Orbits Of Objects Research Articles

A Novel Method for Prediction and Warning for Uncontrolled Re-Entry Object Impact

ABSTRACT The growing Micrometeoroid and Orbital Debris (MMOD) environment in Earth orbit poses an increasing risk not only to active satellites but also to the general public. Of particular concern are the objects in low earth orbit (LEO) which have the potential for catastrophic consequence upon entry and collision with vulnerable terrestrial targets including airborne planes. There are limitations to the ability to predict uncontrolled object re-entry with sufficient precision to give timely or actionable warnings to threatened air traffic zones or surface locations. A system called R-DBAS (Re-entry Direct Broadcasting Alert System) invented by the co-author of this paper, T. Sgobba former head of the European Space Agency Independent Safety Office, has the potential to avoid catastrophic impacts by generating timely surface or air traffic impact warnings. The system includes a self-contained housing with on-board geolocation receiver, processing, memory with debris breakup models, and direct warning broadcast capability.

Periodic Orbits in the Elliptical Relative Motion Problem with Space Surveillance Applications

Periodic orbits with respect to an object in an eccentric Keplerian reference orbit can be found in a variety of ways, including the use of Tschauner–Hempel equations and orbital element differences, which both admit linearized solutions, as well as through direct analyses of two orbits. An alternative parameterization of the last approach is proposed in the current study, using an inertial frame and simple geometrical constructs inherent to the relative motion problem. In this manner, an intuitive and straightforward characterization of periodic orbits is established that retains the nonlinear dynamics. The resulting multidimensional space that defines the periodic orbits is surveyed, archiving 336 orbits and their characteristics, and direct comparisons are made with the Tschauner–Hempel equations to assess the linear region of validity. Applications focus on resident space object (RSO) surveillance and circumnavigation orbits. An orbit’s effectiveness is analyzed in terms of object coverage using coverage figures of merit, including the concept of “RSO tracks”, the analogy of ground tracks on the body-fixed surface of an RSO.

Eddy currents applied to de-tumbling of space debris: Analysis and validation of approximate proposed methods

The space debris population has greatly increased over the last few decades. Active debris removal (ADR) methods may become necessary to remove those objects in orbit that pose the biggest collision risk. Those ADR methods that require contact with the target show complications if the target is rotating at high speeds. Observed rotations can be higher than 60deg/s combined with precession and nutation motions. ‘Natural’ rotational damping in upper stages has been observed for some space debris objects. This phenomenon occurs due to the eddy currents induced by the Earth׳s magnetic field in the predominantly conductive materials of these man made rotating objects. Existing solutions for the analysis of eddy currents require time-consuming finite element models to solve a Poisson equation throughout the volume. The first part of this paper presents a new method to compute the eddy current torque based on the computation of a new tensor called the ‘Magnetic Tensor’. The general theory to compute this tensor by Finite Element Method is given as well as a particular frame model. This last model enables an explicit formula to be determined to evaluate the magnetic tensor. Analytical solutions for the spherical shell, the open cylinder and flat plates are given for the magnetic tensor and the eddy current torque model is validated with existing published work. The second part of the paper presents an active de-tumbling method for space debris objects based on eddy currents. The braking method that is proposed has the advantage of avoiding any kind of mechanical contact with the target. The space debris object is subjected to an enhanced magnetic field created from a chaser spacecraft which has one or more deployable structures with an electromagnetic coil at its end. The braking time and the possible orientation change in the rotation axis is analysed for a metallic spherical shell considering different ratios of conductive versus non-conductive material. The paper finalises with a case study based on the de-tumbling of an Ariane-4 Upper Stage H10 under the effect of the gravity gradient and a preliminary analysis of the non-uniformity of the magnetic field is presented.

The Criticality of Spacecraft Index

The future space debris environment will be governed by the production of fragments coming from massive breakups. In order to identify the most relevant parameters influencing the long term evolution of the environment and to assess the criticality of selected space objects in different regions of the circumterrestrial space, a large parametric study was performed. In this framework some indicators were produced to quantify and rank the relevance of selected fragmentations on the long term evolution of the space debris population. Based on the results of the fragmentation studies, a novel analytic index, the Criticality of Spacecraft Index (CSI), aimed at ranking the environmental criticality of abandoned objects in Low Earth Orbit (LEO), was formulated. It takes into account the physical characteristics of a given object, its orbit and the environment where this is located. The results corresponding to a sample of LEO objects in the initial population at the epoch of January 1, 2020 and mass larger than 100kg are shown.

