arxiv: 2604.24566 · v1 · submitted 2026-04-27 · 🌌 astro-ph.EP

Recognition: unknown

The spin state of asteroid Apophis and a prediction of its change during the 2029 close encounter with Earth

J. Durech , D. Vokrouhlicky , P. Pravec , K. Hornoch , P. Kusnirak , P. Fatka , H. Kucakova , J. Hanus

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M. Ferrais E. Jehin Z. Benkhaldoun O. Humes D. Polishook M. Marsset G. McMillan E. Podlewska-Gaca M. Colazo A. Marciniak K. Kaminski M. K. Kaminska S. Zola M. Drozdz W. Ogloza M. Zejmo B. Carry D. E. Reichart

Authors on Pith no claims yet

Pith reviewed 2026-05-08 01:14 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords Apophisasteroid spin statelight curve inversiontumbling asteroid2029 Earth encounterrotational dynamicsgravitational torque

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The pith

All acceptable models of Apophis's spin from past light curves converge on the same pre-2029 orientation and preserve the short-axis mode after the flyby.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reconstructs Apophis's tumbling spin state by inverting light curves from two apparitions separated by eight years. Multiple combinations of precession and rotation periods fit the data equally well, yet every solution places the asteroid in essentially the same orientation by early 2029. When this orientation is fed into a numerical simulation that includes the gravitational torque from Earth during the April 2029 encounter, the short-axis spin mode survives with high probability even though the exact post-encounter periods become far less certain. The result matters because Apophis will pass only 38,000 km from Earth, and its spin state will influence both future observations and any potential deflection planning.

Core claim

Light-curve inversion for tumbling asteroids applied to data from 2012-2013 and 2020-2021 yields several acceptable period solutions, all of which produce nearly identical pre-encounter orientation in early 2029. Numerical modeling of the spin evolution under Earth's gravitational torque during the close approach then shows that the short-axis mode is preserved with high likelihood, although post-encounter uncertainty grows substantially.

What carries the argument

Light-curve inversion method for tumbling asteroids that fits precession and rotation periods to produce a convex shape model, which is then used as the initial condition for numerical integration of rotational dynamics under planetary torque.

If this is right

Additional observations in 2027 and 2028 will resolve the ambiguity among the current period solutions.
The short-axis spin mode will be preserved with high likelihood after the 2029 encounter.
Post-encounter uncertainty in the spin state will increase substantially because of the close approach.
All currently acceptable models share approximately the same pre-encounter orientation in early 2029.
The stable mode prediction can be used for impact-risk assessments and mission planning.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same inversion-plus-torque approach could be tested on other tumbling near-Earth asteroids ahead of their own planetary encounters.
If post-2029 photometry matches the predicted mode, it would support the assumption that gravitational torque dominates the spin change.
Future radar or spacecraft data after 2029 could provide an independent check on the post-encounter uncertainty growth.

Load-bearing premise

The light-curve inversion from the two apparitions correctly maps the fitted periods onto a reliable pre-encounter orientation, and non-gravitational forces do not significantly alter the spin during the flyby.

What would settle it

New photometric observations in 2027 or 2028 that yield a pre-encounter orientation inconsistent with all current acceptable models would demonstrate that the period solutions do not reliably predict the 2029 state.

Figures

Figures reproduced from arXiv: 2604.24566 by A. Marciniak, B. Carry, D. E. Reichart, D. Polishook, D. Vokrouhlicky, E. Jehin, E. Podlewska-Gaca, G. McMillan, H. Kucakova, J. Durech, J. Hanus, K. Hornoch, K. Kaminski, M. Colazo, M. Drozdz, M. Ferrais, M. K. Kaminska, M. Marsset, M. Zejmo, O. Humes, P. Fatka, P. Kusnirak, P. Pravec, S. Zola, W. Ogloza, Z. Benkhaldoun.

