Orbital Perturbations Research Articles

Drag sail attitude tracking via nonlinear control

A drag sail is a propellantless device suitable for passive deorbiting of satellites after their end-of-life. It exploits atmospheric drag to gradually reduce the kinetic energy of the decommissioned satellite and cause it to lose altitude over time. It is well known that the braking effect of the atmosphere is greater the surface exposed to the flow of the atmospheric particles relative to the satellite. For this reason, a drag sail is essentially a large and lightweight membrane, which is deployed by the satellite when it is to begin orbital decay. For given environmental/initial conditions and inertial characteristics of the deployed system, the braking effect of a drag sail is more intense if its perpendicular axis is constantly aligned with the direction of the relative particle flow. For this purpose, a sliding mode control strategy is adopted. The reference to follow is obtained by propagating the spacecraft orbital dynamics along with its attitude dynamics. Various orbital perturbations and the disturbance torque due to atmospheric drag are implemented in the numerical code to verify the robustness of the proposed control law. It is also assumed that the spacecraft control torque vector is bounded in magnitude and always belongs to the plane of the braking device. The results show that the proposed strategy is effective in accurately tracking the reference attitude and that it is robust, being able to track a reference that varies unpredictably due to both orbital and attitude perturbations.

Low-Earth-Orbit Packing: Implications for Orbit Design and Policy

As more and more operators propose and deploy large constellations, the finite orbital volume in low Earth orbit (LEO) is becoming increasingly congested. Over the last several years, we have been developing a proposal for LEO orbital coordination that uses carefully designed slots in nested concentric shells to avoid the potential for hazardous close approaches between participating spacecraft in their mission orbit. Such a slotting structure provides several benefits, including a reduction in orbital risk, clear analytic tools to understand the opportunity costs associated with a particular shell and slot design, and methods to assess and improve the efficiency with which operators make use of LEO. This paper offers a high-level description of key findings from our previous work on shell design under orbital perturbations and slot reconfiguration, with an emphasis on applications for assessing the efficiency of orbital use. It then explains how these methods could be used for a variety of policy and regulatory purposes, including assessing the efficiency of orbital use, remaining potential admissible slot locations that preserve compatibility, and the efficacy of capacity-expanding measures. Various potential implementation pathways for slotting are presented and compared. Several best practices for safe and efficient constellation design are proposed.

Fuel-optimal acquisition and control of a cartwheel formation in Earth displaced heliocentric orbit

An optimization approach for cartwheel formation acquisition and maintenance in an Earth Displaced heliocentric orbit is presented. This work considers non-gravitational perturbations such as solar radiation pressure, thus extending the studies previously performed for the mission LISA. The problem is tackled as a Nonlinear Programming problem using a multiple shooting method. The optimization process is performed in two steps: first, the orbital elements of each satellite in heliocentric orbit are optimized to guarantee the stability during the science phase hence easing maintenance of the cartwheel formation in presence of orbital perturbations. Then, the obtained initial states are propagated to obtain a set of target orbital states which become the final target of a second optimization covering the transfer phase from Earth. For the science phase optimization presents two alternative cost functions are introduced, one based on the arm-length evolution and one on the arm-length-rate evolution. The performance of each cost function is analysed for different initial displacement angles: for target arm-lengths below 2.5 million kilometers the arm-length cost function provides the best results while no significant difference between the two optimized solutions is observed above this value. The transfer phase optimization presents two different approaches, one considering an injection on a trajectory more favourable for one of the three spacecraft and one considering an injection on an intermediate trajectory which minimizes the overall acquisition cost of all spacecraft. The proposed optimization approach performance are studied on a set of test cases covering both transfer and science phase, showing that stable configuration conditions can be found even in presence of orbital perturbations and that the multiple injection transfer is capable of providing a more homogeneous fuel consumption among the three spacecraft.