Earth’s gravity gradient and eddy currents effects on the rotational dynamics of space debris objects: Envisat case study

The space debris population has grown rapidly over the last few decades with the consequent growth of impact risk between current objects in orbit. Active Debris Removal (ADR) has been recommended to be put into practice by several National Agencies in order to remove objects that pose the biggest risk for the space community. The most immediate target that is being considered for ADR by the European Space Agency is the Earth-observing satellite Envisat. In order to safely remove such a massive object from its orbit, a capturing process followed by a controlled reentry is necessary. However, current ADR methods that require physical contact with the target have limitations on the maximum angular momentum that can be absorbed and a de-tumbling phase prior to the capturing process may be required. Therefore, it is of utmost importance for the ADR mission design to be able to predict accurately how the target will be rotating at the time of capture. This article analyses two perturbations that affect an object in Low Earth Orbit (LEO), the Earth’s gravity gradient and the eddy currents induced by the Earth’s magnetic field. The gravity gradient is analysed using the equation of conservation of total energy and a graphical method is presented to understand the expected behaviour of any object under the effect of this perturbation. The eddy currents are also analysed by studying the total energy of the system. The induced torque and the characteristic time of decay are presented as a function of the object’s magnetic tensor. In addition, simulations were carried out for the Envisat spacecraft including the gravity gradient perturbation as well as the eddy currents effect using the International Geomagnetic Reference Field IGRF-11 to model the Earth’s magnetic field. These simulations show that the combined effect of these two perturbations is a plausible explanation for the rotational speed decay observed between April 2013 and September 2013.

Orbit Design for Approaching Multiple Space Objects in a Circular Orbit

This paper focuses on orbit design for a spacecraft without orbital maneuver approaching multiple objects in a circular orbit. Based on the assumption of no perturbation, a series of relations of approach orbit elements and geocentric angle between objects are established by theory analysis and formula derivation. Then characteristics of approach orbit are derived from a large number of data and numerical analysis. Finally a simulation example with Earth Geostationary Orbit as target circular is shown.

Statistics and Analysis of LEO Objects’ Luminosity

As one of basic properties of space objects, luminosity is frequently used for the identification of space objects, as well as for the calculation of their scattering cross sections. In general, space objects shine only by reflecting sunlight, their brightness observed by ground stations is affected by many factors. Since the multi-object photometric observation equipment operated five years ago, a large number of photometric data have been accumulated. This article estimates the overall accuracy of the data, and lists some typical situations in respect to the phase angle-magnitude (PA-m) relation for space objects. And the statistics are conducted on the luminosity data of more than two thousand low earth orbit (LEO) objects.

Application of the time-delay integration method: Survey observations of geosynchronous orbit objects and short-term variability observations

Abstract “Time-Delay Integration (TDI)” readout technique has been adopted to a mosaic CCD camera equipped with four fully-depleted CCDs. Optical distortion and image deformation due to the TDI operation are discussed. The manner and advantages of the TDI method in survey observations of geosynchronous orbit objects are summarized. We propose a new TDI application method of getting short-term light curves of artificial space objects. This method of detecting a short-term variability can be applied for a variety of objects, ranging from satellites to stars. It can also be used for the light-curve observations of transient objects which might show short-term variability and of which the precise time information is needed.

An analysis of very short-arc orbit determination for low-Earth objects using sparse optical and laser tracking data

The requirement to regularly track an increasing number of objects will result in straining existing tracking networks. This paper investigates the orbit prediction capability of an orbit determination process using very short-arc optical and laser debris tracking data for objects in low-Earth orbits. An analysis is carried out to determine the reduction in orbit prediction accuracy when tracking data over 5s from each pass is only available for an orbit determination.The results show that the reduction in accuracy is not extensive and good orbit predictions are still possible when using only 5s of data from the beginning of each pass. The results are achievable due to an accurate ballistic coefficient estimation and accurate tracking data. The dependence of the results on the perigee altitude of the objects is obvious, indicating modelling error of the atmospheric mass density in lower orbits remains the dominant source of error.

