A trajectory is a question you can ask twice.
Refit the published sky positions of ‘Oumuamua and the outward push its discoverers reported comes back as printed: 4.92 ± 0.16 millionths of a metre per second squared. Then let gravity try alone, plant a known push into the same sky, and cut the arc short to find where the test loses its power. The acceleration and its cause are different questions.
Here we report the detection, at 30σ significance, of non-gravitational acceleration in the motion of ‘Oumuamua.
Micheli and colleagues, Nature
THE CLAIM AT FULL STRENGTH
Published by Micheli and colleagues: A₁ = (4.92 ± 0.16) × 10⁻⁶ m/s² at one astronomical unit, directed away from the Sun, a formal significance of about 30σ. Their Table 1 gives χ² = 1031 for gravity alone and 81 once the push is added.
THIS PAGE’S ORBIT FIT, LIVE
Fitting the frozen sky positions…
Fitted in your browser from the measured sky positions, all six starting-orbit components free in both models. The paper counts 207 positions; the released record yields 208, and the check below explains why the two cannot be reconciled from what is published.
THE DECIDING CONTROL
A force changes a path. It also changes the best starting orbit. Remove the outward push and this page refits every starting position and velocity before judging what is left.
Loading the local numerical record.
Every plotted point keeps its original workbook row.
Counting the positions gravity alone cannot reach…
The paper, for gravity alone: ten positions off by more than 5σ in at least one coordinate, 25 by more than 3σ, and offsets “as large as 22″ for the 2017 October 14 Catalina observation”.
Table 1 of the paper also tried pushes fading as (1 au/r)ᵏ for k from 0 to 3. Change k and the push refits; A₁/σ stays between 30.48 and 30.77 under every law, so the detection survives each of them, but χ² prefers 1/r and 1/r² about equally (81.45 and 82.30, against 99.41 and 98.75).
The paper’s Extended Data Table 1 prints the team’s own 53 ground positions and errors “as used in our analysis”. The released workbook carries other values for 52 of those rows. The default puts the printed values in place of those 53 rows and keeps the workbook for every other position; the other option replays the workbook exactly as released.
THE CLAIM, RECOMPUTED
Left, the numbers as the paper prints them. Right, the same quantities fitted by this page’s engine from the measured positions, before publication, with every fit repeated by the published verifier. The first rows are also live in the instrument above.
| Quantity | As printed | This engine | Agreement | Where printed |
|---|
On the workbook exactly as released, the same engine gives 4.959 ± 0.159 × 10⁻⁶ m/s² (31.12σ), χ² 1059.27 for gravity alone and 90.48 with the push, and 30 gravity-only positions beyond 3σ. The difference is 53 rows. The workbook’s positions for the team’s own ground astrometry differ from the printed table by up to 0.49″ (Pan-STARRS, workbook row 214), and 11 of those rows carry different errors. Put the printed values in and the fit lands on the printed digits.
THE DEPTH LAYER
The paper did not stop at the full arc. Its Methods refit subsets of the observations to ask whether any one part of the record could have manufactured the signal, and printed the significance of each. Below, each of those subsets is refitted here, and then the claimed push is planted into it to measure what that subset would be expected to show if the push were there.
Fitting only data taken after 2017 October 25 or after 2017 November 15 still yields a detection of A₁ at 17σ and 2.5σ confidence, respectively.
Micheli and colleagues, Methods
The headline above stays pinned to the full arc while you change the selection.
See this selection’s residuals ↑
Accelerations in × 10⁻⁶ m/s². “Printed” is the Methods’ significance for that subset. “If the push were there” plants the claimed 4.92 into that subset’s own positions, after moving its real residuals onto a gravity-only path, and refits: it is the significance that subset would be expected to show if the claimed push acted at its claimed size throughout, and it equals 4.92 divided by the subset’s formal error. Select a row to refit it live, with the printed team table and the 1/r² law.
| Subset (select to refit) | Positions | Printed | Fitted A₁ ± σ | This engine | If the push were there | Increment recovered | Capacity |
|---|
The two half-arc tests are the ones to look at. Before 15 November the paper printed 2.8σ and this engine finds 2.73σ; after it, 2.5σ against 2.52σ. Plant the claimed push into those same halves and the refits return 3.07σ and 3.37σ. That is the significance each half would be expected to show with the push present at full size: 4.92 divided by each half’s formal error, 1.604 and 1.462, because the moved residuals carry no push of their own. The printed half-arc results are about what a steady push of the claimed size would produce there. They agree with the claim, and on their own they were unlikely to confirm it: if A₁/σ scatters by 1 around that expectation, as it should when the adopted errors are right, a half carrying the full push reaches this page’s 5σ bar only 2.7% and 5.1% of the time.