Analytic optimal control for multi-satellite assembly using linearized twistor-based model

This paper presents Guidance and Control (G&C) systems for multi-satellite assembly in proximity operations. The systems utilize the twistor model, which is linearized through Taylor’s series. Decentralized control laws, designed using Linear Quadratic Regulator (LQR) and Model Predictive Control (MPC), are employed to track an energy-optimal trajectory generated using the Hamiltonian approach. Data exchange between satellites and their neighbors is represented using graph theory. The decentralized MPC framework is implemented using the CasADi package. To ensure collision avoidance between the satellites, a repulsive control law is designed, considering symmetric input saturation in the actuators. The proposed G&C systems are tested using a high-fidelity nonlinear satellite relative motion model that incorporates orbital perturbations. Numerical simulations are performed in a MATLAB® environment, and the results are visualized using STK®. Furthermore, a comparative study is conducted to evaluate tracking performance and fuel consumption between the two control methods. The results demonstrate that the use of an optimal trajectory reduces fuel consumption for both control algorithms.

Neuro‐adaptive prescribed performance control for spacecraft rendezvous based on the fully‐actuated system approach

AbstractThis paper investigates the control problem of spacecraft rendezvous with obstacle constraint, considering the external disturbance forces caused by orbit perturbation. Firstly, the translational dynamic model of spacecraft rendezvous is given and then rewritten into a second‐order fully‐actuated system form. Then, by employing the prescribed performance control method, the performance function and error transformation are determined, pre‐defining the prescribed performance bounds. Moreover, the fully‐actuated system approach is used to linearize the original nonlinear system, which simplifies the processes of control law design and ensures model accuracy. After that, to ensure that the spacecraft could avoid the dangerous zone during its manoeuvre, the artificial potential function is introduced, based on which a sliding mode surface is designed. Finally, the prescribed performance control–artificial potential function‐based control law is derived, further adopting the neuro‐adaptive method to deal with external interferences. The stability of the close‐loop control system is analysed through the Lyapunov approach and the effectiveness of the proposed control scheme is verified by carrying out a numerical simulation.

Orbital perturbation coupling of primary oblateness and solar radiation pressure

Orbital perturbation coupling of primary oblateness and solar radiation pressure

Impacts of inter-satellite links on the ECOM model performance for BDS-3 MEO satellites

Inter-satellite link (ISL) plays an essential role in current and future Global Navigation Satellite System (GNSS). In this study, we investigate the impact of ISL observations on precise orbit determination for BeiDou-3 Navigation Satellite System (BDS-3) Medium Earth Orbit (MEO) satellites based on different Extended CODE Orbit Models (ECOM). Thanks to the better observation geometry of the Ka-band ISL data compared to the L-band data for BDS-3 MEO satellites, the ISL solution substantially reduces Orbit Boundary Discontinuity (OBD) errors, except for C30, which suffers from unstable Ka-band hardware delay. From the external quality analysis, ISL significantly enhances the reliability of the orbit of MEO satellites manufactured by the China Academy of Space Technology (CAST). The standard deviation (STD) of the satellite laser ranging (SLR) residuals is approximately 2.5 cm, and the root mean square (RMS) is reduced by 10–23% compared to L-band solutions. Besides, the Sun-elongation angle dependent systematic error in SLR residuals nearly vanishes based on the reduced 5-parameter ECOM (ECOM1) or extended 7-parameter ECOM (ECOM2) with ISL data. This is because the ISL reduces the correlation between state parameters and solar radiation pressure (SRP) parameters as well as those among SRP parameters, leading to a more accurate estimation of both orbit and SRP perturbations, particularly those along B direction. This confirms that the deficiency of the SRP models for BDS-3 CAST satellites can be compensated by using better observation geometry from ISL data. On the other hand, for the satellite manufactured by Shanghai Engineering Center for Microsatellites (SECM), the ISL allows for a more accurate estimation of the Bc1 parameter in the ECOM1 model. This only reduces linear systematic error, possibly because the impact generated by the satellite bus cannot be entirely absorbed by the B-direction parameters.

Orbital Tolerance and Intrinsic Orbital Capacity for Electric Propulsion Constellations

Large constellations are typically designed using sets of periodic orbits and satellite control boxes sized to ensure compatible phasing between coorbital constellation planes to prevent conjunction events. This work investigates how the control action for orbit maintenance influences feasible intrashell and intershell distances in a satellite constellation. Two-dimensional lattice flower constellations are simulated in an environment inclusive of orbital perturbations, with onboard sensors and an electric propulsion system constituting the satellite guidance, navigation, and control system. An analysis to define estimates for minimum separation distances is performed as a function of control, propulsion, orbit, environmental, and spacecraft characteristics. An estimate of the intrinsic (geometric) orbital capacity is proposed, based on current and advanced technologies, in order to quantify the number of admissible spacecraft and orbital shells in a selected altitude range. Simulation results are used to improve the fidelity of intrinsic orbital capacity estimates and to understand factors that influence the number of admissible satellite locations in low Earth orbit.