Observations in the thermal IR and visible of a retired satellite in the graveyard orbit, and comparisons to active satellites in GEO

There exists a population of defunct satellites in the geo-stationary arc that potentially pose a hazard to current and future operational satellites. These drifting, non-station-kept objects have a variety of ages and sizes, and many are trapped in libration orbits around the Earth׳s two gravitational potential wells (the non-spherical nature of the Earth gives rise to two geo-potential wells or “stable points” that affect objects in geostationary and geosynchronous orbits), whereas others were boosted to higher altitudes into so-called “graveyard” orbits.We have observed several of the approximately 49 objects in libration orbits about the Western stable point (R. Choc, T. Flohrer, and B. Bastida, “Classification of Geosynchronous Objects,” Issue 13, ESA/ESOC, February 2011), as well as objects in graveyard orbits. We have carried out an observational campaign utilizing The Aerospace Corporation׳s 3–13µm Broadband Array Spectrograph System (BASS), as well as with several optical sensors to collect data on a representative sample of these objects at a variety of solar phase angles. Here we report on recent BASS observations of a retired satellite in the “graveyard” orbit, and compare them with data we had collected over six years ago, while the satellite was still active. Data are also presented on similar satellites that are still active. We describe our methods, the data collected, our results, and our future plans.

Using Magnetometers for Space Object Characterization in Space Situational Awareness Applications

Magnetometer-based detection and characterization of space objects in geosynchronous orbit is motivated and challenges are discussed. Observable constants of motion with and without charge screening are derived in detail. A novel application of orbit and detection constraints is used to generate admissible region boundaries for unobservable states, allowing initial orbit determination and data association of space objects passing near magnetometers. Practical and operational issues are discussed in detail.

Optical orbital debris spotter

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 (<10cm) in Low Earth Orbit (LEO) are of concern because they are abundant and difficult to track or even to detect on a routine basis. Due to the increasing debris population it is reasonable to assume that improved capabilities for on-orbit damage attribution, in addition to increased capabilities to detect and track small objects are needed. Here we present a sensor concept to detect small debris with sizes between approximately 1.0 and 0.01cm in the vicinity of a host spacecraft for near real time damage attribution and characterization of dense debris fields and potentially to provide additional data to existing debris models.

Adaptive optics to enhance tracking of space debris

Since the first artificial satellite was launched in 1957 we have been sending more and more objects into orbit every year. With each launch there are items left behind in space after the functional satellite is delivered. These objects are collectively known as space debris, and range from old rocket motors and fuel tanks to fragments of metal from sacrificial assemblies holding rocket stages together. The space above Earth is full of this debris, which is starting to pose a real hazard to operational satellites.1 An object in orbit has a velocity on the order of kilometers per second, therefore even something the size of a small bolt could be fatal to the delicate hardware of an operational satellite. We can track large pieces of space debris easily from the ground either optically or using radar.2 Derelict satellites and old rocket bodies are objects that we know, catalogue, and track regularly. If there is any danger of one of these colliding with a functional satellite, tracking stations will receive that information and pass it to the satellite operator, who can judge whether to alter their system’s orbit to avoid a collision. Radar tracking works very well in this situation, providing orbital accuracy to within a few kilometers. However, there are many more objects of less than 1m in size that are difficult to track with radar. To address this problem we use Lidar, an active optical tracking technique in which we propagate a laser through a ground-based telescope onto the sky.3 The telescope tracks an object along its trajectory and measures the laser pulse’s round trip time to determine the target range. With this data we can determine precisely the orbit of each object, enabling us to assemble a catalogue and regularly survey the objects. This system is currently limited to tracking items down to approximately 10cm in size in the range 400–1500km, and larger objects at around 2500km. The return signal follows an A=r4 relationship, where the object cross section area is A, Figure 1. A ground-based telescope launches a IR laser ahead of the target (a) such that the object (b) intersects the beam. A laser guide star illuminates a layer of sodium in the atmosphere, producing a reference beacon to measure the atmospheric turbulence.

Active debris multi-removal mission concept based on hybrid propulsion

During the last 40 years, the mass of the artificial objects in orbit increased quite steadily at the rate of about 145 metric tons annually, leading to about 7000 metric tons. Most of the cross-sectional area and mass (97% in low Earth orbit) is concentrated in about 4500 intact abandoned objects plus a further 1000 operational spacecraft. Analyses have shown that the most effective mitigation strategy should focus on the disposal of objects with larger cross-sectional area and mass from densely populated orbits. Recent NASA results have shown that the worldwide adoption of mitigation measures in conjunction with active yearly removal of approximately 0.2–0.5% of the abandoned objects would stabilize the debris population. Targets would have typical masses between 500 and 1000kg in the case of spacecraft, and of more than 1000kg for rocket upper stages. In the case of Cosmos-3M second stages, more than one object is located nearly in the same orbital plane. This provides the opportunity of multi-removal missions, more suitable for yearly removal rate and cost reduction needs. This paper deals with the feasibility study of a mission for the active removal of large abandoned objects in low Earth orbit. In particular, a mission is studied in which the removal of two Cosmos-3M second stages, that are numerous in low Earth orbit, is considered. The removal system relies on a Chaser spacecraft which performs rendezvous maneuvers with the two targets. The first Cosmos-3M stage is captured and an autonomous de-orbiting kit, carried by the Chaser, is attached to it. The de-orbiting kit includes a Hybrid Propulsion Module, which is remotely ignited to perform stage disposal and controlled reentry after Chaser separation. Then, the second Cosmos-3M stage is captured and, in this case, the primary propulsion system of the Chaser is used for the disposal of the mated configuration. Critical mission aspects and related technologies are investigated at a preliminary level. In particular, an innovative electro-adhesive system for target capture, a mechanical system for the hard docking with the target and a hybrid propulsion system suitable for rendezvous, de-orbiting and controlled reentry operations are analyzed. This is performed on the basis of a preliminary mission profile, in which suitable rendezvous and disposal strategies have been considered and investigated by numerical analysis. A preliminary system mass budget is also performed, showing that the Chaser overall mass is about 1350kg, including a primary propulsion system of about 300kg and a de-orbiting kit with a mass of about 200kg. This system is suitable to be launched with VEGA, actually the cheapest European space launcher.

