches and their minimum separation distances or the relative distances.

Estimation of systematic errors in the results of navigational measurements with the use of spacecraft robot onboard facilities

The article presents the results of an analytical study of the accuracy of estimating systematic optical errors of onboard navigation measurements that, along with the vector characterizing the motion of the center of mass of the space robot, are included in the vector of the parameters to be specified. The range to the orbital reference point, the relative speed of its motion and the angles between the directions to the orbital landmark and to the navigational stars, one of which is in the plane of the space robots orbit, and the direction to the second one coincides with the normal to this plane are chosen as the primary navigation parameters to be measured by the space robot onboard facilities. The conditions that make it possible to specify the augmented vector of the parameters to be determined are defined. Estimating the systematic errors of measurements we make assumptions about the central gravitational field of the Earth, the normal law of measurement errors with known variances and the constancy of the unknown systematic errors. Analytical expressions of the covariance matrices that make it possible to estimate the maximum achievable accuracy of solving the task depending on the kind of navigational measurements, variances of measurement errors and the number of measurements during a selected measuring interval are obtained. The presented results can be applied to justify the ways of improving the accuracy of the autonomous navigation of a space robot in diagnosing the technical condition of an orbital object.

Averaged solar radiation pressure modeling for high area-to-mass ratio objects in geosynchronous orbits

Space Situational Awareness, among other efforts, is aimed at providing a comprehensive and accurate knowledge of all Earth-orbiting objects. This is done by maintaining a catalog of space objects’ states (position and velocity). In the absence of observations, the orbits of these objects need to be numerically simulated. In this work, we study the high area-to-mass ratio class of objects which are sensitive to very small changes in perturbations, particularly the attitude dependent solar radiation pressure. This attitude dependency renders the orbit-attitude motion to be coupled. Traditionally, a cannonball model would be used to model these perturbations. While this is acceptable for an attitude stabilized active satellite, for non-functional space debris, the cannonball model does not seem to approximate the true dynamics accurately. Hence, a more precise, albeit computationally expensive propagation model needs to be developed, which warrants a better modeling of the perturbations in the near-Earth space. This work introduces a new model that averages the solar radiation pressure force experienced by multi-layer insulation foil in geosynchronous orbits. While speeding up the computational time by 66%, this model produces errors that are small enough to stay within the field of view of surveying telescopes over the propagation period of four days. The approach is compared with other existing models.

Survey of the Current Activities in the Field of Modeling the Space Debris Environment at TU Braunschweig

The Institute of Space Systems at Technische Universität Braunschweig has long-term experience in the field of space debris modeling. This article reviews the current state of ongoing research in this area. Extensive activities are currently underway to update the European space debris model MASTER. In addition to updating the historical population, the future evolution of the space debris environment is also being investigated. The competencies developed within these activities are used to address current problems with regard to the possibility of an increasing number of catastrophic collisions. Related research areas include, for example, research in the field of orbit determination and the simulation of sensor systems for the acquisition and cataloging of orbital objects. In particular, the ability to provide simulated measurement data for object populations in almost all size ranges is an important prerequisite for these investigations. Some selected results on the distribution of space debris on Earth orbit are presented in terms of spatial density. Furthermore, specific fragmentation events will be discussed.