Weather‐Induced Satellite Orbit Perturbations

AbstractSatellites in Earth's orbit are exposed to Earth radiation, consisting of reflected solar and emitted thermal radiation, thereby exerting a non‐conservative force that causes acceleration and affects the orbits. Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) mission aiming to retrieve the Earth's gravity potential is critically dependent on accounting for this force and all other non‐gravitational forces. There are both diurnal and seasonal variations in the Earth's radiation pressure, of which the seasonal variability can be represented by climatology. Nevertheless, the daily variations in the Earth's radiation pressure, due to the transient changes in the weather; for example, clouds and their properties, are not accounted for in the orbit perturbations studies. We show here that the top‐of‐atmosphere radiation fluxes computed with a numerical weather prediction (NWP) model explain most of the measured short‐term variations in the radial acceleration of the GRACE‐FO satellite. Our physics‐based modeling corrects a hitherto unexplained lack of power spectral density in the measured accelerations. For example, we can accurately model the accelerations associated with a tropical storm in the Indian Ocean in December 2020, which would not be possible when using climatological data. Our results demonstrate that using a global numerical weather prediction model significantly improves the simulation of non‐gravitational effects in the satellites' orbits. In the 7‐day data set, OpenIFS‐simulated acceleration exhibited higher accuracy than climatological‐data‐simulated acceleration (2.5 compared to 2.6 nms−2) and an improved precision (2.6 compared to 3.0 nms−2). This advancement contributes to a more precise orbit determination across various applications in Earth sciences.

Near-Optimal Feedback Guidance for Low-Thrust Earth Orbit Transfers

This research describes a near-optimal feedback guidance, based on nonlinear orbit control, for low-thrust Earth orbit transfers. Lyapunov stability theory leads to proving that although several equilibria exist, only the desired operational conditions are associated with a stable equilibrium. This ensures quasi-global asymptotic convergence toward the desired final orbit. The dynamical model includes the effect of eclipsing on the available thrust, as well as all the relevant orbit perturbations, such as several harmonics of the geopotential, solar radiation pressure, aerodynamic drag, and gravitational attraction due to the Sun and the Moon. Near-optimality of the feedback guidance comes from careful selection of the control gains. They are identified in two steps. Step (a) is an extensive table search in which the gains are changed in a large interval. Step (b) uses a numerical optimization algorithm that refines the gains found in (a), while minimizing the time of flight. For the numerical simulations, two scenarios are defined: (i) nominal conditions and (ii) nonnominal conditions, which arise from orbit injection errors and stochastic failures of the propulsion system. For case (i), gain optimization leads to obtaining numerical results very close to those corresponding to a known optimal orbit transfer with eclipse arcs. Moreover, for case (ii), extensive Monte Carlo simulations demonstrate that the nonlinear feedback guidance at hand is effective in driving a spacecraft from a low Earth orbit to a geostationary orbit, also in the presence of nonnominal flight conditions.

Preliminary design of a space debris removal mission in LEO using a solar sail

This paper discusses a space debris removal mission in low Earth orbit in which, for a preliminary design, a solar sail is used as a chaser satellite to reach, capture and de-orbit a debris object. The sail, which exploits the solar radiation pressure as its main source of thrust, is subject to the effects of aerodynamic forces, Earth’s oblateness and eclipse occurrence. Locally-optimal laws are used to control the transfer with the aim of maximizing (or minimizing) the rate of change of a specific orbital element or a suitable combination of them, depending on the transfer phase. When blended control laws are used to target the debris, the optimal weighting factors are calculated with a genetic algorithm to assess the relative importance of each orbital element. Numerical simulations show the effectiveness of locally-optimal laws in driving the sail towards the target even in the presence of the above-mentioned orbital perturbations. In a test-case scenario, a solar sail with a characteristic acceleration of 0.1 mm/s2, departing from 550 km of altitude, is able to reach the debris orbit at 1200 km of height in less than 200 days with a good accuracy level. The same analysis has been repeated for a solar sail with performance characteristics similar to those of NASA’s planned Advanced Composite Solar Sail System (ACS3) mission.

