Characterizing solar cycle influence on long-term orbital deterioration of low-earth orbiting space debris

Abstract

The rapid increase in space debris poses a major threat to sustainable space operations and underscores the importance of understanding long-term drivers of orbital decay. Because debris objects do not perform station-keeping maneuvers, their orbital evolution directly reflects variations in thermospheric density, unlike that of operational satellites. This makes space debris an effective natural testbed for examining the long-term influence of solar activity on atmospheric drag. This study analyzes the impact of solar activity on the decay of 17 LEO debris objects across solar cycles 22, 23, and 24 using Two-Line Element (TLE) data. TLE-derived decay profiles, combined with sunspot numbers (SSN) and the F10.7 index, reveal a threshold: decay rates rise sharply when SSN exceeds 67%–75% of its cycle peak, corresponding to increased Extreme Ultraviolet (EUV) fluxes, thermospheric density and atmospheric drag. Peak decay rates declined progressively from cycle 22 to 24, reflecting reduced solar activity. Decay profiles for cycle 24 - predicted using ballistic coefficients from earlier cycles and MSIS 2.0 atmospheric densities - match observations well after applying a scaling factor. However, two high-inclination objects showed significant deviations, suggesting possible MSIS limitations at high latitudes, while lower-inclination objects aligned closely. Moreover, geomagnetic activity indices such as AE and Dst show little correlation with long-term orbital decay rates, suggesting a comparatively weaker role at the timescales examined, for Joule heating and particle precipitation than for solar EUV forcing in driving sustained orbital decay. Overall, the findings support solar EUV-driven thermospheric variability as a primary factor influencing long-term orbital decay and emphasize the need to refine atmospheric models, particularly for polar regions, to improve reentry predictions and satellite mission planning.

1 Introduction

Space debris - ranging from defunct satellites and discarded rocket stages to fragments from collisions - poses an ever-increasing threat to active spacecraft and human spaceflight (Graham et al., 1999; Li et al., 2002; Kleinig et al., 2022; Smith et al., 2020; Hayes and Caverly, 2023). As the space industry continues to expand, so does the number of objects in orbit, presenting considerable hazards to functioning satellites, ongoing space missions, and astronaut safety. A pressing issue arises from the risk of cascading collisions, commonly termed the Kessler Syndrome (Kessler et al., 2010), where a single collision can generate substantial additional debris, triggering a domino effect of subsequent collisions. Such collisions, even when involving relatively small objects, have the potential to trigger a cascading chain reaction, threatening operational satellites and progressively increasing the population of high-velocity debris in orbit. A prominent example occurred on 10 February 2009, when Iridium 33 and Cosmos 2,251 collided at an altitude of approximately 790 km, generating more than 1,500 catalogued fragments along with numerous smaller debris particles (Mariappan and Crassidis, 2023). While numerous studies have investigated collision risks and mitigation strategies, less attention has been paid to the long-term data driven analysis of the orbital decay of debris.

One of the key factors influencing orbital decay is the solar activity (Nwankwo, 2018; Klinkrad, 2006; Walterscheid, 1989). Typically, every 11 years, the Sun undergoes active and quiet phases, constituting a solar cycle, resulting in notable variations in the emitted flux of electromagnetic and corpuscular radiation (Lean, 1987; Hathaway, 2015; Richardson and Cane, 2012; Gopalswamy, 2006). Increased solar emissions during active phases heat and expand the thermosphere, thereby raising atmospheric density at orbital altitudes and enhancing drag experienced by orbiting bodies (Harris and Priester, 1962; Clette et al., 2015; Weng et al., 2020; Crisp et al., 2021). This makes the solar cycle variations a crucial component in long-term orbital dynamics. Recent events such as the loss of Starlink satellites linked to mild geomagnetic disturbances (Dang et al., 2022; Kataoka et al., 2022), further highlight the operational importance of understanding magnetospheric and ionospheric disturbances and their impacts on satellite orbits.

