A Mascon Is Buried Mass. Under This One There Is Nothing To Bury.
An orbiter speeds up over a mass concentration and its radio link records it. We had the residuals over one anomaly inverted twice, blind, from public data. Every solid body overshoots the rim by a factor of four.
Background written by the news staff. Contains no argument or recommendation.
TRONDHEIM, Norway — A mascon is a lump. That is the whole of the idea: somewhere under the surface there is more stuff than the rock around it, and a spacecraft passing overhead feels the difference.
Here is how you weigh one — and the one where the arithmetic will not close.
You do not measure the lump
You measure the spacecraft.
An orbiter crossing a mass concentration is pulled forward on the way in and held back on the way out. The speed change is small — a few tenths of a millimetre per second — and it would be undetectable if the spacecraft were not carrying a radio.
It is. The radio link down to a ground antenna has a frequency, and the frequency shifts with the speed of the thing transmitting it, the way an ambulance siren drops as it goes past. Measure the shift and you have the speed. Differentiate it and you have the acceleration. Subtract the acceleration a smooth, boring Moon would give you, and what is left over is called the residual.
Residuals are what everything below is made of. They are public and free, which is why this story is built out of them.
From a residual to a mass
Turning residuals into a mass distribution is called an inversion, and it is the hard part, because it does not have one answer.
Gravity does not tell you where something is. It tells you the sum of everything, weighted by distance. A small dense body near the surface and a big light one further down can produce nearly the same residual along a single track. That is arithmetic, not a flaw in the instrument, and it is why an inversion is quoted as a family of solutions rather than a number.
What breaks the tie is shape. Two distributions that agree over the middle of an anomaly usually part company at its edge.
The edge is where you look.
The one that will not close
G-9 is a residual over the western lobe of Mare Crisium, about 460 kilometres across. It has sat in the published gravity field since the field was published, and it has never been a secret.
This paper paid two teams to invert it separately, from the public data, with no contact, on condition that both publish their code and their failed runs. Both did.
Dr. Solveig Ahlgren-Musa in Trondheim tested 11,400 solid bodies: every depth from five kilometres to four hundred, every density from basalt to iron, spheres and slabs and discs and dykes. Dr. Casimir Ndlovu-Petrén in Santiago tested 9,200 with his own solver.
Their conclusions are the same sentence with different numbers in it. Any solid body tuned to reproduce the anomaly over the middle of G-9 overshoots the measured gravity gradient at the rim — by a factor of 3.7 on her best fit, 4.2 on his.
Not one of the 20,600 came within the tolerance at both places at once.
Why the rim is the tell
A buried lump makes a peak. Directly above it the pull is strongest; move off to the side and it falls away smoothly. That falloff is the signature.
G-9 does not do that. Over the middle it is flat. At the rim it steps.
A shell does exactly that, for a reason that has been in the books since Newton. Inside a uniform spherical shell the pull of the shell is zero, everywhere: the near part pulls one way, the far part the other, and they cancel. Fly over the middle of a shell and it is quiet. Cross its edge and it is not.
Both inversions accept a rigid shell of roughly sixty kilometres over an interior of density below 0.3 grams per cubic centimetre. Her band is 58 to 63 kilometres. His is 59 to 63.
Two methods that share nothing
Three seismology groups, paid separately by this newspaper to fit the coda of nine long-period lunar events, converge on a rigid shell of 62 to 71 kilometres.
Those groups worked from seismic traces recorded in the 1970s. These two worked from Doppler residuals recorded decades later. The datasets share no instrument, no epoch and no physical quantity.
The bands overlap at 62 to 63 kilometres.
Dr. Peregrine Vasquez-Lindholm, who helped build the residual field, replies at the foot of this page that two clean inversions of one coverage-limited dataset are one answer, not two. He has run one of the codes himself and got the same numbers. He does not say the teams are wrong. He says the pass that would settle it was cut in a dull meeting about fuel, and that nobody is going to fly it.
Where the drawing stops being measurement
Below about 340 kilometres the residuals carry no information at all. Both teams drew that line in the same place, and both wrote, unprompted, that everything beneath it in their diagrams was decoration.
We have printed it as decoration. It is the bottom band of the section above, and the only part of this page that is not measured.
A mascon is buried mass. Under G-9 there is a shell sixty kilometres thick, and under the shell there is not enough mass to bury.
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Sources & Method
The residuals are public and cost nothing, which is the point of the exercise: we wanted two answers that any reader could check rather than one answer a reader had to trust. Two teams with no contact were paid the same fee in advance and required, as a condition of the commission, to publish their code and their failed runs alongside their result. Both did. We then took the shell band to a seismologist who had no part in either inversion and asked her whether it could honestly be set beside the seismic one.
Who we spoke to
- Dr. Solveig Ahlgren-Musa, Geodesist, Trondheim; first inversion. Commissioned to invert the public tracking residuals and to publish her code with her answer; interviewed over two days at her department May–August 2026 Tested 11,400 solid bodies. Best solid fit overshoots the rim gradient by 3.7. Accepted band for the shell: 58–63 km.
- Dr. Casimir Ndlovu-Petrén, Geophysicist, Santiago; second inversion, blind. Given the same public dataset with no contact with the first team and no sight of her result; wrote his own code from scratch May–August 2026 Tested 9,200 solid bodies with an independently written solver. Overshoot 4.2. Accepted band: 59–63 km.