Three of the claimants’ subsets have no December or January Hubble position. The two with small errors, ground telescopes only and up to 1 December, sit 2.1 and 2.0 of their own standard errors below the full-arc value; the third, before 15 November, sits 0.3 of its error below it, with an error 3 times larger, too uncertain to say. Their positions overlap the full arc heavily, and the paper’s Table 1 allows a gentler fade than 1/r²; this page does not decide what, if anything, that pattern means.
This page calls a subset capable when the planted fit reaches 5σ and both recovered increments agree with the plant to within 5%. Otherwise it says INCONCLUSIVE for that subset. This is the page’s rule, not a threshold the claimants used: 5σ is the conventional bar for claiming a discovery, and the claimants called 2.5σ a detection. On a 3σ bar both halves would clear on expectation, by 0.07 and 0.37, so the half-arc verdict depends on the bar. On every subset computed here both recovered increments lie between 4.9200 and 4.9201, so the 5% clause never decides a subset; it is there to catch a plant that did nothing, pointed the wrong way or used the wrong unit.
Confidently-determining A₁ in ‘Oumuamua’s trajectory seems to require an arc of around one month.
Seligman and colleagues, Section 5.2
Seligman and colleagues (a later paper including original claimant Karen Meech) wrote that sentence after their own subset fits around the Spitzer observation. On this engine the month before 15 November would be expected to reach 3.07σ with the push there at full strength, short of this page’s 5σ bar; the arc from 25 October on would be expected to reach 16.19σ, well past it.
we searched the Artificial Wasteland corpus, web search for interactive orbit fits and injection recovery, arXiv reanalyses, and Federico Spada’s public orbit_finder repository on 2026-09-22 and did not find a public reader-operated page combining a claimant-astrometry orbit refit, recovery of an added acceleration on those observations, and a comparison of power across shortened observation arcs.
THE CONTROL ON THE CONTROL
These observations already contain the reported acceleration, so a convincing check must find the increment you add. The page propagates two trajectories from the same starting state, one with the extra push, adds their angular difference to a copy of the real measurements, and refits both models from scratch.
The second pair moves the measured residuals onto a gravity-only trajectory, then plants the claimed push there. That baseline is a constructed control built from real residuals, not new observations known to contain no force. Because the moved residuals are the push model’s own, they carry no push: the baseline fits to zero by construction, and the planted fit returns the claimed size with its expected significance, not a draw from noise. What the pair tests is the plumbing, since a plant that did nothing, pointed the wrong way or used the wrong unit fails it. The paired fits are correlated; their difference is not two independent measurements.
Grade A: physical injection into the control’s own measured positions. The estimator receives no injection flag. This checks sensitivity conditional on the force model and the adopted errors; it does not identify a mechanism or validate every calibration.
THE METHOD ON NOTHING
Can the procedure manufacture the headline from nothing? The Gaussian experiment puts paired errors, with the adopted covariance, around a gravity-only trajectory at the actual epochs and stations. The block experiment gives one random sign to all fitted residuals from each station and UTC night, then moves those blocks onto a gravity-only trajectory.
In the Gaussian batch the fitted A₁/σ scatters with a standard deviation of 1.18 across 24 skies, near 1, as it should be when the errors are drawn from the adopted covariance: the fit behaves linearly. This batch cannot say whether the adopted errors are themselves too small. The headline fit’s reduced χ² of 0.20 and the block batch’s 0.66 suggest they are, if anything, too large.
This trial uses the currently selected observations and error floor.
The block experiment preserves the shape of residuals within each observing block. It is a sensitivity check, not a complete model of systematic error. Neither finite batch measures the probability of a 30σ tail. Every seeded trial uses the same two orbit fits as the headline.
