The objects and why they were chosen
The paper draws on Two-Line Element data from the Space-Track database, the standard orbital-mechanics format used to track every object in Earth orbit. Ashruf’s team began with a set of 95 candidate debris objects from the 1960s, then filtered for objects in low Earth orbit below 800 km, with stable near-circular orbits and continuous data across the full period. Seventeen survived that filtering.
The list includes TIROS weather satellites, Thor rocket debris, Delta stage fragments, and two Soviet-era Cosmos objects. They orbit at inclinations ranging from roughly 48 to 99 degrees, and altitudes between about 600 and 800 km, completing a full loop of the planet every 90 to 120 minutes. Their masses range from under 20 kg to over 1,400 kg.
What they share is longevity and passivity. None have performed any orbital adjustment in over sixty years. That makes their altitude history a clean signal: whatever happened to their orbit happened because of the atmosphere, not because of anything onboard.
The threshold
Solar activity is most commonly tracked through sunspot numbers, a count that correlates with the Sun’s emission of extreme ultraviolet radiation. The Sun’s eleven-year cycle moves between quiet periods, when sunspot numbers are low and the thermosphere cools and contracts, and active periods when numbers climb and the upper atmosphere heats and expands. More atmosphere at orbital altitude means more drag on any object passing through it.
Earlier research had established this general connection. What it had not established was where within a solar cycle the drag effect becomes meaningfully stronger. Ashruf’s team fitted a Gaussian curve to the sunspot record for each of the three cycles studied, then identified the point in each cycle where the 17 debris objects showed a transition from slow, gradual decay to markedly steeper decay. That point, consistent across three cycles and across the full range of objects, fell between approximately 67 and 75 per cent of the cycle’s peak sunspot number.
The authors describe this as a threshold beyond which thermospheric density increases sufficiently to drive a clear acceleration in orbital decay. Below the threshold, descent is slow and fairly uniform. Above it, the curve steepens. The threshold appears on the way up through each cycle and again on the way back down.
Cross-checking with direct measurements of extreme ultraviolet flux from the Solar and Heliospheric Observatory confirms the pattern. Within the rapid-decay windows identified by the debris data, EUV flux in the 0.1 to 50 nanometre band ran roughly 50 to 130 per cent above levels seen outside those windows. The debris records and the solar measurements point to the same mechanism: heightened EUV output heats the thermosphere, which expands upward, and the increased air density at orbital altitude increases drag.
Three cycles, one staircase
The three cycles in the dataset were not equal in strength. Solar cycle 22, which peaked around 1989 to 1991, was the most active of the three. Cycle 23, peaking around 2000 to 2002, was moderately active. Cycle 24, peaking around 2014, was historically weak by modern standards.
The debris records reflect that hierarchy directly. Peak decay rates during cycle 22 averaged 0.59 metres per hour across the 17 objects. Cycle 23 produced a mean of 0.54 metres per hour. Cycle 24 came in at 0.25 metres per hour, roughly half of cycle 22’s pace. The staircase is clean: each successive cycle, as solar activity weakened, drove proportionally less orbital decay.
The paper also compared the correlation between decay rates and several different solar and geomagnetic indices. Solar proxies performed strongly: the F10.7 radio flux index explained about 75 per cent of the variance in decay rate across the 17 objects; sunspot numbers accounted for about 67 per cent. Geomagnetic indices fared poorly. The AE index, which tracks auroral electrojet activity driven by particle precipitation and magnetic disturbances, explained less than 2 per cent of the long-term variance. The Dst index, which measures the ring current, explained around 22 per cent. The paper’s interpretation is that geomagnetic storms matter for short-term orbital perturbations, but for sustained, long-term decay the dominant driver is solar EUV forcing of the thermosphere, not geomagnetic disturbance.
The polar gap in the model
The team used ballistic coefficients derived from the cycle 22 and cycle 23 data to model what cycle 24 orbital decay should have looked like, then compared those predictions to what the TLE data actually showed. For 15 of the 17 objects, the model reproduced the observed decay profiles reasonably well, though it required a scaling factor ranging from 0.55 to 0.79 to match observed behaviour. The need for that scaling reflects known limitations in empirical atmospheric density models, particularly around the transition between solar minimum and solar maximum conditions.
Two objects did not fit at all. SAT 733, a Thor Agena D rocket body, and SAT 734, a satellite called OPS 3367A, showed persistent large discrepancies between modelled and observed decay that no scaling factor could close. Both travel near-polar orbits, at inclinations close to 99 degrees. The other 15 objects orbit between roughly 48 and 67 degrees of inclination.
The paper’s interpretation is cautious but direct: the NRLMSIS 2.0 atmospheric model, which is the standard empirical model used for this kind of orbital prediction, likely underestimates atmospheric density variability at high latitudes. The thermosphere at polar regions is influenced by geomagnetic activity in ways that are not fully captured by models built primarily around lower-latitude data. The gap matters because polar and sun-synchronous orbits are common choices for Earth-observation missions, and their reentry predictions may carry larger errors than the model currently reflects.
What the finding offers operators
The practical value of a threshold is that it gives satellite operators a more specific warning indicator than a general solar forecast. Rather than tracking the entire solar cycle, operators can watch sunspot numbers relative to the expected cycle peak. When that ratio climbs past roughly two-thirds of peak, conditions enter the regime where drag-driven decay accelerates. Fuel reserves for orbit maintenance need to be adequate for that period, not just for quiet-Sun operations.
The February 2022 Starlink event sits in the background here. A moderate geomagnetic storm shortly after launch pushed 38 satellites into orbits lower than planned, and atmospheric drag was sufficient to prevent them from reaching their target altitude. Most reentered within weeks. The Starlink case involved a geomagnetic disturbance rather than sustained solar maximum conditions, so the mechanisms are not identical, but the broader point stands: drag at low Earth orbit is not a fixed baseline to plan against, and the Sun’s eleven-year cycle is the primary long-term variable.
The paper notes that missions launched near a solar maximum may consume propellant faster than mission planners expect, particularly if planning tools use average solar conditions rather than the cycle-phase-specific drag rates the new threshold identifies.
What the study does not resolve
The 17 objects all orbit within the 600 to 800 km altitude range. The paper does not claim the same threshold applies at lower altitudes, where atmospheric density is higher and the relationship between solar activity and drag may behave differently. Most of the large satellite constellations being deployed now operate below 600 km, and the paper’s findings do not directly translate to that regime without further work.
The three solar cycles in the dataset were also all relatively moderate by historical standards. The most active cycles on record, including cycle 19 in the late 1950s, produced solar maxima substantially stronger than cycle 22. Whether the 67 to 75 per cent threshold holds under more extreme solar conditions is not something this data can answer.
The polar orbit modelling gap remains open. Ashruf’s team notes it explicitly as a direction for future work, and it is a real limitation for anyone predicting the reentry timing of debris in high-inclination orbits.
Better empirical models for high-latitude atmospheric density are needed, and the debris records in this study now provide one benchmark for testing them.
The paper is published as “Characterizing solar cycle influence on long-term orbital deterioration of low-earth orbiting space debris”, authored by Ayisha M. Ashruf, Ankush Bhaskar, C. Vineeth, and Tarun Kumar Pant, in Frontiers in Astronomy and Space Sciences, volume 13, published 6 May 2026. It is open access.