Early foundational work by (King-Hele and Walker, 1987) shows that upper-atmospheric density can vary by more than an order of magnitude between solar minimum and maximum, resulting in dramatic differences in orbital lifetimes - for example, a satellite at 500 km may re-enter within a year at solar maximum but survive 5–8 years when launched near solar minimum. (Marcos et al., 2005). used satellite drag data from 1970 to 2000 to reveal a secular thermospheric density decrease of about 1.7% per decade, consistent with global thermospheric cooling predicted by theoretical models.

While the influence of solar activity on satellite drag is well recognized, a systematic investigation into its long-term impact on the orbital decay of space debris remains lacking. Nwankwo (2018) discussed the typical orbital decay of a LEO satellite between 1999 and 2014, clearly showing a correlation between solar activity and orbital decay. However, this study covered only a 15-year period. In the present work, we address this gap by analyzing the orbital decay of 17 LEO debris objects-filtered from an initial set of 95 by excluding medium Earth orbit (MEO) debris, objects with higher eccentricity orbits, and objects above 800 km in altitude. The objects in this filtered dataset happen to fall in the 600–800 km altitude range. Since these objects do not have station-keeping, orbital changes directly reflect thermospheric density perturbations. This makes space debris an excellent tool for tracing long-term solar-activity effect on atmospheric drag. Using TLE data spanning three consecutive solar cycles (solar cycles 22, 23, and 24), we correlate decay rates with solar activity, utilizing over 36 years of sunspot numbers, F10.7 indices and EUV flux data. We further attempt to model the orbital decay profiles of these objects by estimating their ballistic coefficients from historical TLE data and using atmospheric density values from the NRLMSIS 2.0 model (Emmert et al., 2021). The methodology is outlined in the next section. Through this analysis, we aim to quantify the long-term influence of solar activity on LEO debris orbital decay, examine the relationship between solar activity indicators and drag-driven decay, and evaluate the capability of the NRLMSIS 2.0 model to reproduce observed debris decay behavior.

The novelty of this study lies not only in its multi-decadal data span but also in its methodological framework and the insights derived from long-lived debris objects. Unlike previous long-term drag investigations that relied on accelerometer measurements from operational satellites or were limited to shorter time intervals or single solar cycles, this work exclusively analyzes uncontrolled debris objects, whose orbital evolution represents a purely natural response to thermospheric variability. By comparing decay behavior across three complete solar cycles (1986–2024), identifying a repeatable solar-activity threshold for accelerated decay, and evaluating the predictive capability of MSIS 2.0 using TLE-derived ballistic coefficients, this study provides a distinct assessment of solar-driven drag effects and atmospheric model performance in the 600–800 km altitude regime. These findings contribute to a better understanding of long-term orbital decay processes and more sustainable space operations.

2 Data and methodology

This study investigates the long-term impact of solar activity on the orbital decay of space debris. The sunspot number constitutes a historical time series spanning from 1700 to the present, capturing the 11-year cyclic and long-term variations in solar activity and, consequently, space weather. Although contemporary observations offer more refined parameters for understanding space-weather impacts, the SSN represents the earliest direct record of solar activity. It serves as an essential link connecting past and present solar behavior Clette et al. (2014), Clette and Lefevre (2016), Jayalekshmi et al. (2022). Along with the SSN data, the F10.7 index is also known to be a fairly good representative of solar activity Chen et al. (2011). The study covers three full solar cycles: solar cycle 22 (September 1986 - August 1996), solar cycle 23 (September 1996 - December 2008), and solar cycle 24 (January 2009 - December 2019). Data for SSN and F10.7 solar radio flux index were obtained from the GFZ Potsdam database (www.gfz-potsdam.de). EUV flux data was obtained from https://lasp.colorado.edu/eve/data_access/eve_data/lasp_soho_sem_data/long/daily_avg/.

