Orbital Lifetime Research Articles

Time-Dependent Satellite Explosion Probabilities for Long-Term Orbital Debris Environment Modeling

On-orbit accidental explosions are a significant contributor to the growth of the orbital debris population. Certain types of satellites have been seen to exhibit different behaviors and timelines of explosions. Recent assessments of on-orbit explosions for three categories of satellites—Russian Sistema Obespecheniya Zapuska (SOZ, Proton 4th-stage attitude and ullage motors) units, spacecraft, and rocket bodies—suggest that on-orbit explosions can be modeled using a continuous, time-dependent probability of explosion. This paper discusses the methodology for developing a time-dependent probability of explosion as a function of the satellite’s orbital lifetime based on historical explosions. The SOZ units are found to be best modeled by a modified Gaussian probability distribution, with the peak probability of explosion occurring around 10.4 years on-orbit. Spacecraft and rocket bodies both exhibit exponentially decaying explosion probabilities, with rocket bodies showing fast-, medium-, and slow-time modes of decay. Total cumulative probabilities of explosion are approximately 57% for SOZ units, 4% for spacecraft, and 2% for rocket bodies. Examples of implementation in a simulation of the orbital debris environment using NASA’s long-term evolutionary model are given, showing that the overall explosion behavior over two centuries is significantly different from that using a previously implemented constant-probability-type-dependent explosion rate model and provides a better representation of the historical explosion record.

Collision probability evaluation of SRM slag during orbital lifetime

At the end of combustion, a solid rocket motor (SRM) in orbit emits combustion products with relatively large particle sizes (slag). ISO 24113:2023 “Space debris mitigation requirements” defines criteria to limit debris emission 1 mm or larger in the LEO protected region. JAXA's “Space debris mitigation standard,” JMR-003E, sets out the same requirements. Hence, JAXA has begun an improvement study on SRM slag emissions as it develops the next generation of SRMs to conserve the orbital environment by significantly reducing SRM slag larger than 1 mm. However, ensuring the complete prevention of larger SRM slag emission is technically challenging. Thus, we are alternatively working to establish a risk evaluation method and criteria based on the collision probability (Pc) of SRM slag during its orbital lifetime. Based on ground firing tests, this study estimated the number and particle size of SRM slag in orbit emitted during the Epsilon and Epsilon S launch missions. The Pc per mission during the orbital lifetime was calculated and provisionally set to 10–3 for currently operational spacecraft. This paper discusses its acceptability to JAXA.

MILP-MPC for Planned Maneuver station-keeping and Collision Avoidance of GEO Satellites Using On-Off Chemical Thrusters

GEO satellites require precise station-keeping and ensuring collision avoidance to maintain their desired orbital positions and ensure uninterrupted communication services. However, maneuvering these satellites poses significant challenges due to various geophysical factors and orbital perturbations. This work proposes a model predictive control for planned maneuver station-keeping and collision avoidance of GEO satellites using south, east, and west maneuvers. These maneuvers have been achieved using on/off chemical thrusters with a short firing time. The station-keeping problem is reformulated as an optimization problem using mixed-integer linear programming. MILP-MPC formulation simultaneously considers multiple objectives and constraints such as fuel consumption, maneuver planning, and collision avoidance for mitigating collision risks. Simulation results demonstrate the effectiveness of the proposed MILP-MPC framework compared to the real-time telemetry in achieving accurate station-keeping and collision-free operation while optimizing fuel consumption. The proposed controller increases the satellite lifetime by reducing the thruster firing time.

Orbital Lifetime Estimation of Rocket Bodies in Eccentric Low Earth, Low Inclination Orbits