**Figure 1.** Figure 1: Period scan. The plots show the residuals (blue points) of the fit for different values of the precession period Pϕ (left) and the rotation period Pψ (right). The dotted vertical lines indicate the positions of the eight best solutions, and the red crosses represent RMS residuals for the high-resolution models. The distances between local minima ∆Pϕ and ∆Pψ are denoted view at source ↗

**Figure 2.** Figure 2: Period scan. The plot shows the same data as in view at source ↗

**Figure 3.** Figure 3: Evolution of Euler angles for models A (blue), B (red), and C (green). The plots show the evolution of Euler angles ϕ, θ, and ψ within a month in different years. All three angles are similar for all three models in the years 2013, 2021, and 2029 because they are separated by 8 years. The Euler angles, and thus the orientation of the models, differ for epochs between these years (e.g., March 2027) view at source ↗

**Figure 4.** Figure 4: Best models A (top) and A* (bottom) with parameters listed in view at source ↗

**Figure 5.** Figure 5: Parameters of the Apophis close encounter with Earth on April 13, 2029. The top panel shows the geocentric (solid line) and selenocentric (dashed line) distance, and the bottom panel shows the relative geocentric and selenocentric velocity. The origin of the abscissa is at the nominal Earth closest approach epoch 62239.90709 (MJD). The horizontal dashed line at the top panel indicates the closest approa… view at source ↗

**Figure 6.** Figure 6: Rotation Pψ and precession Pϕ periods of Apophis before and after the close encounter with Earth in April 2029 calculated from the purely gravitational model of the spin state change. Individual symbols come from 1000 nominal model simulations, with gravitational torques included, using statistically equivalent initial conditions on January 1, 2021. The three colors identify solutions starting from the thr… view at source ↗

**Figure 7.** Figure 7: Dimensionless parameter p = 2BE/L 2 of Apophis’s spin. Left panel: Pre-encounter values at the abscissa and the post-encounter values, calculated from the purely gravitational model of the spin state change, at the ordinate. As in the previous two figures, symbols come from 1000 nominal model simulations. Right panel: Distribution of the p-values, pre-encounter in green, blue, and red for models C, A, and… view at source ↗

**Figure 9.** Figure 9: Same as in view at source ↗

**Figure 10.** Figure 10: Same as in view at source ↗

read the original abstract

On April 13, 2029, the asteroid Apophis will pass near Earth at a geocentric distance of about 38,000 km. Numerical models have suggested that the post-encounter spin state will critically depend on the orientation of Apophis during the flyby. We aim to determine the spin state of Apophis from its photometric observations collected during two apparitions in 2012-2013 and 2020-2021. This will enable us to accurately predict the pre-encounter rotation state and, by accounting for Earth's gravitational torque, predict a range of possible post-encounter states. We used the light curve inversion method for tumbling asteroids to reconstruct the spin state of Apophis and its convex shape model. The result is adopted as the initial condition of a numerical model describing Apophis's future rotation state. The data from the two apparitions are insufficient to determine Apophis's rotation and precession periods uniquely. The formally best-fit solution is 27.374 +/- 0.001 h for the precession period and 262.2 +/- 0.1 h for the rotation period, but at least two other combinations of the periods provide a similarly good fit to the available data. All the currently acceptable models result in approximately the same pre-encounter orientation of Apophis in early 2029. This is because the accurate photometric data were collected during two apparitions separated by 8 years, which is the same interval as from 2021 to 2029. Although the close encounter with Earth in April 2029 hugely increases the post-encounter uncertainty of Apophis's spin state, the short-axis spin mode will be preserved with a high likelihood. Additional observations taken in 2027 and 2028 will break the ambiguity in Apophis's pre-encounter spin solution and allow us to get a more accurate post-encounter spin state prediction

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Multiple period solutions for Apophis all give similar 2029 pre-encounter orientations, supporting a bounded post-flyby prediction, but the spread across solutions is not quantified.