The orbital parameters of satellites and space debris are commonly represented using Two-Line Elements, which consist of up to 69 alphanumeric characters. A detailed description of the TLE format can be found in Vallado and Cefola (2012). For this study, space debris originating in the 1960s were selected, having continuous TLE data with sufficient temporal resolution across solar cycles 22, 23, and 24. Importantly, all selected objects remain in orbit at the time of writing this manuscript and are yet to reenter the atmosphere, despite having been in orbit since the 1960s. An initial set of 95 debris objects was identified using Space-Track website (www.space-track.org). To refine the dataset for consistent orbital characteristics, we excluded debris in MEO, those with high eccentricities, and those at altitudes above 800 km. This filtering resulted in a final dataset of 17 LEO debris objects, as listed in Table 1. The corresponding TLE data, starting from 01 September 1986 were obtained from the Space-Track website and used for the analysis. Given that the objects analyzed in this study are located below 800 km in altitude, the influence of direct solar radiation pressure is minimal and was thus excluded (Sang et al., 2013). Additional physical characteristics - mass and maximum, minimum, and average cross-sectional areas - were obtained from the DISCOS (Database and Information System Characterising Objects in Space) database (https://discosweb.esoc.esa.int/) where available, and are also included in Table 1.

The TLE elements for each debris object were used to construct a database of orbital parameters across different epochs. This database served as the foundation for all subsequent analyses. The semi-major axis ‘’ of the orbit of each space debris at a given epoch is obtained from mean motion using the following Equation 1,

Where is the mass of the Earth, is the universal gravitational constant and is the mean motion in revolutions per day.

Once the time series of semi-major axes was established, the altitudes were computed and plotted alongside sunspot number as a function of time. To handle outliers within the data points, we applied a z-score filtering method: any data point with a semi-major axis z-score greater than three was considered an outlier and excluded from the analysis. This procedure was used only to remove isolated extreme deviations that are physically not possible when compared with adjacent epochs and are most likely attributable to TLE fitting artifacts. The proportion of excluded data points is small and does not influence the estimated decay slopes or the identification of the solar-activity threshold.

To better quantify the impact of solar activity, we calculated the decay rates for all 17 objects during the peaks of solar cycles 22, 23, and 24. The resulting values, for each cycle, are listed in Table 2. Additionally, we examined the relationship between the initial altitude of the debris and its decay rate near the peak of each solar cycle. Histograms were generated to visualize the distribution of peak decay rates across the different cycles. Furthermore, we examined the correlation between orbital decay rates and SSN and the F10.7 index.

The method proposed by Sang et al. (2013) was used to estimate the ballistic coefficient (BC) of LEO space debris based on historical TLE data. The BC is computed as where is the drag coefficient, is the cross-sectional area and is the mass of the object. In this approach, BC is derived from variations in the mean semi-major axis extracted from the TLEs. Data from solar cycles 22 and 23 were utilized for BC estimation, using the following Equation 2,

Where is Earth’s standard gravitational parameter, i.e., = GM, is the semi-major axis of the debris, is the difference in semi-major axis of the object between epochs and , is the atmospheric density, is the satellite velocity, is the time difference between epochs and and is the velocity of the debris relative to the co-rotating atmosphere. Since the atmospheric velocity is significantly lower than the satellite velocity - with the average rotational speed of the atmosphere at 400 km being about 180 m/s (King-Hele et al., 1970), compared to satellite velocities of around 7 km/s - we approximate as . The estimated BC values were subsequently used to predict the orbital decay of the debris objects during solar cycle 24 and part of solar cycle 25, and the results were compared against the actual decay profiles derived from TLE data for the same period.

To model the decay profile, initial TLE data at the beginning of solar cycle 24 is utilized to propagate the orbit every 15 s, in order to obtain the latitude-longitude values. The altitude is determined using the drag equation to estimate changes in orbital velocity. The change in velocity resulting from atmospheric drag over a time interval, , can be calculated as Equation 3

For a satellite in orbit around the Earth, the gravitational force is balanced by the centripetal force (Equation 4).

Where, is the radius of the Earth, is the altitude of the satellite and m is the satellite mass. This equation can be re-arranged to obtain the Equation 5 for the altitude,

The resulting new altitude due to the drag force can be computed as Equation 6,

The drag coefficient quantifies the interaction between the surface of the spacecraft and the impinging atmospheric molecules within the free-molecular flow regime (Doornbos and Klinkrad, 2006). Although the drag coefficients of these objects are not directly available, the computed BC values were used to estimate the drag coefficients for 13 objects with known mass and cross-sectional area information.