THE OBJECTION, WITH ITS REPLIES
The reported collapse of the scatter of nearly contemporaneous coordinate residuals upon inclusion of the non-gravitational term in the orbital fits is difficult to understand.
Katz, 2019
Katz’s abstract also argues that the implied gas-to-dust ratio would be at least 100 times that of known Solar System comets. That bears on the cause, which this page leaves open. The objection tested here is the one about the residuals.
Seligman and colleagues answered that the observatories carried very different errors. A smooth change in the orbit moves every position taken the same night by nearly the same angle, but divided by a 0.2″ error that angle is large and divided by a 3″ error it is small. The table below shows it on this engine’s own fits for the night Katz singled out.
Choose a display. The model-to-model shift is gravity-alone residual minus push residual, which is the change in predicted position. Beside it, the same shift from the authors’ own published residual pair for that row.
| Row / station | Reported error RA / Dec, ″ | Gravity alone RA / Dec | With the push RA / Dec | Shift, this engine | Shift, authors’ residuals |
|---|
Spada ran a test Katz had suggested: add noise to the six positions taken between 20:39 and 20:51 UTC on 19 October and refit both models. If the push were merely soaking up scatter, it would pull noisy points in too. Katz asked for noise “with dispersion three times the formal uncertainty”, and Spada added noise of “an amplitude equal to three times their formal uncertainties”; here the noise has a standard deviation of three times each position’s reported error. Spada obtained (4.90 ± 0.15) × 10⁻⁶ m/s² with his own implementation; the claimant-associated reanalysis reported 26σ, below the original 30σ. All are reanalyses of existing astrometry, not new observations.
Uses the current selection, which must contain the six positions from 19 October.
THE CHECK
The orbit fit will report its convergence and selection here.
The paper counts 177 ground and 30 Hubble positions, 207 in all. The workbook marks 209 of 216 rows accepted and repeats one measurement at worksheet rows 103 and 104. Keeping one copy leaves 208, the count Spada’s reanalysis of the same supplementary data also describes: 178 ground and 30 Hubble positions. This page excludes only the seven rejected rows and that repeated copy; it does not invent another exclusion to reach the paper’s count.
The paper’s Extended Data Table 1 lists the team’s own 53 ground positions “as used in our analysis”, and says the Pan-STARRS and OGS rows are manual re-measurements rather than the values at the Minor Planet Center. The workbook disagrees with the table beyond its printed rounding on 52 of those rows. Three Pan-STARRS positions from 18 and 19 October move by more than 0.2″, the largest by 0.49″, and 11 rows carry different errors. This page transcribed the table twice by machine at two resolutions and once by eye, and uses it by default.
| Row | Station | Printed minus workbook, RA / Dec, ″ | Printed error, ″ | Workbook error, ″ |
|---|
The workbook’s published residuals tell the same story from the other side. Subtract them from this engine’s workbook-replay residuals, station by station: at 16 of 28 stations the difference is below 0.005″, and at 12 there is an offset shared by that station’s positions, up to 0.38″ (station 291). The Methods say positions not tied to the Gaia catalogue were corrected for star-catalogue errors of up to 0.4″. Those offsets have that size and shape, and the released positions do not carry them.
| Station | Positions | Mean offset RA / Dec, ″ | RMS RA / Dec, ″ |
|---|
Shifting each position by its own difference from the authors’ gravity-only residuals, then refitting, reproduces every published push-model residual to within 0.0022″ and moves A₁ by +0.0026. Those upstream corrections matter for single points, not for the headline. That replay borrows the authors’ fitted residuals, so it is an explanation, never an input.
Summing the workbook’s published residuals over their errors gives 1281.87 for gravity alone and 104.86 with the push, not Table 1’s 1031 and 81; Spada’s footnote 4 had noted the gravity-only mismatch, which he called a “small inconsistency”. With this page’s timing covariance the same residuals give 1060.00 and 90.12. The positions with the printed team table reproduce all five Table 1 values to within 2.03, which is consistent with the residual file having been computed against the workbook’s positions rather than the printed ones.