The dense population of Low Earth Orbit (LEO) due to frequent launches necessitates precise knowledge of the orbital lifetime of rocket bodies in this region. This study focuses on estimating the orbital lifetime of rocket bodies in eccentric, low-inclination LEO. Using the open-source software General Mission Analysis Tool (GMAT), the orbital lifetimes of rocket bodies with masses of 1000 kg, 1200 kg, and 1400 kg were calculated for altitudes ranging from 250 km to 500 km and inclinations of 0˚, 10˚, and 20˚. The orbital lifetimes of the defunct rocket bodies ranged from 3 to 832 days. GMAT-derived orbital lifetimes were compared with those obtained using Systems Tool Kit (STK). A subsequent 2D interpolation code was developed to interpolate the lifetime for a user-provided configuration of mass and orbital altitude. The Python code interpolated the orbital lifetimes for the given configurations with a maximum error of 5% compared to the GMAT-simulated lifetime values. This approach provides essential data for assessing post-mission disposal plans for rocket bodies and ensuring alignment with the Inter-Agency Space Debris Coordination Committee (IADC) 25-year guideline. Key findings reveal that the orbital lifetime of a rocket body increases with inclination. Additionally, it was observed that the orbital lifetime increases with mass due to slower orbital decay.

Autonomous orbit maintenance takeover control of ultra-low orbit spacecraft with event-triggered mechanism

In this paper, the problem of high-precision autonomous orbit maintenance takeover control of ultra-low orbit (ULO) spacecraft with event-triggered mechanism (ETM) and tangential continuous low thrust is addressed. First, the ETM I is proposed to reduce the communication burden between Global Navigation Satellite System (GNSS) cellular satellite and controller cellular satellite. Second, a fuzzy adaptive controller is proposed to maintain the orbit altitude of the ULO spacecraft. Furthermore, the ETM II is provided to ensure that the control thrust changes infrequently to extend the lifetime of electric thrust cellular satellite. In addition, the ETM II can lighten the communication burden between controller cellular satellite and electric thrust cellular satellite. By combining fuzzy adaptive control method and ETMs, the ETM-based fuzzy adaptive controller is established. Finally, the simulation is provided to verify the effectiveness of the developed control method.

Feasibility of orbital capture of near-earth asteroids based on the planar-circular restricted three-body problem

With the goal of efficiently extracting samples or even materials from the surface of an asteroid, this study proposed and investigated a method to change the velocity vector of a near-Earth asteroid and place it into an orbit where it is captured by the Earth’s gravitational field. The change in the orbit of an asteroid is not directly discussed in relation to the change in the velocity vector but is indirectly considered by the change in the Jacobi integral, which is the first integral of the circular-planar restricted three-body problem. In addition, the distribution of the smaller alignment index (SALI) is investigated to find a capture point where the asteroid is not put into a chaotic orbit. The proposed method is numerically demonstrated for fictional asteroid capture missions. The results show that several asteroids can be put into stable captured orbits. Additionally, we propose a method to optimize the value of the Jacobi integral, aiming to stabilize periodic captured orbits. Numerical integration confirms that when the Jacobi integral is optimized, the orbital lifetime of the captured orbit exceeds 500 years.

Orbital lifetime design and optimization of CORBES based on lunisolar perturbation

In order to design the orbit for the COntellation of Radiation BElt Survey(CORBES) mission orbit that meets the mission requirements and deorbit constraints, this paper proposed a universal method to design optimal orbital parameters for Highly Elliptic Orbit(HEO). The impact of lunisolar perturbation on perigee altitude is evident, and once a portion of the orbital parameters is determined, the mathematical relationship between the amplitude of the long-period variation in perigee (referred to as “perigee variation”) and the orbital parameters to be designed can be described. The perigee variation exhibits a significant correlation with the orbital lifetime. The initial optimization of orbit parameters is conducted by considering the correlation between lunisolar perturbations and orbital lifetime. Based on this, the orbital parameter RAAN is designed using an improved Decimal Ant Colony Optimization(DACO), and the corresponding launch window is given. The simulation results and comparisons with previous methods validate the effectiveness and efficiency of the initial optimization and the improved DACO in providing optimal feasible solutions, taking into account the law of lunisolar perturbation on orbital lifetime. This method can be well applied to design and estimate the lifetime of orbits dominated by lunisolar perturbation, such as HEO and Geostationary Transfer Orbit(GTO).