3 Observations

Figure 1 shows the orbital decay of a representative LEO debris object (Delta 1 debris) alongside solar activity indicators - SSN and F10.7 index - over solar cycles 22, 23, and 24. In the top panel, the apparent altitude , obtained by subtracting Earth’s mean radius from the mean semi-major axis derived from TLE data, is plotted. The object’s altitude decreases from roughly 690 km at the start of solar cycle 22 to about 550 km at the end of solar cycle 24. The three solar cycles are indicated by color-coded blocks (blue for cycle 22, green for cycle 23, and red for cycle 24). The vertical red dashed lines serve as markers for areas characterized by nearly linear and rapid orbit decay during each solar cycle.

FIGURE 1

These boundaries are determined by computing the local orbital decay rate from adjacent semi-major axis data points. A 27-day centered moving average is then applied to reduce short-term variability in the derived decay rates. For each solar cycle, a transition level is defined to identify the onset of rapid decay. For Solar Cycles 22 and 23, this level is set at 1 below the mean of the smoothed decay rate within the respective cycle. Because Solar Cycle 24 is comparatively weaker, a more stringent criterion of 3 below the mean is adopted. To define a representative cycle threshold, the earliest date across all objects during the rising phase and the latest date during the declining phase of each solar cycle were selected.

The rate of change of the semi-major axis is calculated as Equation 7:where is the observation time and is the corresponding apparent altitude. To remove short-term fluctuations, the decay-rate series is smoothed using a 27-day centered moving average (Equation 8):This produces the smoothed decay rate used for the analysis. For each solar cycle S, a statistical threshold is defined as given in Equation 9.where, is the mean of the smoothed decay rate during the cycle, is the corresponding standard deviation and k is 1 for solar cycles 22 and 23, while k is three for solar cycle 24. A rapid orbital decay event is identified whenThe start and end epochs correspond to transitions across this threshold defined in Equation 10. These boundaries thus determined were then visually compared with the decay rate versus epoch plots to ensure that the selected intervals correspond to sustained periods of enhanced orbital decay and do not include intermittent returns to quiet-time levels. Based on this consistency check, minor adjustments of at most a few months were applied to the ensemble boundaries (a few months for Solar Cycle 23 and about 1 month on the declining phase of Solar Cycle 24). The threshold identification process was therefore performed semi-manually. These adjustments do not affect the threshold detection for individual objects but ensure that the reported cycle windows consistently capture the elevated decay phase across the full dataset.

The second panel shows the cumulative sunspot number, which increases rapidly during solar maximum and gradually levels off toward solar minimum. The third panel presents the SSN together with a fitted Gaussian curve (shown in blue). The threshold level is identified from the intersection of the Gaussian fit with the red dashed lines. The individual threshold levels derived for each object are listed in Table 3. For Solar Cycle 22, the ascending-phase thresholds range from 63% to 72%, with a median of 71%, while the descending-phase thresholds range from 70% to 74%, with a median of 73%. For Solar Cycle 23, the ascending-phase thresholds range from 68% to 83%, with a median of 70%, and the descending-phase thresholds range from 75% to 78%, with a median of 77%. For Solar Cycle 24, the ascending-phase thresholds range from 63% to 67%, with a median of 64%, and the descending-phase thresholds range from 67% to 78%, with a median of 70%. These statistics demonstrate that, despite object-to-object variability, the transition consistently occurs within a relatively narrow band—generally between approximately 63% and 78% of the cycle peak—with medians clustering near two-thirds of the maximum of the Gaussian-fitted SSN curve.

The F10.7 index values are plotted in the fourth panel, and the MSIS 2.0 model-derived global mean atmospheric density at 600 km is plotted in the bottom panel. Both parameters exhibit pronounced enhancements during solar maxima, coincident with the intervals of rapid orbital decay identified in the altitude time series.

A similar transition is evident in the EUV flux measured by the Solar EUV Monitor (SEM) onboard the Solar and Heliospheric Observatory (SOHO), although SEM data are available only from 1996 onward (Figure 2). The red dashed lines marking the rapid orbital decay phase consistently coincide with enhanced EUV flux levels in both wavelength bands (26–34 nm and 0.1–50 nm). For the 0.1–50 nm band, the mean EUV flux within the rapid-decay windows is 5.51 photons (solar cycle 23) and 3.26 photons (solar cycle 24), compared to a median value of 2.39 photons outside these windows. This corresponds to an increase of approximately 50%–130% relative to near-solar minima periods. A similar enhancement is observed in the 26–34 nm band, where the median flux increases from 1.22 photons outside the windows to 2.75 photons (solar cycle 23) and 1.64 photons (solar cycle 24) within the rapid decay intervals. These quantitative differences confirm that the identified rapid-decay phases are systematically associated with elevated EUV irradiance.

