Figure 2 - uploaded by Allan Shtofenmakher
Content may be subject to copyright.
AVM vs. debris diameter for various RSO-CST ranges, assuming diffuse Lambertian spheres in accordance with IADC standards [15]. The thin horizontal lines correspond to various sensor AVM cutoffs, while the shaded green region represents the regime which can be detected by typical CSTs. Plots for SpinSat (adapted from [13]) and for POPACS (using data from [14]) are shown as vertical dotted lines for comparison.
Source publication
The U.S. Space Surveillance Network (SSN) currently tracks over 23,000 resident space objects (RSOs) in low-earth orbit (LEO). The SSN uses ground-based radar and optical methods, which are susceptible to variations in atmosphere, weather, and lighting conditions. These barriers limit surveillance capabilities to objects with characteristic length...
Contexts in source publication
Context 1
... results of Eqn. 5, using debris diameter as the input variable, are plotted in Fig. 2 across three different RSO-CST ranges (1 km, 10 km, and 100 km). As before, the AVM cutoff value for each imager listed in Table 2 is also shown as a horizontal line. Dotted vertical lines represent the plots for SpinSat (56 cm) and POPACS (10 cm). DMSP-5D2 F7 (930 cm) does not appear in Fig. 2 for scaling reasons. It is worth noting ...
Context 2
... diameter as the input variable, are plotted in Fig. 2 across three different RSO-CST ranges (1 km, 10 km, and 100 km). As before, the AVM cutoff value for each imager listed in Table 2 is also shown as a horizontal line. Dotted vertical lines represent the plots for SpinSat (56 cm) and POPACS (10 cm). DMSP-5D2 F7 (930 cm) does not appear in Fig. 2 for scaling reasons. It is worth noting that increasing the RSO-CST range by an order of magnitude increases the AVM (i.e., makes dimmer) of a particular debris particle by 5 units, which is consistent with expectations from Eqn. 5. This is comparable to the difference between the AVM cutoff values for the HP CST and the FI CST, ...
Context 3
... intersections of the horizontal AVM cutoff lines in Fig. 2 with the thick range lines offers insights into the smallest debris particle that can be detected by each imaging sensor at a given range. In broad terms, the results indicate that all three CST classes depicted should be able to detect debris as small as 1 cm at the relatively close range of 1 km and debris larger than 42.5 cm at the ...
Citations
... Since the vast majority of currently active satellites feature at least one CST, recent research has investigated the potential for leveraging the thousands of commercial star trackers already on orbit as part of a near-zerocost distributed space surveillance system [4], [10], [11], [12], [15], [16]. Various noteworthy endeavors include: assessing the effectiveness of observing and detecting RSOs in simulated CST images [15]; exploring methods for estimating the positions and velocities of such RSOs [11], [12]; and developing methods for increasing the accuracy of RSO orbit estimates using multiple CSTs distributed across space and time [10]. ...
... Recently, we have begun investigating the potential for using CSTs to detect and track debris particles smaller than 10 cm. We explored the relationship among the apparent visual magnitude (AVM) of the RSOor the apparent brightness of the RSO as perceived by the observing CST-RSO size, and RSO-CST distance, establishing a parameter space (in terms of the latter two parameters) within which a given CST can feasibly detect debris particles in LEO [16]. For completeness, we restate the assumptions, methods, and key findings of this earlier effort, which were first presented at the 9th Annual Space Traffic Management Conference of the International Academy of Astronautics (IAA STM 2023), in this paper. ...
... mately as large as 1.6 km [18]. However, our recent work [16] demonstrates that both microsatellite-class CSTs (e.g., [19]) and nanosatellite-class CSTs (e.g., [20]) are capable of detecting debris particles of these size classes at larger target-observer ranges for less than 10% of the power. Although there may be a use-case for space-based radar systems with regards to debris particles smaller than 1 cm in characteristic length, for particles between 1 cm and 10 cm in characteristic length, CSTs offer a more promising solution-especially with the potential for opportunistic, distributed space surveillance at scale. ...
... In particular, the formal representation of an existing space situational awareness (SSA) system within a digital twin framework encourages investigation into the establishment of novel DTFs for similar aerospace processes that are forthcoming or in development. For instance, at the time of this writing, no such formal DTF exists for space-based detection of debris and other RSOs using sensors external to the SSN, in spite of recent publications exploring the feasibility and value of such an approach [11,[13][14][15][16][17][18][19]. As an example, recent work by Shtofenmakher and Balakrishnan indicates that commercial optical sensors available onboard most active satellites can, under appropriate lighting conditions, be used to detect sub-10-cm-class debris in LEO [17,18]. ...
... For instance, at the time of this writing, no such formal DTF exists for space-based detection of debris and other RSOs using sensors external to the SSN, in spite of recent publications exploring the feasibility and value of such an approach [11,[13][14][15][16][17][18][19]. As an example, recent work by Shtofenmakher and Balakrishnan indicates that commercial optical sensors available onboard most active satellites can, under appropriate lighting conditions, be used to detect sub-10-cm-class debris in LEO [17,18]. These space-based measurements could be transmitted to the ground through radio frequency or optical communication methods and received by a corresponding ground station [20]. ...