Statistical Impact Prediction of Decaying Objects

This paper describes a method for statistically predicting the impact time and location of an orbital object under 200 km altitude. It also investigates the influence of the chief parameter uncertainties on the statistical dispersion. Unlike the main methods used nowadays, which derive drag parameters from historical state data, a shape model is used to acquire aerodynamic coefficients in the various flow regimes. As a test object, the Delta-K rocket stage is chosen, due to the high data availability for validating the tool. Using a Monte Carlo sequence, multiple six-degrees-of-freedom simulations are executed, in which the initial state and the density output of the atmosphere model are varied within their uncertainty windows. By kernel density estimation, the resulting data are used to derive a probability density function of the impact time and infer a ground track expressing impact probability. In a comparative study with the Tracking and Impact Predictions published by the United States Space Surveillance Network, the method’s performance is tested. In this comparison, a decrease in impact window size is observed, while maintaining the reliability. Moreover, by a variance-based sensitivity analysis, the uncertainty in the density model is identified as the prime contributor to footprint dispersion and it is shown that knowledge of the rotational state can be critical in decreasing impact windows.

Rendezvous with and Capture / Removal of Non-Cooperative Bodies in Orbit: The Technical Challenges

Removal of debris from orbit becomes an increasing ur- gency because the growing amount of non-controlled spacecraft, residuals from launchers and other items or- biting around the Earth pose an increasing threat of colli- sion with operational satellites. Also, for larger bodies in lower orbits the threat of uncontrolled impact on ground after re-entry exists. Whereas in very low orbits all bodies will decay after some time due to the residual atmosphere, in higher orbits they will stay for considerable time or practically forever. For objects in higher orbits and for those posing the threat of uncontrolled impact, active re- moval will be the sole remedy. The tasks to be performed from approach to contact and the technical challenges to be mastered to achieve capture and removal from orbit are discussed in this paper. The major challenges are the far range approach without navigation interfaces on the tar- get, relative position control of the chaser in close vicinity of a tumbling target, capture of such target without cap- ture interfaces and the establishment of a structural con- nection, which is stiff enough for controlled deorbitation. 1 DEBRIS IN DIFFERENT ALTITUDES ABSTRACT Removal of debris from orbit becomes an increasing ur- gency because the growing amount of non-controlled spacecraft, residuals from launchers and other items or- biting around the Earth pose an increasing threat of colli- sion with operational satellites. Also, for larger bodies in lower orbits the threat of uncontrolled impact on ground after re-entry exists. Whereas in very low orbits all bodies will decay after some time due to the residual atmosphere, in higher orbits they will stay for considerable time or practically forever. For objects in higher orbits and for those posing the threat of uncontrolled impact, active re- moval will be the sole remedy. The tasks to be performed from approach to contact and the technical challenges to be mastered to achieve capture and removal from orbit are discussed in this paper. The major challenges are the far range approach without navigation interfaces on the tar- get, relative position control of the chaser in close vicinity of a tumbling target, capture of such target without cap- ture interfaces and the establishment of a structural con- nection, which is stiff enough for controlled deorbitation. ABSTRACT Removal of debris from orbit becomes an increasing ur- gency because the growing amount of non-controlled spacecraft, residuals from launchers and other items or- biting around the Earth pose an increasing threat of colli- sion with operational satellites. Also, for larger bodies in lower orbits the threat of uncontrolled impact on ground after re-entry exists. Whereas in very low orbits all bodies will decay after some time due to the residual atmosphere, in higher orbits they will stay for considerable time or practically forever. For objects in higher orbits and for those posing the threat of uncontrolled impact, active re- moval will be the sole remedy. The tasks to be performed from approach to contact and the technical challenges to be mastered to achieve capture and removal from orbit are discussed in this paper. The major challenges are the far range approach without navigation interfaces on the tar- get, relative position control of the chaser in close vicinity of a tumbling target, capture of such target without cap- ture interfaces and the establishment of a structural con- nection, which is stiff enough for controlled deorbitation. 1 DEBRIS IN DIFFERENT ALTITUDES