FIGURE 2

This correspondence supports the interpretation that increased EUV-driven heating and the associated thermospheric expansion are the key drivers of the observed acceleration in orbital decay. It should be noted that SSN and F10.7 are long-term proxies of solar EUV flux, whereas SOHO/SEM provides direct measurements of solar EUV irradiance, which is the physical driver of thermospheric heating and expansion. It has been discussed in Chen et al. (2011) that F10.7 does not serve as an ideal proxy for solar EUV irradiance during the extended solar minimum of 2007–2009. However, in the context of our analysis, a comparison between NEUVAC-derived EUV and SOHO/SEM observations does not indicate a breakdown of the proxy-EUV relationship during the SC23-24 minimum. Any deviations appear small relative to the solar-cycle-scale variability that forms the basis of our comparisons. The EUV irradiance reconstructed with the NEUVAC model (which uses F10.7 as its input) tracks the long-term behavior observed by SOHO/SEM reasonably well across both SC23 and SC24 (Figure 2). Importantly, this agreement also holds during the deep minimum of 2007–2009. The modeled EUV captures the overall trend seen in the measurements, and we do not observe any clear systematic divergence specific to that interval.

From Figure 1, it can be seen that solar cycle 22 exhibits the highest overall solar activity, followed by cycle 23, while cycle 24 is comparatively weak-a pattern mirrored by the varying steepness of the orbital decay slopes. As expected, the decay rate is significantly higher during solar maxima and becomes more gradual as the cycle approaches its minimum. The repeated intersection of the red dashed lines with the Gaussian-fitted SSN curves, F10.7 and EUV fluxes at approximately 67%–75% of peak values suggests the existence of a threshold solar activity level beyond which thermospheric density increases sufficiently to drive rapid orbital decay.

The overall behaviour is consistent with the established understanding that increased solar activity increases the thermospheric scale height and density, primarily due to enhanced EUV emission from the Sun (Mlynczak et al., 2018). As the drag force experienced by orbiting objects is strongly influenced by atmospheric density, this leads to a corresponding increase in orbital decay. The acceleration experienced by the object due to drag force is expressed as,

Six distinct regions with different orbital decay rates can be identified in Figure 1. Three of these regions - marked by red dashed lines corresponding to the peaks of the solar cycles - display noticeably steeper slopes, indicating periods of enhanced decay, while the remaining three show a more gradual decline. Figure 3 depicts the slopes computed over these six segments, alongside the average F10.7 index during each interval. As expected, regions with higher F10.7 values (regions 1, 3, and 5) correspond to steeper slopes, reflecting the higher solar input to the Earth’s atmosphere during those periods.

FIGURE 3

Figure 4 presents histograms of the peak orbital decay rates-estimated as the slopes of the curves enclosed within the red vertical lines in Figure 1-for 17 debris objects across solar cycles 22, 23, and 24. Each cycle depicts distinct patterns that reflect the varying levels of solar activity. Solar cycle 22 exhibits the highest decay rates, with a mean of −0.59 m/h and a median of −0.52 m/h. Most objects during this cycle experience relatively steeper decay, consistent with strong solar activity that enhances thermospheric density and, consequently, atmospheric drag. Solar cycle 23 shows slightly lower decay rates, with a mean of −0.54 m/h and a median of −0.43 m/h. In contrast, solar cycle 24 displays a marked reduction in decay rates. The mean drops to −0.25 m/h and the median to −0.15 m/h. The decay rates are more tightly clustered around zero, reflecting weak solar activity and reduced thermospheric heating-resulting in lower atmospheric drag and slower orbital decay. Overall, the magnitude of decay rates decreases progressively from cycle 22 to cycle 24, closely mirroring the corresponding decline in solar activity. These histograms strongly supports the connection between solar activity and orbital decay, showing that peak decay rates are directly influenced by the intensity of solar cycles. Higher solar input, indicated by increased F10.7 and EUV flux and sunspot numbers, leads to enhanced thermospheric density, which in turn accelerates orbital decay.