Study of orbital relocation of objects in GEO via orbital perturbations and solar sail

Study of orbital relocation of objects in GEO via orbital perturbations and solar sail

Uncovering Hidden Massive Black Hole Companions with Tidal Disruption Events

Dynamical perturbations from supermassive black hole (SMBH) binaries can increase the rates of tidal disruption events (TDEs). However, most previous work focuses on TDEs from the heavier black hole in the SMBH binary (SMBHB) system. In this work, we focus on the lighter black holes in SMBHB systems and show that they can experience a similarly dramatic increase in their TDE rate due to perturbations from a more massive companion. While the increase in TDEs around the more massive black hole is mostly due to chaotic orbital perturbations, we find that, around the smaller black hole, the eccentric Kozai–Lidov mechanism is dominant and capable of producing a comparably large number of TDEs. In this scenario, the mass derived from the light curve and spectra of TDEs caused by the lighter SMBH companion is expected to be significantly smaller than the SMBH mass estimated from galaxy scaling relations, which are dominated by the more massive companion. This apparent inconsistency can help find SMBHB candidates that are not currently accreting as active galactic nuclei and that are at separations too small for them to be resolved as two distinct sources. In the most extreme cases, these TDEs provide us with the exciting opportunity to study SMBHBs in galaxies where the primary SMBH is too massive to disrupt Sun-like stars.

Platinated azulenes: Structures and electronic spectroscopy

Eight PtII-azulenes σ-complexes were synthesized with the aim of understanding the effect of metalation on the electronic structures, spectroscopy and luminescence of the organic chromophore. Trans-[PtII(PEt3)2(X)]+ (Et = ethyl, X = Br− or I−) groups were attached to the 3-position or 1,3-positions of azulene to form two mononuclear PtII-azulene complexes (1a and 1b) and two binuclear complexes (2a and 2b). Coordination of trans-[PtII(PEt3)2(X)]+ group(s) to 1‑bromo-3-ethynylazulene or 1,3-diethynylazulene led to two mononuclear (3a and 3b) and two binuclear (4a and 4b) Pt-acetylide complexes.Molecular structures of the complexes were characterized by X-ray diffraction and NMR spectroscopy. The electronic structures of the complexes were elucidated by DFT calculations which showed small contributions of the Pt 5dπ orbitals in the HOMOs of the metalated complexes, whereas the LUMOs have no contribution from the Pt orbitals. Attaching the trans-[PtII(PEt3)2(X)]+ fragment directly to azulene in 1a,b and 2a,b destabilizes the HOMOs, LUMOs and LUMO+1 s to different extents. However, the bonding of the trans-[Pt(PEt3)2(X)(CC)]-group to azulene in 3a,b and 4a,b destabilizes its HOMO, but stabilizes the LUMO and LUMO+1. The extent of orbital perturbations increases with the number of Pt-substituents, but do not depend on the halide ligands X. UV–vis absorption spectra of the complexes show red-shift of azulene-centered absorption bands with the S0→S2 transition more red-shifted than the S0→S1 transition. As a result, the “window” between the transitions is red-shifted and reduced to ∼8548 cm−1 in the case of 4a and 4b (c.f. 12,000 cm−1 in azulene). Despite reduction of the energy gap between the S1 and S2 excited states in all the platinated-azulene complexes, the complexes still violate Kasha's rule, displaying S2→S0 fluorescence in solutions which are red-shifted with respect to the fluorescence of azulene.