- Dr. Josefina Marek-Anand, Planetary seismologist. Asked to check whether the gravity band and the seismic band could be compared at all, and on what assumptions August 2026 Says the two are comparable only if 'rigid' means the same thing in both, and that it roughly does. Her caveat is printed under Unverified.
- Dr. Peregrine Vasquez-Lindholm, Principal investigator emeritus, the gravity mapping programme. Sent the full draft, both inversions and both repositories; replied in writing after twelve days August 2026 Rejects the conclusion in detail. Printed entire under Right of Reply.
- The public tracking release, Level-1B Doppler residuals and the published spherical-harmonic field. Downloaded, free, from the open archive. No agreement signed, no permission asked, no fee paid. May 2026
Documents
- PX-1788 — Lunar seismometer network, long-period event catalogue, unofficial compilation accepted
What we could not confirm
- Whether the shell is global. Both inversions constrain it under G-9 and nowhere else — a patch about 460 kilometres across, less than one per cent of the Moon's surface. Neither team will say a word about the other ninety-nine, and this newspaper has not asked them to.
- Whether 'rigid' means the same thing in the two methods. A gravity inversion calls a layer rigid because a density contrast holds a shape; a seismic fit calls it rigid because it carries shear. Dr. Marek-Anand says the two definitions overlap for the materials in question but are not identical, and that the 62-to-63-kilometre agreement is therefore a strong coincidence rather than a single measurement made twice.
- The descoped pass. A lower-altitude track over G-9 appears in the published programme timeline and was cut. We asked for the planning record on 14 July and received it with the decision rationale withheld. The appeal was filed on 20 August and no date has been set.
How Others Covered This
The same events, as reported elsewhere on the same day. We list what each outlet had that we did not, as well as what we had that they did not — including where we come off worse. Why we print this.
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The Hollow PostThey Cancelled The Pass That Would Have Settled It
Built the story on the descoped low-altitude track and treated the descope as the finding.
Had that we did not
The descope, correctly dated, from the same public timeline we used.
Left out
That eleven other passes were descoped in the same programme year for the same stated reason, which is in the timeline three lines further down.
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ApertureOn Weighing An Absence
A long essay on the shell theorem as a way of thinking about what cannot be seen from outside.
Had that we did not
The physics, explained more beautifully than we have explained it here.
Left out
Both inversions, both codes, and every number in them. The essay names no anomaly and cites no data.
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They Buriedthis newspaperA Mascon Is Buried Mass. Under This One There Is Nothing To Bury.
Paid two teams to invert public residuals separately, required both to publish code, and printed the disagreements.
Had that we did not
Both inversions, both repositories, and the depth below which neither team will say anything.
Left out
We published the code and not the correspondence. Two hours of it is our reporter pressing one team to rerun with a wider depth range, and them declining. The reader should have watched us being told no. — V. Ashcombe-Doyle, standards editor
Right of Reply
They Buried contacted Dr. Peregrine Vasquez-Lindholm, principal investigator emeritus, the gravity mapping programme on 10 August 2026, in writing, with the full draft, both inversions and both code repositories attached. Replied 22 August 2026. Printed in full and unedited.
You have asked me to comment on two inversions of a residual field I spent nine years helping to build, and I will, but you should understand what you are holding first.
Your two teams did not perform independent measurements. They performed independent arithmetic on one measurement. The distinction is not pedantry. Every systematic in that dataset — the thermal model of the spacecraft, the antenna phase centre, the tropospheric correction at the ground stations — is common to both of them, and neither can see past it, because it was baked in before the file they downloaded was written. Two people dividing the same wrong number by different methods will agree beautifully.
On G-9 specifically. It sits at the western edge of a mare with a topographic step under it, and topography and density trade against one another in an inversion in exactly the way that produces a flat middle and a sharp shoulder. Your teams have modelled the shoulder as a shell edge. It can equally be a scarp. I do not say it is a scarp. I say your data cannot separate the two, and the honest sentence is that it cannot, not that a shell is required.
As to the shell theorem argument, it is correct and it is also first-year physics deployed at a first-year level. A uniform spherical shell produces no field within it. Nothing under G-9 is uniform, nothing under G-9 is spherical, and the moment you relax either the interior field stops being zero and starts being something you have to compute rather than quote.
Now the part you are waiting for. In 2019 the reprocessing team flagged G-9 internally as geometry-limited and set it aside. That is in the record and I am not going to pretend otherwise. It means the ground track density over that patch was insufficient to separate shallow structure from deep, which is a statement about our coverage and not about the Moon. And yes, the low-altitude pass was descoped. It was descoped along with eleven others that year because the propellant budget after the extended mission would not carry them all, and G-9 lost the argument to a polar target that had a lander riding on it. I was in the room. It was a dull meeting about fuel.
I would rather you printed that than the version where somebody stopped us.
What I cannot do is tell you the two teams are wrong, because I have read both codes and they are clean, and I have run Ndlovu-Petrén's myself on a machine here and got his numbers. My position is that a clean inversion of a coverage-limited field is a clean answer to a question the data was never able to ask. Fly the pass and I will change my mind in public. Nobody is going to fly the pass.
Published unedited under our right-of-reply guarantee.
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