FIGURE 4

We further examined the role of geomagnetic activity by checking correlations between the 27-day smoothed orbital decay rate and several geomagnetic indices (Ap, AE, and Dst), and compared these with solar activity proxies (F10.7 and SSN). As summarized in Table 4, the decay rate exhibits a strong correlation with F10.7 (mean 75%) and SSN (mean 67%) across the 17 objects analyzed. In contrast, the geomagnetic indices show substantially weaker relationships. The Kp index (considering all eight 3-hourly components) explains only 11%–21% of the variance. Similarly, Dst and Ap account for only 22% and 18% of the variance, respectively, while AE explains less than 2%. The comparatively low variance indicates that geomagnetic activity plays only a secondary role in long-term orbital decay. This further demonstrates that the observed threshold of accelerated orbital decay during a solar cycle is primarily governed by solar EUV forcing rather than by geomagnetic disturbances. Figure 5 illustrates the geomagnetic activity trends over the three solar cycles for reference.

FIGURE 5

The ballistic coefficients for the 17 debris objects were initially estimated using TLE data from solar cycles 22 and 23, combined with atmospheric densities from the MSIS 2.0 model at the corresponding locations. The MSIS 2.0 model requires latitude, longitude, altitude, and epoch as input parameters, with the latter two obtained directly from the TLEs. Latitude and longitude were derived using the EarthSatellite module from the Skyfield Python library. These initial BC estimates were then used to predict the altitude decay profiles of 17 objects during solar cycle 24. However, it was observed that the predicted profiles did not align with the TLE-derived profiles unless the BCs were scaled by a factor . The derived BCs, the applied scaling factors, and the resulting scaled BCs are summarized in Table 5.

Interestingly, for two debris objects-SAT 733 and SAT 734-the decay profiles could not be accurately reproduced, even after applying various scaling factors. Unlike the other objects, which had inclinations between 45 and 70, these two were in highly polar orbits with inclinations near 99. The top panel of Figure 6 shows the best-fit modeled decay for SAT 734. Although both the modeled and TLE-derived profiles exhibit a general downward trend consistent with orbital decay, significant discrepancies exist, especially over extended time periods. This suggests potential limitations in the MSIS 2.0 model’s ability to accurately represent atmospheric densities in polar regions. We also examined whether the largest model-data differences for these near-polar objects preferentially occur during periods of enhanced geomagnetic activity. It was seen that the largest deviations between the modeled and TLE-derived decay profiles do not systematically coincide with intervals of elevated AE or Dst indices. Although individual storm-time periods introduce short-term variability, the largest differences are not clustered around major geomagnetic disturbances and show no clear correlation with peak AE or Dst values.

FIGURE 6

In contrast, the bottom panel of Figure 6 presents the decay profile for SAT 029, where the modeled and TLE-derived curves show excellent agreement. As shown in Table 5, for the 15 objects with well-matched profiles (excluding SAT 733 and SAT 734), the scaling factors ranged from 0.55 to 0.79, with a mean value of 0.71.

The scaled TLEs have been used to calculate the values for objects where both mass and cross-sectional area information are available, which applies to 13 of the objects. These values are presented in Table 5. However, since the predicted decay profiles for objects 733 and 734 do not closely match the actual TLE-derived curves, the BC values and consequently the values derived for these two objects can be disregarded. It is important to emphasize that the reported values represent effective drag coefficients derived from TLE-based ballistic coefficient reconstruction in combination with an empirical atmospheric density model. As such, they should be interpreted as compounded parameters that incorporate multiple sources of uncertainty, including uncertainties in MSIS density estimates and area-to-mass ratio, TLE-derived orbital errors, and limitations inherent in the ballistic coefficient estimation method itself.

4 Discussion and conclusion

The rapid expansion of the space sector and the corresponding growth in space debris population have made it increasingly important to understand the long-term drivers of orbital decay. Many debris objects remain in orbit for decades, making their orbital evolution particularly sensitive to sustained variations in the space environment. In this context, the present study provides a systematic, multi-decadal investigation of LEO debris decay across three complete solar cycles-solar cycles 22, 23, and 24-using continuous TLE data spanning 1986-2024.