... As mentioned in Section I, recent advancements in space-based RSO sensing and state estimation capabilities have promoted discussions regarding leveraging on-orbit satellites for improving overall space situational awareness [11,[13][14][15][16][17][18]. Ref. [17], in particular, suggests that existing commercial optical sensors onboard thousands of active satellites have the potential to enable opportunistic detection of sub-10-cm-class orbital debris on a massive scale. ...
As interest in digital engineering within a variety of technical domains begins to accelerate, industries continue to encounter obstacles with regard to implementing—and benefiting from—digital twin technologies. One key challenge facing digital twin adoption in the aerospace industry, in particular, is a lack of standardized digital twin frameworks (DTFs). Adapting existing DTF standards intended for use in other domains towards aerospace applications may offer a path forward for overcoming this obstacle. To demonstrate the feasibility of this approach, the recently published ISO 23247 standard, Digital Twin Framework for Manufacturing, is adapted for the first time for use in a non-manufacturing aerospace application—collision avoidance (COLA) in low Earth orbit (LEO) for resident space objects (RSOs) greater than 10 cm in characteristic length. The result is the first known formal representation in a standardized digital twin framework of this well-established prescriptive COLA process. To further demonstrate the value of establishing a standard aerospace DTF, this framework is,in turn, adapted into a novel descriptive digital twin architecture for space-based detection of sub-10-cm-class orbital debris, which can later be integrated with the existing collision avoidance framework to improve overall space situational awareness (SSA). The paper concludes with recommendations for future work on the development of increasingly sophisticated digital twins of the LEO space environment, leveraging these frameworks as a baseline.
... Since the vast majority of currently active satellites feature at least one CST, recent research has investigated the potential for leveraging the thousands of commercial star trackers already on orbit as part of a near-zerocost distributed space surveillance system [4], [10], [11], [12], [13], [14]. However, the majority of these efforts has focused on improving state estimates for those RSOs that are already tracked by the SSN-that is, those with characteristic length larger than 10 cm in general. ...
... More recently, we have begun investigating the po-tential for using CSTs to detect and track debris particles smaller than 10 cm [14]. We explored the relationship among the apparent visual magnitude (AVM) of the RSO-or the apparent brightness of the RSO as perceived by the observing CST-RSO size, and RSO-CST distance, establishing a parameter space (in terms of the latter two parameters) within which a given CST can feasibly detect debris particles in LEO [14]. ...
... More recently, we have begun investigating the po-tential for using CSTs to detect and track debris particles smaller than 10 cm [14]. We explored the relationship among the apparent visual magnitude (AVM) of the RSO-or the apparent brightness of the RSO as perceived by the observing CST-RSO size, and RSO-CST distance, establishing a parameter space (in terms of the latter two parameters) within which a given CST can feasibly detect debris particles in LEO [14]. In this paper, we relax the zero-phase-angle assumption used in [14] and explore the effect of Sun-RSO-CST phase angle on useful RSO-CST detection range. ...
The recent proliferation of resident space objects (RSOs) in low Earth orbit (LEO) threatens the sustainability of space as a resource and requires persistent monitoring to avoid collisions involving valuable space assets. State-of-the-art ground-based space surveillance techniques, due to their susceptibility to atmosphere, weather, and lighting conditions, tend to focus on RSOs with characteristic length greater than 10 cm. Consequently, millions of smaller LEO RSOs remain untracked by ground-based methods, which reduces overall space situational awareness. Onboard satellite sensors offer a space-based method for tracking RSOs. Prior research has investigated the feasibility of using commercial star trackers (CSTs)—optical sensors prevalent on most active spacecraft—to observe, detect, and estimate the position and velocity of RSOs larger than 10 cm. In a recent effort, we expanded on these feasibility studies by assessing the capabilities of CSTs to detect debris particles smaller than 10 cm in characteristic length. In this paper, we extend our previous study by relaxing its zero-phase-angle assumption and characterizing the effect of Sun-RSO-CST phase angle on debris detection range. We identify a number of representative CSTs with publicly available optical characteristics and consider the effects of properties such as pixel pitch, focal length, aperture diameter, and field of view (FOV) on the capability of each CST to detect debris at a given distance and relative velocity (in the form of streak speed). We find that, for debris particles modeled as diffuse Lambertian spheres, Sun-RSO-CST phase angles as high as 57° result in no more than 20% reduction to the useful RSO-CST detection range. In addition, we find that, rather than aperture diameter, pixel pitch and focal length tend to determine the capability of a given CST to resolve two distinct RSOs. Furthermore, streak speed may serve as a stronger limiting factor for detection of smaller debris particles than for larger ones. Though we identify a general reduction in the feasible region, the results indicate that CSTs have the potential to substantially enhance space-based debris detection.
