Three Physicists Ran It Blind. Fifty-One Minutes, 4.5 Millisieverts, No Lethal Case Found.
None of the three had been told what the trajectory was for. Their answers land within 0.6 millisieverts of each other. A sweep of 900 assumption sets, published entire, produced no configuration that endangers a crew.
A standing series in which this newspaper investigates a widely held claim and reports that it could not substantiate it.
MADISON, United States — Four and a half millisieverts. Fifty-one minutes.
That is the crew dose for one crossing of the radiation belts on the outbound leg of a translunar injection, and three health physicists who have never met arrived at it separately, from a published trajectory, having been told nothing about why they were being asked.
Their answers were 4.31, 4.52 and 4.91 millisieverts. The spread is 0.60.
A chest scan is about seven.
What they were given
Each received the same package: an ephemeris, a mass statement, a shielding distribution and a crossing geometry. None was told the year. None was told the vehicle.
Each was asked one question — what dose would a person inside this shielding receive on this path — and paid the same fee, in advance, whatever came back.
Two of the three worked out what they were holding anyway, and said so in their reports, and we have printed those reports entire.
The sweep
One answer is not an argument, so we swept it.
Five belt models — the two standard sets, two later empirical fits and one deliberately pessimistic envelope — by six launch epochs across a solar cycle, by six shielding masses from 4 to 14 grams per square centimetre, by five trajectory inclinations. Nine hundred runs.
The protocol, the script and the input tables went up before the first run, in the same way we published the pre-registered protocol in PX-2161, so that we could not choose where to stop.
The highest result in the sweep is 31.4 millisieverts. The lowest is 1.9. The dose at which a healthy adult faces a serious prospect of dying is around four thousand.
There is no configuration in the sweep that endangers anybody. We looked for one for nine weeks.
The four we got wrong
Four runs came back between 2,700 and 3,900 millisieverts, and we spent a fortnight on them.
They were ours. In four of the nine hundred input files an electron flux column had been read as particles per square centimetre per second where the source gives them per square centimetre per day — a factor of 86,400.
All four rows are in the repository with the error, the corrected value and the commit that fixed it. Dr. Solveig Amankwah-Reint, who supplied the tables we mis-pasted, objects below to our publishing them at all, and she is not wrong about what will be done with them.
Where the lethal number comes from
The figure quoted for six decades is 25 rad an hour. It is real. It was measured, by an unshielded counter, at the flux maximum of the inner belt, and it appears in a 1962 paper that has never been retracted because there is nothing in it to retract.
It is an instrument reading. The instrument was bare, and it stayed.
Twenty-five rad an hour will kill a person in about a day. It does very little to a shielded crew crossing the same region in fifty-one minutes at ten kilometres a second, and the paper's author said exactly that, in a caveat of four sentences appended to his own results.
The caveat is in the journal issue. It is not in the reprint, which ran to eleven pages where the original ran to fourteen, and the reprint is the version that got photocopied.
Forty-one letters
Dr. Leland Whitmarsh-Osei spent twenty-two years correcting his own number.
The file at Madison holds 41 letters written between 1972 and 1994 to authors, broadcasters, editors and members of the public. Every one is courteous. Several enclose the missing paragraph, retyped by him.
The last is dated 6 April 1994, to a schoolteacher in Wisconsin who had written to ask which figure she should give her class. It runs to two pages and answers her question completely. At the foot of it, in pen, he has written that he no longer thinks this a good use of the time he has.
He was eighty-one. He died in 1999.
What this desk takes from it
The arithmetic is one page. Any health physicist can do it in an afternoon, three of them did, and the result has not been news since 1962.
What we have bought, for £11,400 in fees and £1,400 of rented compute, is a demonstration that it is dull — and that the dullness survives nine hundred attempts to make it interesting.
That is a small thing to have spent nine weeks on. Dr. Amankwah-Reint's letter, printed below in full, says so more sharply than we would, and adds the point we should have led with: the sum was never missing. It was done in 1962, in the paragraph that got cut, by the man who spent the rest of his working life posting it back out again.
The six o'clock edition
Three stories a morning, in your inbox before the coffee is made.
Sources & Method
We wanted the arithmetic done by people with no stake in the answer, so we commissioned three health physicists separately, told none of them what the trajectory was or when it flew, and paid all three in advance on terms that made publication unconditional and identical. The sweep protocol, the script and the input tables were published before the first run, and every one of the 900 runs is in the repository, including the four we got wrong.
Who we spoke to
- Dr. Solveig Amankwah-Reint, Health physicist, Uppsala; first computation. Commissioned without being told what the trajectory was; paid in advance on terms making publication unconditional April – June 2026 Returned 4.31 mSv, and a note saying she had guessed the vehicle by page two. Her reply is at the foot of this page and is the most serious objection we received.
- Dr. Bartholomew Nkemdi-Falk, Health physicist, Johannesburg; second computation, no contact with the first. Given the identical package with the same instructions and the same fee April – June 2026 Returned 4.91 mSv. The only one of the three who modelled the heat shield as present, which moves his answer by 0.28 mSv.
- Dr. Ingrid Sauvageau-Prosper, Medical physicist, Lyon; third computation, hospital dosimetry rather than space. Commissioned deliberately from outside the field, on the same package and the same terms May – June 2026 Returned 4.52 mSv. Asked us twice whether the geometry described a real vehicle. We did not answer either time.
- The Whitmarsh-Osei papers, Madison, Both editions of the 1962 paper, the publisher's page-count file, and 41 letters written 1972–1994. Read in the reading room over three days; the two editions collated line by line; quoted with the library's permission and the family's May 2026 His own numbered list of the letters, in the same box, runs to 44.
