⚡ electrical engineering

Assessing Collision Probability in Low-Thrust Deorbit

This paper assesses the collision risk associated with low-thrust satellite deorbit missions and conducts parametric studies to analyze the relationship between re-entry time and collision probability.

Original authors: Shuta Fukii, Daisuke Sakai, Yasuhiro Yoshimura, Yuri Matsushita, Toshiya Hanada, Yuki Itaya, Tadanori Fukushima

Published 2026-08-19

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CC BY 4.0

Original authors: Shuta Fukii, Daisuke Sakai, Yasuhiro Yoshimura, Yuri Matsushita, Toshiya Hanada, Yuki Itaya, Tadanori Fukushima

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The space around Earth is becoming increasingly crowded. Beyond the familiar satellites that power our global communications and weather forecasts, there is a growing population of defunct spacecraft and fragments from past collisions, all orbiting at high speeds. This debris poses a serious threat to active satellites; a single collision can shatter a spacecraft into thousands of new pieces, creating a chain reaction that could render entire orbital regions unusable. To prevent this, space agencies and operators follow a rule that requires satellites to be removed from orbit within twenty-five years of finishing their work. However, as companies plan to launch tens of thousands of new satellites in the coming decade, simply waiting for natural forces to pull them down may no longer be enough. For satellites that have broken down or cannot move on their own, we need new ways to push them out of the sky safely.

One promising method involves using a laser to gently nudge a stranded satellite toward Earth. Instead of physically grabbing the object, a laser beam strikes the satellite's surface, heating a tiny spot until material vaporizes and shoots away like steam. This creates a small, continuous push that slowly lowers the satellite's orbit. While this sounds efficient, the process is incredibly slow, taking years to complete. The longer a satellite lingers in the crowded upper atmosphere, the higher the chance it will crash into another object. Researchers Shuta Fukii and his team at Kyushu University and SKY Perfect JSAT Corporation set out to understand this delicate balance. They wanted to know how the speed of this laser push affects the risk of a collision and whether there is a "sweet spot" where the satellite gets down quickly enough to be safe, but not so fast that the laser runs out of time.

To find the answer, the team built a detailed computer simulation of a 150-kilogram satellite, roughly the size of a small car, drifting in a high orbit. They imagined a service satellite hovering nearby, firing a laser to push the target. The researchers tested four different strategies for how long the laser should fire during each orbit. In one extreme case, the laser fired constantly, pushing the satellite the entire time. In the other, it fired only for a quarter of the orbit, specifically when the satellite was at its highest point. The goal was to see how these different firing patterns changed the time it took for the satellite to fall back to Earth and how many years it spent in the most dangerous, debris-filled zones.

The simulations revealed a surprising trade-off. When the laser fired constantly, it used up its available energy very quickly, leaving the satellite to drift down on its own for many years afterward. This long, slow drift through the upper atmosphere actually increased the total risk of a crash. Conversely, firing the laser too briefly meant the satellite took a very long time to descend, also increasing the risk. The team found that the best approach was to fire the laser for half of the orbit, centered around the highest point. This strategy allowed the satellite to lower its path efficiently without wasting the laser's energy. By using this "fifty percent" method, the satellite could reach the lower atmosphere in about four years, whereas the constant-firing method took nearly nine years to complete the same journey.

The study also looked at the consequences of a crash. Even if a collision occurred, the researchers calculated the likelihood of a catastrophic explosion that would create a massive cloud of new debris. Their results showed that the chance of such a disaster was extremely low, well below the safety limits set by international space guidelines. However, they did find that the longer a mission takes, the more fragments are likely to be generated if a collision does happen. This is because the satellite spends more time exposed to the stream of space junk. The researchers also examined the angles at which the satellite might be hit, but found that the shape of the orbit did not significantly change the direction of incoming debris, meaning the risk profile remained consistent regardless of the specific firing pattern.

Ultimately, this work provides a clear roadmap for designing future space cleanup missions. It shows that simply pushing as hard as possible is not the most effective way to clear space. Instead, a measured approach that balances the use of the laser with the natural drag of the atmosphere yields the safest result. By choosing the right firing schedule, operators can ensure that a stranded satellite is removed from the sky in the shortest time possible, minimizing its exposure to the crowded environment and protecting the future of spaceflight for everyone.