A review of global long-term changes in the mesosphere, thermosphere and ionosphere: A starting point for inclusion in (semi-) empirical models

The climate of the upper atmosphere, including the mesosphere, thermosphere and ionosphere, is changing. As data records are much more limited than in the lower atmosphere and solar variability becomes increasingly dominant at higher altitudes, accurate trend detection and attribution is not straightforward. Nonetheless, observations reliably indicate that, on average, the mesosphere has been cooling, the density in the thermosphere has been decreasing, and ionospheric layers have been shifting down. These global mean changes can be largely attributed to the increase in CO2 concentration, which causes cooling and thermal contraction in the middle and upper atmosphere. The decline in thermosphere density is particularly relevant from a practical viewpoint, as this reduces atmospheric drag and thereby increases orbital lifetimes and the build-up of space debris. Long-term changes in the ionosphere can have further practical implications and are not only driven by the increase in CO2 concentration, but also by changes in the Earth’s magnetic field. The empirical models that are mostly used to inform applications in industry on the state of the upper atmosphere, as well as being widely used in science, do not yet properly account for long-term trends in the mesosphere, thermosphere and ionosphere. This is problematic when long-term future projections are needed or models rely strongly on older data. This review provides an overview of the main evidence of long-term trends observed in the mesosphere, thermosphere and ionosphere, together with the latest insights on what causes these trends. It is hoped that this may serve as a starting point to include long-term trends in (semi-) empirical models to benefit all users of these models. We also offer some thoughts on how this could be approached.

Secular dynamics and the lifetimes of lunar artificial satellites under natural force-driven orbital evolution

In this paper, we study the long-term (time scale of several years) orbital evolution of lunar satellites under the sole action of natural forces. In particular, we focus on secular resonances, caused either by the influence of the multipole moments of the lunar potential and/or by the Earth’s and Sun’s third-body effect on the satellite’s long-term orbital evolution. Our study is based on a simplified secular model obtained in ‘closed form’, i.e., without expansions in the satellite’s orbital eccentricity. Contrary to the case of artificial Earth satellites, in which many secular resonances compete in dynamical impact, we give numerical evidence that for lunar satellites only the 2g−resonance (ω̇=0) affects significantly the orbits at secular timescales. We interpret this as a consequence of the strong effect of lunar mascons. We show that the lifetime of lunar satellites is, in particular, nearly exclusively dictated by the 2g resonance. By deriving a simple analytic model, we propose a theoretical framework which allows for both qualitative and quantitative interpretation of the structures seen in numerically obtained lifetime maps. This involves explaining the main mechanisms driving eccentricity growth in the orbits of lunar satellites. In fact, we argue that the re-entry process for lunar satellites is not necessarily a chaotic process (as is the case for Earth satellites), but rather due to a sequence of bifurcations leading to a dramatic variation in the structure of the separatrices in the 2g resonance’s phase portrait, as we move from the lowest to the highest limit in inclination (at each altitude) where the 2g resonance is manifested.

Probabilistic assessment of disposal orbit lifetime for CubeSat rideshares on resonant decaying geosynchronous transfer orbits

Recent years have seen an increase in CubeSat missions on rideshares to geosynchronous orbit. The typical practice for these missions is to deploy the CubeSat on a geosynchronous transfer orbit (GTO) which results in a perigee altitude that is low enough that atmospheric drag will cause the apogee altitude to decay and eventual reentry. However, for GTOs, demonstrating compliance with limits on orbital lifetime in orbital debris mitigation guidelines is not straightforward due to a solar resonance phenomenon that exists which can cause high variability of the orbital lifetime of the satellite. This paper presents a procedure for determining the likelihood that orbital lifetime of a rideshare CubeSat on a resonant GTO will have an orbital lifetime below a 25-year and 5-year limit. The procedure uses a Monte Carlo analysis in which uncertain parameters are randomly varied, including the launch time/initial RAAN and the drag coefficient. The Aerospace precision propagation tool TRACE is used with a high-fidelity force model to enable precision integration through the atmosphere at perigee. It is shown in the study that there is a systematic variation in likelihood of staying below a 25- and 5-year orbital lifetime limit and that drag enhancement devices may be needed to meet the 5-year limit for CubeSat rideshares. The study also presents findings on a solar radiation pressure induced resonance that was observed for high area-to-mass ratios which suggests that there can be a diminishing return when increasing the area of a drag enhancement device to quicken deorbit.