read the letter

Apophis has several spin solutions that all point to roughly the same body orientation before the 2029 Earth flyby. This lets the authors integrate the gravitational torque and conclude that the short-axis mode is likely preserved afterward, even as the detailed state becomes much less certain after the encounter. The paper combines photometry from the 2012-2013 and 2020-2021 apparitions, runs light-curve inversion for a tumbling body, and uses the results as initial conditions for the forward model. What it does well is stay transparent about the non-unique periods—the best fit is given as 27.374 h precession and 262.2 h rotation, with at least two other combinations fitting nearly as well—and it correctly notes that the eight-year gap between the two data sets matches the interval to 2029, which helps keep the extrapolated orientations aligned. The methods are standard and the acknowledgment of growing post-encounter uncertainty is straightforward. The soft spot is the missing quantification of how much the 2029 orientations actually differ across the acceptable solutions. The stated period uncertainties are small, but over thousands of cycles they can produce phase shifts of tens of degrees, and the paper supplies no numbers on the resulting dispersion or on what the torque integration produces at the edges of that range. The assumption that non-gravitational forces can be ignored during the flyby is also stated without further checks. This work is aimed at people who need a practical forecast for Apophis itself or who are planning observations in 2027-2028 to resolve the remaining ambiguity. Asteroid dynamicists and planetary-defense researchers will find the concrete prediction useful even with the caveats. The analysis shows clear thinking and honest engagement with the data limits, so it deserves peer review. Referees can ask for the error propagation on the pre-encounter states while the core result remains intact.

Referee Report

2 major / 2 minor

Summary. The paper applies light-curve inversion to photometric data from Apophis's 2012-2013 and 2020-2021 apparitions to reconstruct its tumbling spin state and convex shape. While the precession period (best-fit 27.374 ± 0.001 h) and rotation period (262.2 ± 0.1 h) are not uniquely determined, the authors show that all acceptable period combinations produce approximately the same body orientation in early 2029 because the 8-year observational baseline matches the interval to the encounter. They then integrate the gravitational torque from Earth during the 38,000 km flyby and conclude that the short-axis spin mode is preserved with high likelihood, although post-encounter uncertainty grows substantially. Additional 2027-2028 observations are recommended to resolve the ambiguity.

Significance. If the central claim is substantiated, the work supplies a concrete, observationally anchored prediction for Apophis's spin evolution across the 2029 encounter. This is directly relevant to planning for the OSIRIS-APEX mission and to any ground-based or spacecraft observations timed around closest approach. The demonstration that multiple period solutions converge on the same pre-encounter state is a useful methodological point for tumbling-asteroid studies, and the use of standard torque integration provides a clear, falsifiable forecast.

major comments (2)

[results on acceptable period solutions] The central claim that 'all currently acceptable models result in approximately the same pre-encounter orientation' (abstract and results section) is load-bearing for the post-encounter prediction, yet the manuscript provides no quantitative measure of the dispersion in 2029 orientations across the family of acceptable solutions. Given the stated period uncertainties, an explicit propagation of phase errors over the ~8-year interval (or a table/figure showing the range of Euler angles at the 2029 epoch) is required to confirm that the torque integration always yields short-axis-mode preservation at the edges of the solution space.
[numerical integration of future rotation state] The post-encounter analysis assumes that only gravitational torque from Earth acts during the flyby and that non-gravitational forces (outgassing, YORP, etc.) are negligible. While this is stated, no quantitative bound is placed on the possible contribution of such effects over the encounter timescale, which directly affects the claimed 'high likelihood' of short-axis-mode preservation.

minor comments (2)

[abstract and results] The abstract states that 'at least two other combinations of the periods provide a similarly good fit' but does not list their values or goodness-of-fit metrics; these should be tabulated in the main text for reproducibility.
[figures] Figure captions and axis labels for the orientation plots should explicitly note the time epoch (e.g., 'early 2029') and the coordinate frame used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of the manuscript's relevance to OSIRIS-APEX planning and for the constructive comments. We agree that the two major points require strengthening and will revise the manuscript to address them directly.