The Methods give dates, not times. This page reads every date as 00:00 UTC. Read as the end of that day instead, the test after 25 October gives 14.70σ, after 15 November 1.73σ and before 15 November 4.23σ, against the printed 17, 2.5 and 2.8. Taking a fit to mean agreement within half the last printed digit plus 0.1σ, the rule the verifier applies to every robustness test, the midnight reading fits all three and the end-of-day reading fits none.
The spec for this page fixed an acceptance envelope before this page’s engine ran any fit: A₁ within 0.05 × 10⁻⁶ m/s² of the published value, its formal error within 0.02, significance from 29σ to 34σ. Both input options pass it. Only the input with the printed team table also matches the printed digits, and it still counts one more position than the paper.
The forward model includes the Sun, eight planets, the Moon, Pluto, sixteen large asteroids and the solar relativistic correction. Locally frozen Horizons vectors supply the perturbing bodies and the ground observers. Hubble’s geocentric positions are transcribed from Extended Data Table 2. Light travel time includes the Sun’s barycentric displacement.
The fit uses ICRF directions, TDB dynamics, astronomical units and days internally; the push is converted from m/s². Six initial state components are free in both models, and the push model adds A₁, which may take either sign. Covariance comes from the full scaled design matrix and is never reduced when reduced χ² is below one.
A one-second timing allowance is projected into both sky coordinates, with their covariance, using sky rates frozen at the common starting trajectory so both models use identical weights. Hubble’s velocity for that projection is estimated from adjacent published positions with a circular-chord approximation. Its measured position is never approximated by Earth’s centre.
| Changed numerical or physical setting | Change in A₁ | Change in σ(A₁) |
|---|
Units × 10⁻⁶ m/s². Timing omitted, asteroids omitted and heliocentric light time are sensitivity diagnostics, never silently used for the headline.
Unresolved: which one extra position the paper did not count; which of the two claimant records is the true input for the 53 team rows (this page follows the paper’s own statement); the catalogue corrections, which the released positions do not carry and this page does not apply. The formal error is conditional on these choices, not a measure of every possible systematic error.
REFUSED: epochs outside the observed arc or the frozen geometry, unknown observers, invalid coordinates or uncertainties, unlabelled time scales, distance laws outside k = 0 to 3, singular fits and injections without a physical unit. The instrument cannot predict the object’s present position, find an origin star, establish the push at every instant, select a unique distance law or identify the cause.
THE RECORD’S VERDICT
VINDICATED, as of 2026-09-22. The detected non-gravitational acceleration over the observed arc is the vindicated claim. The cause remains open.
The original model comparison supplies the detection. Later reanalyses with separate software support it: one by Seligman and colleagues, whose authors include original claimant Karen Meech, and one by Spada, still a preprint. A 2023 review by Jewitt and Seligman, neither an author of the 2018 paper, treats the acceleration as established and its cause as open: “A central puzzle is that 1I/‘Oumuamua showed no visible coma in deep composite images, and yet had a non-gravitational acceleration of 30σ significance.” A 2026 paper about a different object, whose authors include five of the original claimants, writes that “1I/‘Oumuamua was clearly affected by non-gravitational accelerations”, and adds no new observation of this visitor. This page reproduces the published fit and its robustness tests from the measured positions: a check of the analysis, not new evidence about the object.
Original detection · Independent software · Review · Current context
A reproducible re-reduction of the original images, or a documented correction to the positions, timing, observer geometry or error model, that removes the acceleration across the full arc and also accounts for the independent reanalyses, would change this verdict. A better orbit fit alone would not establish any particular cause.
Measurements and derived geometry are supplied as independently structured numerical factual extracts. The Nature publication and source workbook remain all rights reserved; no open licence is claimed for them. The original PDF, workbook presentation and figures are linked, not redistributed. NASA/JPL geometry is credited separately in the notice.
Source workbook: the paper’s supplementary residual workbook, sheets ab and cd. The publisher’s article page labels this file “Source Data ED Figure 1”; its contents are the positions and residuals plotted in the paper’s Figure 2, and the file that page labels for Figure 2 holds a list of comets’ A₁ values instead. The article page. Paper with the Extended Data tables. Every figure on this page is drawn from the numerical extract.