Ground replenishment strategy optimization of LEO satellite constellations considering performance degradation

This paper optimizes a ground replenishment strategy for large-scale LEO satellite constellations, aiming for ensuring high economic efficiency and performance requirements. Firstly, the uncertainties of influential elements are analyzed and satellite lifetime distributions are estimated to determine satellite operating statuses. Secondly, satellite statuses are used for obtaining real-time constellation status and simulating data package transmission paths. Performance degradation function is then derived by selecting time delay as the key performance. To confront with the performance degradation, an optimization model of ground replenishment strategy is established with the objective of minimizing the overall replenishment cost under the time delay and loading capacity constraints. The model is solved by a Dichotomous-domain algorithm. Finally, a case study of a large-scale STARLINK constellation is adopted to validate the effectiveness of the model and sensitivity analyses are conducted to verify its robustness.

Reliability analysis of deep space satellites launched 1991–2020: Bulk population and deployable satellite performance analysis

AbstractFlight data for deep space satellites launched and operated between 1991 and 2020 is analyzed to generate various reliability metrics. Satellite reliability is first estimated by the Kaplan‐Meier estimator, then parameterized through the Weibull distribution. This general process is applied to a general satellite data set that included all deep space satellites launched between 1991 and 2020, as well as two data subsets. One subset focuses on deployable satellites, while the other introduces a methodology of normalizing satellite lifetimes by satellite design life. Results from the general data set prove deep space satellites suffer from infant mortality while the results from the deployable data subset show deployable deep space satellites are only reliable over short periods of time. Results from the design life normalized data set give promising results, with satellites having a relatively high chance of reaching their design life. Available information regarding specific modes of failure is also leveraged to generate a percent contribution to overall satellite failure for eight distinct failure modes. Satellite failure due to crashing, in‐space propulsion failure, and telemetry system failure are proven to drive both early in life failure and later in life failure, making them the main causes of decreased reliability.

Energy-efficient regeneration routing in satellite optical networks under translucent optical payload architectures.

The translucent optical payload architecture is most economical and feasible for optical switching in the satellite optical network (SON) using laser inter-satellite links (LISLs), where the wavelength division multiplexing (WDM) technology enables lightpaths to transparently pass through relay satellites, minimizing on-board processing. For the long-distance lightpath in SONs, lightpath regeneration is necessary to ensure the acceptable quality of transmission (QoT), where optical-electrical-optical (OEO) conversion causes non-negligible energy consumption. The rechargeable battery is an important component for low-earth-orbit (LEO) satellites, and unrestrained use batteries at a deep depth of discharge (DOD) will accelerate battery aging and shorten satellite lifetime, causing extremely high expenditure costs. How to improve energy efficiency in lightpath regeneration is a key problem in SONs, which has no related studies. This paper proposes energy-efficient regeneration routing (EE-RR) in SONs under translucent optical payload architectures, which is to reduce the battery life consumption of lightpath regeneration. We define the maximum bypass hops (MBH) to ensure the bit error rate (BER) requirement of lightpaths in SONs, considering the noise accumulation of amplifier spontaneous emission (ASE) and Doppler shift (DS) crosstalk. Two greedy baselines are proposed for EE-RR, which are the regeneration routing scheme minimizing the number of regeneration nodes (RRS-MRN) and the regeneration routing scheme minimizing single satellite's battery life consumption (RRS-MBL), respectively. Based on two greedy baselines, the regeneration routing scheme using genetic algorithms (RRSGA) is developed to improve the optimization ability of EE-RR. To our knowledge, this is the first study to propose taking battery aging into account in lightpath regeneration in SONs. Through numerical simulation, we find that blindly reducing the number of regeneration nodes in lightpaths may not reduce overall battery life consumption, and RRSGA can effectively reduce battery life consumption of lightpath regeneration in SONs.

Evaluation of the effectiveness of the 5-year rule — impact on the orbital environment at each altitude by reducing the post-mission disposal lifetime

This paper examines the effect of shortening the post-mission disposal (PMD) orbit lifetime (remaining orbit lifetime after PMD) from 25 years to 5 or 1 year. Using NEODEEM, the debris evolutionary model developed by Kyushu University and JAXA, the change in the orbital environment at various altitude bands for long-term stability and short-term safety are discussed. It was confirmed that the PMD compliance rate is more important than shortening the orbit lifetime for improving the long-term stability of the orbital environment. In the short term, the 5- or 1-year rule reduced the collision rate and collision avoidance frequency at an altitude below 700 km, more than the 25-year rule, thus shortening the PMD orbit lifetime improves short-term safety, especially at low altitudes. The paper also evaluates the effect of large constellations (LCs) and it was shown that shortening the PMD orbit lifetime of LCs improves short-term safety, but the long-term impact is dominated by the number of LCs that remain at high operational altitudes due to PMD failure. It shows that the post-mission disposal lifetime and required compliance rate should be set according to the number and size of objects expected to be launched in the future.