read point-by-point responses

Referee: The central claim that 'all currently acceptable models result in approximately the same pre-encounter orientation' (abstract and results section) is load-bearing for the post-encounter prediction, yet the manuscript provides no quantitative measure of the dispersion in 2029 orientations across the family of acceptable solutions. Given the stated period uncertainties, an explicit propagation of phase errors over the ~8-year interval (or a table/figure showing the range of Euler angles at the 2029 epoch) is required to confirm that the torque integration always yields short-axis-mode preservation at the edges of the solution space.

Authors: We agree that an explicit quantitative measure of dispersion is needed to make the claim robust. In the revised manuscript we will add a new figure (and accompanying text) that propagates the stated period uncertainties forward to the 2029 epoch for every acceptable period combination. The figure will display the resulting range of Euler angles at the start of the encounter, demonstrating that the orientations remain clustered within a few degrees and that short-axis-mode preservation holds at the boundaries of the solution space. revision: yes
Referee: The post-encounter analysis assumes that only gravitational torque from Earth acts during the flyby and that non-gravitational forces (outgassing, YORP, etc.) are negligible. While this is stated, no quantitative bound is placed on the possible contribution of such effects over the encounter timescale, which directly affects the claimed 'high likelihood' of short-axis-mode preservation.

Authors: The referee correctly notes the absence of a quantitative bound. The encounter duration is only a few hours, during which YORP-induced spin changes for an Apophis-sized body are expected to be <10^{-5} deg and outgassing (if present) would produce negligible torque compared with Earth's gravitational effect. We will revise the text to include this order-of-magnitude estimate and a short paragraph justifying why non-gravitational contributions can be neglected on this timescale, thereby supporting the stated high likelihood of short-axis-mode preservation. revision: yes

Circularity Check

0 steps flagged

No circularity; spin-state fitting and torque integration remain independent

full rationale

The derivation begins with light-curve inversion applied to photometric data from two apparitions (2012-2013 and 2020-2021) to obtain candidate period pairs and a convex shape. These fitted parameters are then used as initial conditions for a separate numerical integration of Earth's gravitational torque during the 2029 encounter. The statement that all acceptable models produce approximately the same pre-encounter orientation in early 2029 is reported as a direct computational outcome of propagating the fitted periods over the matching 8-year baseline; it is not imposed by definition or by renaming the input data. Post-encounter mode preservation is likewise an output of the independent torque physics applied to those orientations. No self-citations are invoked as load-bearing uniqueness theorems, no fitted quantities are relabeled as predictions, and no ansatz is smuggled via prior work. The chain is therefore self-contained against external photometric data and standard rigid-body dynamics.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on fitted periods from photometric data and standard domain assumptions in asteroid photometry and gravitational dynamics; no new entities are introduced.

free parameters (3)

precession period = 27.374 h
Best-fit value of 27.374 h obtained by light-curve inversion to match observed brightness variations.
rotation period = 262.2 h
Best-fit value of 262.2 h obtained by light-curve inversion to match observed brightness variations.
convex shape model parameters
Parameters of the convex shape model adjusted during the inversion process to reproduce the light curves.

axioms (2)

domain assumption Light-curve inversion for tumbling asteroids can reconstruct spin state and convex shape from photometric data.
Invoked as the method to obtain the spin solutions from the 2012-2013 and 2020-2021 observations.
domain assumption Earth's gravitational torque during the flyby can be modeled numerically to predict spin-state evolution.
Basis for the post-encounter simulation that shows preservation of the short-axis mode.

pith-pipeline@v0.9.0 · 5808 in / 1642 out tokens · 74172 ms · 2026-05-08T01:14:58.852660+00:00 · methodology

discussion (0)

Reference graph

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