Debris characterization techniques via unresolved long-wave infrared imaging from a space-based platform

Every space launch increases the overall amount of space debris, especially when circumstances result in the orbital objects being stranded in orbit with no deorbiting capabilities. Studies contributing to the understanding of space debris aid spacecraft operators in mitigating risk associated with Earth-orbiting debris objects. Accurately characterizing the debris threat to a spacecraft is of vital importance in maximizing the lifespan and mission capabilities of the spacecraft. This investigation aims to develop long-wave infrared radiometric-based techniques for detection and characterization of typical debris objects via signal analysis of unresolved imagery. Tumble rate, absorptivity-to-emissivity ratio, and cross-sectional area are analyzed and estimates made regarding their values. Fusion of astrometric and radiometric data allows for a more accurate, and less ambiguous, hypothesis to be reached concerning the cross-sectional area of debris objects.

Analytic characterization of measurement uncertainty and initial orbit determination on orbital element representations

This paper presents an approach to characterize the uncertainty associated with the state vector obtained from the Herrick-Gibbs orbit determination approach using transformation of variables. The approach is applied to estimate the state vector and its probability density function for objects in low Earth orbit using sparse observations. The state vector and associated uncertainty estimates are computed in Cartesian coordinates and Keplerian elements. The approach is then extended to accommodate the $$J_2$$ perturbation where the state vector is written in terms of mean orbital elements. The results obtained from the analytical approach presented in this paper are validated using Monte Carlo simulations and compared with the often utilized similarity transformation for Kepler, mean, and nonsingular elements. The measurement uncertainty characterization obtained is used to initialize conventional nonlinear filters as well as operate a Bayesian approach for orbit determination and object tracking.

On Lambert’s problem and the elliptic time of flight equation: A simple semi-analytical inversion method

In the two-body model, time of flight between two positions can be expressed as a single-variable function and a variety of formulations exist. Lambert’s problem can be solved by inverting such a function. In this article, a method which inverts Lagrange’s flight time equation and supports the problematic 180° transfer is proposed. This method relies on a Householder algorithm of variable order. However, unlike other iterative methods, it is semi-analytical in the sense that flight time functions are derived analytically to second order vs. first order finite differences. The author investigated the profile of Lagrange’s elliptic flight time equation and its derivatives with a special focus on their significance to the behaviour of the proposed method and the stated goal of guaranteed convergence. Possible numerical deficiencies were identified and dealt with. As a test, 28 scenarios of variable difficulty were designed to cover a wide variety of geometries. The context of this research being the orbit determination of artificial satellites and debris, the scenarios are representative of typical such objects in Low-Earth, Geostationary and Geostationary Transfer Orbits. An analysis of the computational impact of the quality of the initial guess vs. that of the order of the method was also done, providing clues for further research and optimisations (e.g. asteroids, long period comets, multi-revolution cases). The results indicate fast to very fast convergence in all test cases, they validate the numerical safeguards and also give a quantitative assessment of the importance of the initial guess.

Space Debris Measurement Using Joint Mid-Latitude and Equatorial Optical Observations

A system for orbital object monitoring is analyzed, based on a mid-latitude and an equatorial observatory. The enhancements with respect to the use of a single telescope located at mid-latitude, for space debris detection and tracking are highlighted in terms of surveying volume, object identification, and orbital determination accuracy. The need to improve observation capabilities in monitoring and cataloguing such kinds of objects is constantly growing, due to the constant increase of operative satellites and space debris in both geostationary Earth orbit (GEO) and low Earth orbit (LEO) regions. After the considerations on the feasibility of the whole system, an overview of the observatories' design is sketched, on the basis of previous Italian experience in space debris observation, and taking into account constraints imposed by the instrumentation. In particular the main characteristics of components, software for image analysis and observation methodologies are analyzed and a possible configuration is given, based on the ALMASCOPE observatory realized by the Space Robotics Group at the University of Bologna. This observatory was used for the 2010 test campaign carried out from the Broglio Space Center in Kenya.