A key strength and novelty of this work lies in its exclusive focus on space debris rather than operational satellites. Because debris objects do not perform station-keeping or orbit-raising maneuvers, their orbital evolution reflects a purely natural response to atmospheric drag and thus thermospheric density variations. The analysis is based on a carefully curated set of 17 debris objects, originating in the 1960s and remaining in orbit for over 5 decades, all within the 600–800 km altitude range. This homogeneous, long-lived population allows cycle-to-cycle differences in decay behavior to be resolved in a way that is not possible with shorter datasets or actively controlled satellites.

A central result of this study is the clear and consistent influence of solar activity on orbital decay rates across three consecutive solar cycles. Although the general connection between enhanced solar activity and increased atmospheric drag is well known, the multi-decadal nature of our dataset allows this relationship to be quantified in a new way. In particular, we identify a repeatable SSN/F10.7 index threshold - approximately 67%–75% of the cycle maximum - beyond which debris objects undergo a marked transition to accelerated orbital decay. This transition coincides with enhanced measurements of solar EUV flux, as shown by SOHO/SEM observations, and reflects a critical level of thermospheric heating at which atmospheric expansion significantly increases drag at LEO altitudes. Identifying such a threshold provides new physical insight into the onset of rapid decay while also offering clear operational value, as it helps identify periods with elevated decay rates and increased re-entry risk in advance, thereby supporting improved fuel budgeting, lifetime prediction, and mission planning during solar-maximum conditions.

The long-term dataset also reveals a systematic decline in peak decay rates from solar cycle 22 to solar cycle 23 and further to solar cycle 24. The steepest orbital decay is observed during solar cycle 22, followed by moderately reduced but still comparable decay rates in cycle 23, and the weakest decay in cycle 24, closely mirroring the well-documented progressive weakening of successive solar cycles. This behavior is consistent with long-term reductions in thermospheric density driven by declining solar EUV output. Although such trends are theoretically expected, this study provides direct observational, cycle-resolved evidence based on debris objects at altitudes between 600 and 800 km, complementing earlier studies that focused on lower altitudes, shorter time windows, or individual satellites.

Despite differences in mass, geometry, and orientation among the debris objects, all exhibit a clear separation between solar-maximum and solar-minimum behavior, underscoring the dominant role of solar EUV forcing. To further investigate predictability, ballistic coefficients derived from TLE data during solar cycles 22 and 23 were used to model orbital decay during solar cycle 24 and part of solar cycle 25, in combination with atmospheric densities from the NRLMSIS 2.0 model. For 15 of the 17 objects, the modeled decay profiles matched observations well after applying scaling factors in the range 0.55–0.79. These scaling requirements highlight limitations in both historical TLE-based ballistic coefficient estimation and empirical atmospheric density models, particularly during transitions between solar minimum and maximum.

Two debris objects with near-polar orbits ( inclination) exhibited large discrepancies between modeled and observed decay, even after applying a wide range of scaling factors. This behavior may point to significant limitations of the MSIS 2.0 model at high latitudes, where thermospheric density variability may not be fully captured. In contrast, mid and low-inclination objects showed excellent agreement, suggesting that MSIS 2.0 performs more reliably within approximately 70° latitude. These findings emphasize the need for targeted improvements to empirical atmospheric models in polar regions. Looking ahead, improving empirical atmospheric density models will be crucial for more reliable orbital decay predictions, especially as the population of debris in LEO continues to grow.

Overall, this study highlights the unique value of long-term debris observations for probing solar-driven variability in the thermosphere, identifying limitations in commonly used atmospheric models, and improving our ability to predict orbital decay. By bringing together a uniquely long debris dataset, a three solar cycle comparative analysis, the identification of a clear solar activity threshold, and a critical assessment of atmospheric model performance, this work advances our understanding of how long-term solar variability governs drag-driven orbital decay. These findings have direct relevance for debris re-entry forecasting, collision avoidance, and the long-term sustainability of the near-Earth space environment.

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