COSMIC: a UK Active Debris Removal Mission

In recent years, the escalation of space activities has led to an alarming surge in space debris within low Earth orbit (LEO). This paper addresses the pressing need for Active Debris Removal (ADR), a two-pronged strategy to stabilize space debris: maintaining shorter satellite lifetimes and actively removing defunct satellites. In 2022, the UK Space Agency issued funding to explore the launch of a 2026 mission to remove uncooperative debris in LEO. Astroscale’s COSMIC (Cleaning Outer Space Mission through Innovative Capture) mission has been conceived to meet this challenge. Leveraging Astroscale’s expertise and heritage from the ELSA-M mission, which is designed for magnetically capturing prepared clients, COSMIC advances the field of ADR by transitioning from magnetic capture to robotic capture, enabling the removal of unprepared and uncooperative debris. This paper explores the development of COSMIC and its mission to pioneer institutionally funded debris removal with robotic capture, representing a significant milestone in ADR and the broader realm of space exploration. Keywords: Active Debris Removal, In-orbit Servicing, Rendezvous Proximity Operations, Spacecraft Detumbling, Robotic Capture

Periodicity and lifetime of orbits around elongated asteroids

This paper presents dynamics and control of orbits around an asteroid that is modelled as a uniformly rotating homogeneous rectangular parallelepiped (HRP). Aside from the non-uniform gravitational field of the asteroid, we include the solar radiation pressure (SRP) as a perturbing force. A simple model based on the polyhedral method is employed for calculating the gravity around the HRP. First, circular periodic orbits are identified both in the presence and absence of solar radiation pressure. Then, families of general non-circular periodic orbits in the presence of SRP are determined and subsequently analysed for stability. Next, for a general orbit in the equatorial plane, its stability against a catastrophic impact of an orbiting spacecraft onto the asteroid’s surface is checked in the presence of SRP. Orbits, where the solar radiation pressure is less/more dominant over the central body’s gravity, are identified with the aim of finding the best orbits for parking a spacecraft. Then, for long-period orbits, SRP is averaged and the time averaged evolution of the orbital elements is obtained. For a special set of initial condition, a closed form solution for the evolution of the orbital eccentricity is obtained. Using this solution, a lower limit for the life-time of a spacecraft that is left uncontrolled is derived in a closed form. Finally, active control strategies are developed for orbit-keeping ofspacecraft for any choice of orbital parameters. A linear-quadratic regulator (LQR) is designed to track a given Keplerian orbit with minimum fuel expenditure. Fuel expenditure on various orbits are calculated and compared to determine the orbits of cheapest operation. The work presented is applicable to small body (asteroids and comets) exploration missions which require online cancellation of the perturbing forces with minimal knowledge of the accurate shape, size, and composition of the small body prior to the mission.

Improving Thermospheric Density Predictions in Low‐Earth Orbit With Machine Learning

AbstractThermospheric density is one of the main sources of uncertainty in the estimation of satellites' position and velocity in low‐Earth orbit. This has negative consequences in several space domains, including space traffic management, collision avoidance, re‐entry predictions, orbital lifetime analysis, and space object cataloging. In this paper, we investigate the prediction accuracy of empirical density models (e.g., NRLMSISE‐00 and JB‐08) against black‐box machine learning (ML) models trained on precise orbit determination‐derived thermospheric density data (from CHAMP, GOCE, GRACE, SWARM‐A/B satellites). We show that by using the same inputs, the ML models we designed are capable of consistently improving the predictions with respect to state‐of‐the‐art empirical models by reducing the mean absolute percentage error (MAPE) in the thermospheric density estimation from the range of 40%–60% to approximately 20%. As a result of this work, we introduce Karman: an open‐source Python software package developed during this study. Karman provides functionalities to ingest and preprocess thermospheric density, solar irradiance, and geomagnetic input data for ML readiness. Additionally, it facilitates developing and training ML models on the aforementioned data and benchmarking their performance at different altitudes, geographic locations, times, and solar activity conditions. Through this contribution, we offer the scientific community a comprehensive tool for comparing and enhancing thermospheric density models using ML techniques.

