Every eight hours, a set of files is refreshed on a SpaceX server. Each one predicts where a Starlink satellite will be for the next 72 hours, minute by minute, with its velocity and a covariance matrix alongside. The point of the exercise is to keep the constellation from running into other satellites and spent rocket stages. The files reach the public through the Space-Track website, and SpaceX has mirrored them on its own server, a change the paper dates to July 2025.
One week of those files has now been turned into something else: a map of how dense the air is at 482 kilometres, drawn by latitude and longitude. The tomographic analysis is the work of Mamoru Yamamoto at Kyoto University’s Research Institute for Sustainable Humanosphere, published as an Express Letter in Earth, Planets and Space. He writes that he believes it is the first report of the analysis carried out on real data; the earlier proposal had only ever been run on synthetic numbers.
The neutral gas is the part that resists observation
Thermospheric density is the term for the neutral gas between roughly 100 and 1,000 kilometres up. At 300 kilometres it is 2 x 10-11 times as dense as the air at sea level, or about one part in fifty billion.
More than 99 percent of the upper atmosphere is electrically neutral and less than 1 percent is ionised, and it is the ionised remainder that bends radio waves and is therefore relatively easy to observe. The neutral bulk is harder to reach, and watching how quickly satellites sink through it has long been an important way in.
An earlier paper had proposed exactly that on a large scale, under the name satellite orbit tomography: if enough objects are being slowed at once, the pattern of their slowing should carry the shape of the gas. It described the method and verified it on synthetic data.
The files SpaceX puts out for collision avoidance
The standard public format for satellite orbits is the Two-Line Element set, a compressed summary. The richer format, the Vector Covariance Message, is normally available only under specific contracts with the data source. Starlink’s files use a format SpaceX’s own documentation calls Modified ITC, and the paper describes their content as identical to a Vector Covariance Message. Anyone can download them.
A previous study had already shown that these files respond to space weather, with satellite energy falling during geomagnetic storms. It stopped short of estimating density.
Drag shows up in the energy budget
The measurement is made in energy. A satellite in a bound orbit holds a fixed specific mechanical energy, kinetic plus potential per kilogram, and for the satellite worked through in detail in the paper that figure averaged minus 29.1 megajoules per kilogram. Drag subtracts from it and thruster burns add back.
So each satellite is propagated forward with GMAT, NASA’s open-source mission analysis software, once under a no-drag condition, and that frictionless twin is compared against the ephemeris prediction. The difference is the energy the atmosphere took plus whatever the engine contributed, both as predicted. What actually happened comes from the next file eight hours later, whose first data point the paper treats as an observation. Station-keeping burns appear as sudden steps and are removed as discrete jumps, and the satellite’s inverse ballistic coefficient is then found by re-propagating with different drag settings until the residual slope flattens to zero.
In the first dataset for the roughly 1,200 satellites in the 482-kilometre shell, manoeuvres were detected in 80 percent of the data. Isolating drag also requires assuming each burn went as planned, which the paper says its overall results suggest is valid while adding that a rigorous test is still wanted.
The reconstruction ran nineteen times
The analysis used data from 1 to 7 September 2025, drawn from a single Starlink shell of about 1,200 satellites at 482 kilometres and an inclination of 53 degrees, and produced 19 separate reconstructions. The number of satellites feeding each one ranged from 850 to 1,100. One case, the fifth, had only 354 data points, and its result did not stand out from the rest.
The map behind those numbers is a spherical harmonic expansion truncated at degree one, four coefficients in all, and density is assumed to fall off exponentially with a single scale height fixed at 60 kilometres, a value chosen because it minimised the residuals. Only the daily cycle is modelled. In the three cases the paper maps, peak density sits between 200 and 220 degrees of the paper’s local-time longitude, where noon is set at 180 degrees, and between 0 and 20 degrees of latitude, though the exact position of the peak moves from case to case.
Pushing the expansion past degree one fails. It throws up false density peaks and troughs at high latitudes, chiefly because a shell inclined at 53 degrees never climbs higher than that, which leaves the fit with no data above 53 degrees of latitude. The maps cover the whole globe. The data behind them do not.
SWARM supplied the independent check
The European Space Agency’s SWARM satellites derive density along their own tracks from onboard GPS positioning, and the results are published openly. SWARM A flies 440 to 470 kilometres up and SWARM B 490 to 520, which the paper puts at 35 kilometres below and 15 above the reconstruction, on polar orbits about 90 degrees apart in longitude.
Individual reconstructed density values ran from 0.5 to 1.5 times the SWARM numbers. The per-case averages, a different quantity, ran from 0.6 to 1.2 times, and the average across all 19 case means was 0.95. Only the narrower of those two ranges appears in the paper’s abstract.
Near the peaks of the variation, the reconstruction, the SWARM data and the existing atmospheric model all agreed. Near the minima, the reconstruction tracked SWARM more closely than the model did.
That model is NRLMSIS 2.1, and it is not only the thing being compared against. It also supplies the starting values for the fit, though Yamamoto states that the analysis is not sensitive to that initial guess. The abstract’s own summary of the outcome is that the tomography “captures features of thermospheric density that the NRLMSIS 2.1 model predicts.”
The input carries a deeper version of the same problem. The ephemerides come out of SpaceX’s tracking system rather than straight off a sensor, and the paper says that system “likely serves as a filter, blending real observations with model predictions,” so biases from the filtering could carry into the density estimate, particularly when density is changing sharply. Whichever atmospheric model SpaceX uses to generate its predictions is somewhere in the files.
The article is an Express Letter, and its author describes the results as preliminary and low-resolution. Its claim is procedural: a method that works on public data refreshed every eight hours.
Storms are the case not yet tested
Density sets how fast dead satellites and debris come down, and how confidently anyone can say where a spacecraft will be next week, which is what collision avoidance rests on. Better numbers would be worth having.
The condition that makes those numbers most valuable is the one this reconstruction has least to say about. Density swings hardest during geomagnetic storms, and that is precisely when the paper says the filtering behind its input data most needs watching. It reports no test of the method through a storm.
So the method is demonstrated, on seven days of September 2025, against a model it mostly reproduces. What happens to it the first time the thermosphere lurches?
