Formation Flying and Change Detection for the UNSW Canberra Space ‘M2’ Low Earth Orbit Formation Flying CubeSat Mission

The University of New South Wales, Canberra (UNSW Canberra) embarked on an ambitious CubeSatellite research, development, and education program in 2017 through funding provided by the Royal Australian Air Force (RAAF). The program consisted of M1 (Mission 1), M2 Pathfinder, and concludes with the formation flying mission M2. M2 is the final mission comprising two 6U CubeSatellites flying in formation using differential aerodynamic drag control. The M2 satellites were launched in a conjoined 12U form factor on RocketLab’s ‘They Go Up So Fast’ launch in March 2021. On 10th September 2021 the spacecraft divided into two 6U CubeSats (M2-A and M2-B) under the action of a small spring force in their near-circular 550km, 45-degree inclination orbit. The formation is controlled by varying the spacecrafts’ attitude, which creates a large variation in the aerodynamic drag force due to the change in the cross-sectional area from the large, double-deployable, solar arrays located on the zenith face of the spacecraft. This paper presents the outcomes of the Formation Flying and Change Detection primary mission objectives for the mission. The results are generated by collecting and analysing optical and RF (Radio Frequency) space domain awareness sensor data from the ground and validating them against GPS (Global Positioning System) and attitude data downlinked from the spacecraft. The outcomes of the broader mission objectives, which include increasing the Technology Readiness Level for a suite of intelligent on-board optical and RF sensor technologies, will be presented in subsequent publications. The results presented here comprise two major campaigns: 1.) The spacecraft separation campaign when the original 12U form factor deployed following launch split in half to form the M2-A and M2-B satellites, and 2) the demonstration of active formation control of the spacecraft via differential aerodynamic drag. M2-A and M2-B underwent several major configuration changes during the spacecraft separation campaign. The results from ground-based sensors detecting the 12U spacecraft separating into two distinct (6U) objects are presented. The effect of the double-deployable solar arrays deployment on the relative orbital motion of the M2-A and M2-B spacecraft is illustrated and compared to data from optical and RF ground-based measurements taken during this window. The formation control campaign involved actively controlling the spacecraft via differential aerodynamic drag in order to significantly alter the separation distance. The mission demonstrated the capability to switch the leading spacecraft’s position between M2-A and M2-B and to actively control separation distance ranging from 130km down to 1km. Formation control is achieved via open-loop, pre-scheduled, commands issued from the UNSW Canberra Space ground station. A two-stage modelling and simulation process is used to derive the scheduled attitude states. Firstly, a batch least squares orbit determination algorithm is applied to GPS data from a steady-state differential drag actuation period (where one spacecraft is in maximum drag and the other in its minimum drag attitude configuration). The batch least squares orbit determination is conducted out using the NASA General Mission Analysis Tool (GMAT), resulting in precise state estimates for each spacecraft and drag coefficient (Cd) estimates for both the maximum and minimum drag configurations. Predictions of trajectory for various attitude profiles can be produced by tailoring the spacecraft’s drag coefficients between the maximum and minimum values generated by the batch least squares state estimation process. Ground-based optical and RF space domain awareness (SDA) sensor measurements collected during the manoeuvre campaign are compared to the spacecraft’s GPS and attitude telemetry data. The SDA sensors are actively seeking to detect changes in the separation distance between the spacecraft. Initial results from an investigation into whether changes observed in photometric light curve signatures can signal the commencement of a differential drag manoeuvre are presented

Effect of surface stress and thermal loads on the stiffness of cantilever beams and plates

© 2013 Dr. Michael J. LachutNanomechanical doubly-clamped beams and cantilever plates are often used to sense a host of environmental processes, including biomolecular interactions, mass measurements and responses to chemical stimuli. Understanding the effects of surface stress on the stiffness of such nanoscale devices is essential for proper analysis of experimental data. In this thesis, we present a rigorous theoretical treatment of this problem, and explore both linear and nonlinear effects. In Chapter 2, we begin by examining effects of surface stress on the stiffness of cantilever plates and doubly-clamped beams, in the linear stiffness regime. The relative physical mechanisms causing a stiffness change in each case is explored. Specifically, Poisson's ratio is found to exert a dramatically different effect in cantilevers than in doubly-clamped beams, and here we explain why. The relationship between the change in spring constants and resonant frequency is also discussed. The relative change in effective spring constant is also examined, and its connection to the relative frequency shift is presented. Interestingly, this differs from what is naively expected from elementary mechanics. A discussion of the practical implications of our theoretical findings is provided, which includes an assessment of available experimental results and potential future measurements on nanoscale devices. Buckling of elastic structures can occur for loads well within the proportionality limit of their constituent materials. Given the ubiquity of beams and plates in engineering design and application, their buckling behaviour has been widely studied. However, buckling of a cantilever plate is yet to be investigated, despite the widespread use of cantilevers in modern technological developments. In chapter 3, a theoretical study into the buckling behaviour of a cantilever plate that is uniformly loaded in its plane is presented. Applications of this fundamental problem include loading due to uniform temperature and surface stress changes. This is achieved using a scaling analysis and full three-dimensional numerical solution, leading to explicit formulas for the buckling loads. Unusually, we observe buckling for both tensile and compressive loads, the physical mechanisms for which are explored. We also examine the practical implications of these results to modern developments in ultra sensitive micro- and nano-cantilever sensors, such as those composed of silicon nitride and graphene. In chapter 4, the influence of the cantilever geometry is investigated and shown to play a critical role, with V-shaped cantilevers displaying greatly enhanced sensitivity to surface stress in comparison to rectangular cantilevers. The physical mechanisms controlling the effect on V-shaped cantilever stiffness are discussed. We also investigate the buckling behaviour of V-shaped cantilevers and demonstrate that they too can buckle under tensile and compressive loads. The analysis concludes with an assessment of the stiffness and stability of V-shaped cantilevers made of silicon and graphene, under surface stress loads

An analysis of the 2016 Hitomi breakup event

Abstract The breakup of Hitomi (ASTRO-H) on 26 March 2016 is analysed. Debris from the fragmentation is used to estimate the time of the event by propagating backwards and estimating the close approach with the parent object. Based on this method, the breakup event is predicted to have occurred at approximately 01:42 UTC on 26 March 2016. The Gaussian variation of parameters equations based on the instantaneous orbits at the predicted time of the event are solved to gain additional insight into the on-orbit position of Hitomi at the time of the event and to test an alternate approach of determining the event epoch and location. A conjunction analysis is carried out between Hitomi and all catalogued objects which were in orbit around the estimated time of the anomaly. Several debris objects have close approaches with Hitomi; however, there is no evidence to support the breakup was caused by a catalogued object. Debris from both of the largest fragmentation events—the Iridium 33–Cosmos 2251 conjunction in 2009 and the intentional destruction of Fengyun 1C in 2007—is involved in close approaches with Hitomi indicating the persistent threat these events have caused in subsequent space missions. To quantify the magnitude of a potential conjunction, the fragmentation resulting from a collision with the debris is modelled using the EVOLVE-4 breakup model. The debris characteristics are estimated from two-line element data. This analysis is indicative of the threat to space assets that mission planners face due to the growing debris population. The impact of the actual event to the environment is investigated based on the debris associated with Hitomi which is currently contained in the United States Strategic Command’s catalogue. A look at the active missions in the orbital vicinity of Hitomi reveals that the Hubble Space Telescope is among the spacecraft which may be immediately affected by the new debris. Graphical abstract