Forecasting air drag with deep learning helps predict when uncontrolled satellites and rocket stages fall to Earth

On May 10, 2025, a spacecraft built in the Soviet Union to land on Venus came home. Launched in 1972, Cosmos-482 was stranded by a failed upper stage of its rocket and circled Earth for 53 years. In its last days, several space agencies and research groups forecasted when it would fall, and therefore where. Roscosmos later reported that it came down in the Indian Ocean, west of Jakarta.

Cosmos-482 is not alone. By the end of 2025, low Earth orbit held 25,060 cataloged objects, nearly twice as many as a decade earlier, according to the European Space Agency. Many old satellites and spent rocket stages will one day fall back without control and may come down anywhere on Earth.

In a study published in Acta Astronautica, we combine two tools to predict these falls: a neural network and the laws of orbital motion. The work was led by M. Khawariz Andaristiyan of the Research Center for Satellite Technology at Indonesia's National Research and Innovation Agency (BRIN), with Affiani Machmudah and Wahyudi Hasbi of the same center and Ridanto Eko Poetro of the Institut Teknologi Bandung.

Why minutes matter

An object near the end of its life in orbit still flies at about 7.8 kilometers per second (4.8 miles per second). An error of one minute in the time of its fall shifts the place where it falls by about 460 kilometers (290 miles) along its path, and an error of one hour by about 28,000 kilometers (17,400 miles), two-thirds of the way around Earth. To say where an object will fall, we must first say when.

An atmosphere that breathes with the sun

What brings these objects down is drag, the braking by the thin air of the upper atmosphere. When the sun is active, it heats the upper atmosphere, which swells, so that the air at a given height grows denser and low orbits decay faster. The sun's activity rises and falls in a cycle of about 11 years, and the three falls we studied all came in its recent active years, from 2023 to 2025.

How strongly the air slows an object is measured by its ballistic coefficient: its drag coefficient times its cross-section, divided by its mass. A compact sphere shows the air the same face from every side. A tumbling rocket stage, or a satellite with wide solar panels, shows it a different face from one moment to the next. And in the last days, when the braking grows fastest, fresh tracking data often become scarce. A common simplification holds the coefficient fixed at a value estimated from past tracking.

Physics for the orbit, learning for the drag

Our idea is to divide the work between physics and learning. The motion of the object obeys Newton's laws, so we compute it using Earth's gravity and flattening, along with the drag given by a standard model of the upper atmosphere driven by solar and geomagnetic activity. What we cannot write down is how the ballistic coefficient will change, so we let a neural network learn it.

For each object, we first read the history of its coefficient from 11 years of public tracking data, one full solar cycle, by measuring how fast its orbit shrank. A network with a memory, of the kind built for sequences, then learns, for that object alone, to forecast the coefficient from the object's past and from forecasts of solar and geomagnetic activity.

During the prediction, the two parts work in turn: every three hours, the rhythm at which a standard index of geomagnetic activity is updated, the network receives the new orbit and returns a new coefficient. The calculation stops at 80 kilometers (50 miles), the height taken as the threshold of reentry. To estimate how much the network's forecast varies, we run it 100 times with random parts switched off; the spread of the answers gives a window of uncertainty around the predicted time.

Three falls, three tests

We tested the method after the fact, on three objects that have already fallen. For Cosmos-482, our prediction is 06:22 UTC, give or take 11.4 minutes; Roscosmos reported 06:24. For NEOWISE, the NASA infrared telescope launched in 2009 to map the sky and later turned to asteroids and comets, we predict 00:54 UTC on Nov. 2, 2024, give or take 7.8 minutes; the mission's website reported 00:49.

For the upper stage of a Chinese Long March 4B rocket, launched in 2006, we predict 22:45 UTC on March 26, 2023, give or take 13.2 minutes; its debris was seen over Murcia and Almería, in southeastern Spain, between 22:33 and 22:36. In all three cases, the time given by Roscosmos, by the mission or by the observers lies inside our window.

What does forecasting the coefficient buy? To find out, we repeated each prediction with the coefficient frozen at its last estimated value. For Cosmos-482, a compact sphere, the predicted fall moves by only five minutes. For NEOWISE, with its solar panels and sunshield, and for the rocket stage, a hollow cylinder prone to tumbling, it comes 31 and 36 minutes later, outside our windows and further from the reported times.

What comes next

These were hindcasts: like the reconstructions that agencies publish after a fall, they use tracking data up to shortly before it. Three objects are few, and each had been tracked for at least 11 years, a whole solar cycle. The real test is to predict objects still in orbit, including younger ones with a shorter history; this is where our work goes next.

As an applied mathematician, I see in this work a lesson that reaches beyond satellites. Where the equations are known, as for gravity, we should solve them. Where they are not, as for the way a tumbling object meets an atmosphere stirred by the sun, data can teach a network to fill the gap. Here physics and learning are not rivals: each covers what the other cannot.

This story is part of Science X Dialog, where researchers can report findings from their published research articles. Visit this page for information about Science X Dialog and how to participate.

Denys Dutykh is an applied mathematician and Associate Professor of Mathematics at Khalifa University of Science and Technology in Abu Dhabi, United Arab Emirates, where he is also Acting Associate Dean of Graduate Studies of the College of Computing and Mathematical Sciences. Before joining Khalifa University in 2022, he spent 14 years as a researcher of the French National Center for Scientific Research (CNRS) at the University Savoie Mont Blanc. His research develops numerical methods for problems of physics and engineering, from tsunamis and water waves to the vibrations of black holes. The work described here comes from a collaboration with the Research Center for Satellite Technology of Indonesia's National Research and Innovation Agency (BRIN) and with the Institut Teknologi Bandung: it was carried out by M. Khawariz Andaristiyan, of the center, under the supervision of Affiani Machmudah, Ridanto Eko Poetro, Wahyudi Hasbi and Dutykh.