Orbit Transfer Design and Analysis for the SMILE Satellite

Solar Wind Magnetosphere Ionosphere Link Explorer (SMILE) aims to understand the interaction between the solar wind and the Earth’s magnetosphere. The initial orbit of the SMILE satellite is a low Earth orbit, while the target orbit is a highly elliptical orbit. This paper presents the design and analysis of orbit transfer for the SMILE satellite with the constraints of ground stations. According to the maneuver constraints, design principles and strategies have been determined. The orbit transfer strategy is to raise the apogee first and then the perigee, and no active control is carried out for the argument of perigee and the right accession of ascending node. Besides balancing the number of orbit maneuvers and the fuel loss, the orbit transfer is decomposed into 11 maneuvers. To increase the solvability, the idea of multistep approaching the target has been adopted. After a three-step design, the orbit transfer scheme satisfying the observational constraints of the maneuvers by the ground stations has been achieved. Results reveal that the fuel consumed during the orbit transfer is estimated to be 1440 kg, within the fuel budget. Furthermore, the orbital lifetime is calculated to be 7.08 years, which can fully meet the mission’s requirements.

Magnetic Storm Effects on the Occurrence and Characteristics of Plasma Bubbles

AbstractThe Communications/Navigation Outages Forecast System satellite mission was designed to investigate the ionospheric conditions that lead to the formation of irregularities. Here, we have studied the effect of magnetic storms on the formation and evolution of plasma bubbles during the satellite's lifetime (2008–2015). During this period encompassing solar minimum and maximum conditions, many magnetic storms of varying intensity developed, producing a unique and rich data set of 248 storms (14 intense, 69 moderate, and 165 weak) that occurred during the same timeframe to examine the role of external magnetospheric drivers in the production and dynamics of equatorial plasma bubbles. We have used the Planar Langmuir Probe and Ion Velocity Meter instruments to elucidate the role of magnetic storm intensity on the bubble's depth, internal speed, width, occurrence, and lifetime. The pre‐reversal enhancement (PRE) tends to increase during the main phase and when BZ is southward. New bubbles occur during large excursions of the PRE value. The bubble lifetime extends and remains active during the main and part of the recovery phase. The plasma velocity within the bubbles increases and typically becomes over 100 m/s during significant PRE and BZ negative times. The depth of bubbles reaches values close to 100% during intense storms. In general, the intensity of the storms seems to control and augment the plasma bubbles' depth, width, and internal velocity.

Dynamics of dust and meteoroids due to electromagnetic transport in the heliosphere

ABSTRACT Observations of dust in the Solar system have indicated the existence of structures at higher ecliptic latitudes, the origin of which is still an ongoing debate. In a previous study, we studied how the interplanetary magnetic field affects the orbital motion of charged dust particles that are moving in co-orbital motion with Jupiter. Our findings revealed that the Lorentz force causes oscillations in orbital inclinations that lead to electromagnetic transport of the dust particles to higher ecliptic latitudes. In this work, using numerical simulations, we investigate how this transportation depends on orbital lifetime, strength of the background magnetic field, planetary mass, and distance from the Sun. In addition, we study the dynamics also outside resonance. We present our findings using the saturation curve, which gives a relation between the maximum amplitude in inclination with respect to the particle size ranging from 1 to 501 $\mu$m. We further study the influence of the solar radiation pressure, the Poynting–Robertson, and the solar wind effects on the shape of the saturation curve and find that a stronger gravitational influence of the planet leads to a steeper curve, decreasing the strength of the electromagnetic transport. The radiative forces lead to a gradual dampening of the latitudinal oscillations of particles inside resonance, while they are unchanged for objects outside of resonance. We argue that the dynamics of dust and meteoroids in the Solar system can only be understood by including space weathering effects.