Technical Summary: Assessing Collision Probability in Low-Thrust Deorbit

Problem Statement
The increasing density of objects in Low Earth Orbit (LEO), driven by the deployment of large satellite constellations, elevates the risk of collision events. While Post-Mission Disposal (PMD) is a standard mitigation strategy, the "25-year rule" may become insufficient for future high-density environments. For malfunctioned or non-maneuverable satellites, Active Debris Removal (ADR) or End-of-Life (EOL) support missions are required. This paper specifically addresses the collision risks associated with deorbiting missions utilizing low-thrust propulsion, such as laser ablation. Unlike high-thrust maneuvers, low-thrust deorbiting is a time-consuming process, during which the target satellite remains in the debris environment for extended periods, potentially increasing the probability of collision. The study aims to quantify this risk and analyze the relationship between deorbit duration and collision probability to inform safer mission designs.

Methodology
The study employs a numerical approach to simulate orbital propagation and assess collision risks across four distinct low-thrust scenarios.

Orbital Propagation: The authors utilize Cowell's method with special perturbation theory to simulate the target satellite's trajectory. The equations of motion account for Earth's geopotential, solar and lunar gravitational attraction, atmospheric drag, solar radiation pressure, and shadowing effects. The target is modeled as a box-wing satellite (150 kg) in a tumbling state, with an effective cross-sectional area calculated as one-quarter of its total surface area. The low-thrust acceleration is modeled as a laser-ablation force applied in the anti-velocity direction.
Deorbit Scenarios: Four scenarios are defined based on the percentage of the orbital period during which thrust is active around the apogee: 25%, 50%, 75%, and 100%. The thrust is assumed to be constant in magnitude (0.72 mN) and available for a maximum of two years.
Risk Assessment: Collision analysis is conducted using the ESA MASTER–2009 model. The study calculates the mean number of collisions ( $N$ ) and the probability of at least one collision ( $P(X \ge 1)$ ) based on debris flux, the target's cross-sectional area, and the duration spent in specific altitude zones.
Catastrophic Collision and Fragmentation: The study evaluates catastrophic collision risk by calculating the energy-to-mass ratio ( $\varepsilon$ ), defining a catastrophic event as one where $\varepsilon > 40$ kJ/kg. Furthermore, the expected number of fragments generated upon collision is estimated using NASA's breakup model, considering fragments larger than 1 mm.

Key Results

Deorbit Duration vs. Thrust Range: The relationship between the thrusting range and the total time to deorbit is non-linear. The 50% thrust scenario proved most efficient, achieving deorbit in approximately 4.1 years. In contrast, the 100% scenario, despite using thrust continuously, exhausted the available two-year thrust window early, relying on atmospheric drag for the remaining 6.9 years, resulting in a total deorbit time of 8.9 years. The 25% scenario took 6.7 years, and the 75% scenario took 7.9 years.
Collision Probability: The probability of at least one collision is directly correlated with the total time to deorbit. The 50% scenario exhibited the lowest collision probability ( $P(X \ge 1) \approx 6.67\%$ ), while the 25% scenario showed the highest ( $P(X \ge 1) \approx 11.08\%$ ). This trend aligns with the finding that the mean number of collisions is proportional to the mission duration.
Catastrophic Risk and Fragments: The probability of catastrophic collision ( $P_{cata}$ ) remained well below the 0.1% threshold recommended by ISO space debris mitigation guidelines for all scenarios. However, the expected number of fragments generated in a worst-case scenario varied significantly, ranging from approximately 596 fragments (50% scenario) to 1,282 fragments (100% scenario).
Impact Characteristics: Analysis of impact angles and relative velocities revealed no significant differences among the four scenarios. This is attributed to the low eccentricity of the orbits (maximum eccentricity ~0.06), which approximates circular orbits, thereby minimizing variations in collision geometry despite different thrust profiles.
Annual vs. Total Risk: Interestingly, when risk is normalized per year, the 50% scenario shows a higher annual risk than the 100% scenario. This is because the 50% scenario spends a longer duration in the high-flux altitude zone (around 800 km) relative to its total mission time, whereas the 100% scenario passes through this zone more quickly but remains in orbit for a much longer total duration, accumulating higher total risk.

Significance and Conclusions
The paper concludes that while low-thrust deorbit missions are feasible and can be conducted safely without violating catastrophic collision probability limits, the design of the thrust profile is critical. The study demonstrates that maximizing thrust application (100% scenario) does not necessarily minimize collision risk; rather, an optimal balance (50% scenario) minimizes the total time spent in the debris environment.

The authors assert that mission designers must evaluate not only the efficiency of deorbiting (fuel or time consumption) but also the collision risk profile introduced by the specific deorbit trajectory. The results suggest that for laser-ablation assisted deorbiting, a thrust profile that avoids exhausting the available thrust time too early—thereby preventing a prolonged decay phase driven solely by atmospheric drag—is essential for minimizing the generation of space debris and ensuring mission safety. The findings are applicable to other low-thrust deorbit missions beyond laser ablation.

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