Impact of orbiting satellites on star formation rate evolution and metallicity variations in Milky Way-like discs

ABSTRACT At least one major merger is currently taking place in the Milky Way (MW). The Sagittarius (Sgr) dwarf galaxy is being tidally destroyed while orbiting around the MW, whose close passages perturb the disc externally. In this work, using hydrodynamical simulations, we investigate how massive dwarf galaxies on quasi-polar Sgr-like orbits impact the star formation (SF) inside the MW-like discs. First, we confirm that interactions with orbiting satellites enhance the SF rate in the host. However, prominent SF bursts are detected during the very close passages (<20 kpc) of massive (2 × 1010 M⊙) gas-poor satellites. For gas-rich satellites, while we observe substantial enhancement of the SF, we do not detect prominent peaks in the SF history of the host. This can be explained by the steady gas accretion from the satellite smoothening short-term variations in the SF. The impact of the satellite perturbations, especially its first encounters, is seen mainly in the outer (>10 kpc) disc. We also found that the close passages of satellites cause the formation of low-metallicity stars in the host, and the effect is the most prominent for gas infall from the satellites resulting in the dilution of the mean stellar metallicity. Our simulations are in favour of causality between the recent passages of the Sgr and the bursts of the SF in the solar neighbourhood (≈1 and ≈2 Gyr ago); however, to reproduce the SF burst at its first infall (≈6 Gyr), we require a very close passage (<20 kpc) with subsequent substantial mass-loss of the Sgr precursor.

Flying Parker Solar Probe to touch the Sun

For the first time in history, Parker Solar Probe touched the Sun in April 2021 when it entered the Sun's corona—humanity's first mission ever that reached the Sun—for a scientific in-situ study to unlock the mystery of our star. To reach the Sun is extremely difficult because, unlike any other space exploration destination, the Sun is the solar system's central body, around which Earth and other planets revolve. Earth orbits the Sun at a velocity of about 30 km/s, so for a spacecraft to reach the Sun from Earth the spacecraft must cancel out its velocity in the Earth orbit so it can fall to the Sun. That requires an excessively large energy higher than that required to reach any destination in the solar system, which is beyond the capability of current rockets. This paper describes how Parker Solar Probe is delivered to the Sun through a unique V7GA trajectory that enables it to attain the excessive energy through planetary gravity assists of Venus, flying by Venus seven times to ultimately come within 9.86 solar radii (RS) of the Sun. An emphasis is on in-flight trajectory control of the probe through the intricate V7GA trajectory in actual operation in an unprecedented space environment around the Sun, where unpredictable orbit perturbations plus their ripple effects on the consecutive seven Venus flybys could easily drive the flight trajectory out of control. A novel systematic 2-level control method is developed and has been applied to solve the complicated trajectory control problem in flight operation, using in-flight trajectory re-optimization to select the targets of Venus flybys as trajectory control points and then using trajectory correction maneuvers to target a Venus flyby at the control point. This method enables effective and efficient control of the intricate V7GA trajectory and has resulted in significantly better than pre-launch anticipated flight performance, saving tremendous ΔV. Four years from launch, Parker Solar Probe has completed 5 of the 7 Venus gravity-assist flybys and 12 of the 24 planned solar encounters, passing by the Sun at 13 RS in its orbit. Flight results and performance of the completed flight to date are also described.

The increased Diels–Alder reactivity of umpolung tropone: analysis of individual atoms and bonds using QTAIM and IQA along complete IRC paths

AbstractA fruitful debate took place recently in literature, discussing the enhanced Diels–Alder reactivity of tropone derivatives for which the carbonyl polarity was reversed by means of umpolung. Karas et al. sustained that the umpolung increases the antiaromatic character of the ring, affecting the highest occupied molecular orbital (HOMO)/least unoccupied molecular orbital (LUMO) energies, speeding up the reaction. Tiekink et al. challenged this interpretation by sustaining that the asynchronicity of the reaction mechanisms, rather than orbital energy perturbation, was the main responsible for the smaller reaction barriers. We shed light on this dispute by computing full interaction quantum atom (IQA) and quantum theory of atoms in molecules (QTAIM) analyses over complete intrinsic reaction coordinate (IRC) paths for the Diels–Alder reaction of tropone and its umpolung derivatives, using the same systems studied by Karas et al. and Tiekink et al. Our results confirm that the asynchronicity is indeed very high for those reactions with smaller reaction barriers and offer an atom‐by‐atom and bond‐by‐bond analysis of the entire IRC pathways. Even though asynchronicity and lower reactions barriers seem to be related, antiaromaticity and lower barriers are related as well, but discussing both these interpretations does not necessarily require arguments on HOMO/LUMO energies to be invoked.

Effect of α-Substitution on the Reactivity of C(sp3)-H Bonds in Pd0-Catalyzed C-H Arylation.