- Marguerite Odusola-Pike, Retired schoolteacher, Wisconsin; recipient of the letter of 6 April 1994. Interviewed by telephone twice and sent the passage about her before publication June and July 2026 Still has the letter. Read the whole of it to our correspondent, unprompted, including the part in pen at the bottom.
Documents
- PX-2161 — Cumulative radiofrequency exposure study — signed protocol, published before recruitment accepted
What we could not confirm
- The as-flown attitude. All three assumed a slow passive roll, which is the standard assumption and which nothing in the published record confirms minute by minute for this crossing. A vehicle held in one attitude with its thin side to the flux would give a higher number. Our own sweep says not more than about three times higher, which is still nowhere near dangerous, but three times is three times and we did not measure it, we modelled it.
- Whether the caveat was cut for length. The reprint runs eleven pages where the journal ran fourteen. The publisher's file records the reduction and contains no correspondence about the paragraph, and the editor who made the cut died in 1988. 'Cut for length' is what a compositor's mark-up implies. It is not what anybody wrote down.
- Whether all the letters survive. The Madison file holds 41. Whitmarsh-Osei's own numbered list, in the same box in his hand, runs to 44. Three letters are unaccounted for and we do not know who received them, which means our count of twenty-two years of courtesy is a floor and not a total.
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 PostThe Belt Numbers Nobody In Government Will Recalculate
Framed the absence of a recent official recalculation as a refusal, and did not attempt the calculation, which takes an afternoon and no permission.
Had that we did not
The 1962 figure, correctly transcribed and correctly given in rad per hour, which most retellings get wrong by a factor of ten.
Left out
The author's caveat, which is on page 13 of the original journal issue and free to read in any university library that holds the volume.
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ApertureA Man Who Wrote Forty-One Letters
An essay on correction as a form of hope, built entirely from the Madison file. It is better written than this piece and we are not pretending otherwise.
Had that we did not
The 1994 letter in facsimile, including the line at the foot of it, which they found first.
Left out
The dose. The essay never once says what the number is, which is the only thing the forty-one letters were ever for.
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They Buriedthis newspaperThree Physicists Ran It Blind. Fifty-One Minutes, 4.5 Millisieverts, No Lethal Case Found.
Paid for the arithmetic three times over from people told nothing, then spent nine weeks trying to break it.
Had that we did not
All three computations entire, the 900-row sweep with its protocol timestamped before the first run, and the four rows we got wrong.
Left out
We put a dead man's worst sentence under a subheading and used it to end the piece, having established in paragraph six that the finding itself is not news. — V. Ashcombe-Doyle, standards editor
Right of Reply
They Buried contacted Dr. Solveig Amankwah-Reint, health physicist, Uppsala on 27 June 2026 with the full draft, the sweep repository, the four erroneous rows and three weeks to answer. Replied by letter on 16 July 2026, asking that it run entire and that we not soften the first paragraph. Printed unedited.
You did not blind me and you should stop using the word.
You sent an ephemeris with an epoch in it and a mass statement in pounds and a shielding distribution with a service module in it. I knew what I was working on before the end of the second page. I wrote that at the top of my report, in the first line, and you have printed my report entire, which is to your credit, and you have also put the word blind in your headline, which is not. What you ran was a computation by three people who were not told, which is a different and weaker thing, and the difference is exactly the part a reader cannot check.
Second. The three of us agreeing to within 0.6 millisieverts is not the corroboration you are selling. We agree because we all used AE-8 and AP-8, because AE-8 and AP-8 are what there is. Three people reading the same map and arriving at the same village have not confirmed the village. If the belt models carry a shared bias — and they carry several, and the community argues about them in public — all three of us are wrong together by the same amount, and our beautiful spread of 0.6 tells you nothing whatever about that. Your sweep addresses this and your headline does not, and readers read headlines.
Third, and this is the one I would ask you to sit with. You have published four runs that came back near four thousand millisieverts, with the error marked, with the corrected value beside it, with the commit that fixed it. You will call that transparency and in your own terms you are right. Here is what will actually happen. Four rows containing my name, because my name is on the input tables you mis-pasted, and the number 3,900, will be lifted out of your repository within the month and will circulate without one word of the paragraph you have written around them. I will be answering for those rows at conferences in 2034. I told your correspondent this on the telephone and he said, honestly, that he thought I was probably right and that you were publishing them anyway. I have decided I would rather you did. I want it on the record that I said what it would cost, and that the cost is mine and not yours.
Fourth, about money. You paid me £3,800 for four days' work and then wrote in your own piece that the calculation takes an afternoon. Both statements are true. Only one of them is fair, and you have arranged them so that the reader ends on the cheap one.
Now the part where I concede something, because I do concede it.
I thought this commission was silly when I took it. I took it because the fee was good and the terms were clean and because I have been asked about the belts by strangers at parties for eleven years and have never once had a number of my own to give them. I have one now. It is 4.31 millisieverts and it took me four days and I am glad to have it.
But do not tell your readers that the reason this misunderstanding has lasted sixty years is that nobody had done the sum. Whitmarsh-Osei did the sum, in the paper itself, in the paragraph that got cut. Four of my own teachers did it in lectures I sat in. It is in two textbooks I own. Doing it again, carefully, in public, with the workings, is worth doing — I would not have taken your money if I thought otherwise — but it is not the missing piece, and a newspaper that tells its readers it has supplied the missing piece is doing the same thing to me that the reprint did to him.
Published unedited under our right-of-reply guarantee.
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