We report mechanistic studies on the reactivity of different α-substituted C(sp3)-H bonds, -CHnR (R = H, Me, CO2Me, CONMe2, OMe, and Ph, as well as the cyclopropyl and isopropyl derivatives -CH(CH2)2 and -CHMe2) in the context of Pd0-catalyzed C(sp3)-H arylation. Primary kinetic isotope effects, kH/kD, were determined experimentally for R = H (3.2) and Me (3.5), and these, along with the determination of reaction orders and computational studies, indicate rate-limiting C-H activation for all substituents except when R = CO2Me. This last result was confirmed experimentally (kH/kD ∼ 1). A reactivity scale for C(sp3)-H activation was then determined: CH2CO2Me > CH(CH2)2 ≥ CH2CONMe2 > CH3 ≫ CH2Ph > CH2Me > CH2OMe ≫ CHMe2. C-H activation involves AMLA/CMD transition states featuring intramolecular O → H-C H-bonding assisted by C-H → Pd agostic bonding. The "AMLA coefficient", χ, is introduced to quantify the energies associated with these interactions via natural bond orbital 2nd order perturbation theory analysis. Higher barriers correlate with lower χ values, which in turn signal a greater agostic interaction in the transition state. We believe that this reactivity scale and the underlying factors that determine this will be of use for future studies in transition-metal-catalyzed C(sp3)-H activation proceeding via the AMLA/CMD mechanism.

Mitigating potentially hazardous asteroid impacts revisited

Contact. Potentially hazardous asteroids (PHA) in Earth-crossing orbits pose a constant threat to life on Earth. Several mitigation methods have been proposed, and the most feasible technique appears to be the disintegration of the impactor and the generation of a fragment cloud by explosive penetrators at interception. However, mitigation analyses tend to neglect the effect of orbital dynamics on the trajectory of fragments. Aims. We aim to study the effect of orbital dynamics of the impactor’s cloud on the number of fragments that hit the Earth, assuming different interception dates. We investigate the effect of self-gravitational cohesion and the axial rotation of the impactor. Methods. We computed the orbits of 105 fragments with a high-precision direct N-body integrator of the eighth order, running on GPUs. We considered orbital perturbations from all large bodies in the Solar System and the self-gravity of the cloud fragments. Results. Using a series of numerical experiments, we show that orbital shear causes the fragment cloud to adopt the shape of a triaxial ellipsoid. The shape and alignment of the triaxial ellipsoid are strongly modulated by the cloud’s orbital trajectory and, hence, the impact cross-section of the cloud with respect to the Earth. Therefore, the number of fragments hitting the Earth is strongly influenced by the orbit of the impactor and the time of interception. A minimum number of impacts occur for a well-defined orientation of the impactor rotational axis, depending on the date of interception. Conclusions. To minimise the lethal consequences of an PHA’s impact, a well-constrained interception timing is necessary. A too-early interception may not be ideal for PHAs in the Apollo or Aten groups. Thus, we find that the best time to intercept PHA is when it is at the pericentre of its orbit.

Adaptive Estimation of Distribution Algorithms for Low-Thrust Trajectory Optimization

A direct adaptive scheme is presented as an alternative approach for minimum-fuel low-thrust trajectory design in non-coplanar orbit transfers using fitness landscape analysis (FLA). The spacecraft dynamics is modeled with respect to modified equinoctial elements by considering orbital perturbations. Taking into account the timings of thrust arcs, the discretization nodes for thrust profile, and the solution of multi-impulse orbit transfer, a constrained continuous optimization problem is formed for low-thrust orbital maneuvers. An adaptive method within the framework of the estimation of distribution algorithms (EDA) is proposed, which aims at conserving the feasibility of the solutions within the search process. Several problem identifiers for low-thrust trajectory optimization are introduced, and the complexity of the solution domain is analyzed by evaluating the landscape feature of the search space via FLA. Two adaptive operators are proposed, which control the search process based on the need for exploration and exploitation of the search domain to achieve optimal transfers. The adaptive operators are implemented in the presented EDA and several perturbed and nonperturbed orbit transfer problems are solved. The results confirm the effectiveness and reliability of the proposed approach in finding optimal low-thrust transfer trajectories.