The spin states of meter-sized asteroids should evolve rapidly due to the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. While these asteroids are very challenging to observe, artificial geosynchronous (GEO) satellites are convenient analogues given that they are driven primarily by solar torques, evolve rapidly, and are easy to observe. These artificial objects could provide insight about the evolution of their natural counterparts. Recent studies of YORP for defunct GEO satellites with full and tumbling-averaged models have uncovered rich dynamical structure with tumbling cycles, angular momentum sun-tracking, and tumbling resonances. Applying the tumbling-averaged YORP models to meter-sized pseudo asteroids, we find that the solar torque structure yields sun-tracking precession in many cases, particularly for asteroids with at least some elongation. Precession about the sun line results in the long-term obliquity averaging to roughly 90 degrees. As a result, the sun-tracking behavior could potentially shut off Yarkovsky drift for these asteroids and thereby limit their mobility out of the main asteroid belt. For some asteroid shapes, tumbling cycles with alternating spin up and spin down are also observed. These tumbling cycles offer a possible avenue to prevent spin-driven disruption of meteoroids.

We develop a dynamics-based, "shape model free" spin state estimation and prediction framework for uncontrolled space objects. The framework accounts for solar radiation and terrestrial gravity gradient torques, most relevant in medium earth orbit (MEO), geosynchronous earth orbit (GEO), and beyond. Additional averaged perturbations (e.g. eddy current torques) can be incorporated. This framework averages a uniformly rotating object's attitude dynamics over its intrinsic rotation and earth orbit, enabling fast, accurate spin state propagation months or years into the future. By averaging, we distill solar radiation torques to constant curves that are readily modeled and estimated as Fourier series. Requiring no object a priori information and using just light curve-derived synodic spin rate measurements (although other measurement types can be readily incorporated), we estimate an object's inertial spin rate and spin axis as well as its Fourier solar torque and gravity gradient coefficients in a least squares batch filter. Inertial spin axis information is provided by: 1) differences between the inertial and observed (i.e. synodic) spin rate due to time-varying observation geometry, and 2) torque-driven dynamical coupling between the spin rate and spin axis which ties together long-term observations, strongly constraining viable states and breaking solution ambiguities. In GEO simulations with no a priori satellite information, we demonstrate convergence to the true state within one year using sparse synodic spin rate measurements. We apply the framework to real light curves of the defunct GEO satellite Telstar 401 and compare our spin pole estimate to independent Deep Space Network radar solutions, showing clear consistency. This light-weight framework can be readily applied to existing light curve databases, some of which span many years for specific objects. State estimates can be used for long-term spin state prediction and updated through catalog maintenance observations. (c) 2026 The Author(s). Published by Elsevier B.V. on behalf of COSPAR. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

Dimorphos, the secondary member of the binary asteroid (65803) Didymos, was impacted by NASA's Double Asteroid Redirection Test (DART) spacecraft on September 26, 2022. Images taken with the DART's DRACO camera before the impact showed that Dimorphos's original shape was nearly rotationally symmetric, close to an oblate spheroid, and it was probably in a synchronous spin state. As such, it did not show a detectable secondary brightness variation before the DART impact in the integral light from the binary system. However, numerical impact models predicted that the DART impact could change both its shape and spin state, signatures of which could be detected with high-quality lightcurve observations. We have analyzed the best photometric observations of the Didymos-Dimorphos system that were taken during its favorable observing and geometric conditions in December 2022 and January 2023 and detected a significant secondary rotational lightcurve with amplitudes (in the total light from the primary and secondary) ranging from 0.008 to 0.031 mag at 7 distinct epochs. We estimate that the apparent cross section of Dimorphos varied with a relative amplitude (normalized to the mean cross section) between +/- 0.07 and +/- 0.24 over its rotation on the individual epochs. The observed changes of Dimorphos's apparent cross-section amplitude over its rotation suggest an attitude instability, showing variations of Dimorphos's obliquity. The lightcurve minima are approximately aligned, to within 30 degrees in mean anomaly, with the mutual events between the components of the binary system. The observations suggest that Dimorphos is in an excited, non-principal axis (NPA) spin state where, on average, it is tidally locked. By comparing the observations to high-fidelity simulations, we find that a moderate amount of NPA rotation in Dimorphos after the DART impact is required to reproduce the observed lightcurves. This NPA rotation is limited to around on-average synchronous or anti-synchronous configurations of Dimorphos. We also find Dimorphos elongations with the equatorial axis ratios a/b between 1.1 and 1.4 are generally consistent with the observed mean apsidal precession rate. We predict that when the ESA's Hera spacecraft arrives to the Didymos-Dimorphos system in late 2026, it will still find Dimorphos in the NPA spin state, which places additional constraints on the operations of the spacecraft to achieve its objectives.

Photon counters and exposure-based cameras cannot simultaneously provide exquisite temporal and spatial resolution in one sensor. Event (i.e. neuromorphic) cameras provide both. Their potential space domain awareness (SDA) applications include short-arc orbit determination and high frequency light curve analysis. Until now, no dynamic event camera simulations for non-resolved objects have been conducted. In this work, we develop numerical and analytical event camera models to better understand potential applicability to SDA efforts. We approximate the event pixel dynamics as a first order differential equation driven by logarithmic photon flux. Photon arrivals are modeled as a stochastic Poisson process. We consider static point sources with constant and time-varying brightness as well as moving sources. We then compare simulated and real event data, showing clear consistencies. For moving sources, we find that the event structure is sensitive to near-instantaneous rates. This sensitivity could provide significant astrometric advancements. We also explore event camera simulations for sinusoidal mean brightness variations, illustrating the complex dependence of frequency estimates on brightness amplitude, oscillation frequency, and event circuit parameters. The presented models improve our fundamental understanding of event data for non-resolved objects. Also, the analytical moving point source model facilitates event-based observability studies and matched filter template generation for object detection, tracking, and characterization. The sensitivity to target parameters observed for the simulated and real event data demonstrates the great potential of event cameras for high spatio-temporal resolution astrometry and photometry.

We explore the effects of the 2029 Earth encounter on asteroid (99942) Apophis' non-principal axis spin state, leveraging refined orbit, spin state, and inertia information provided by more recent optical and radar observations. Propagating the asteroids' coupled orbit and rigid body attitude dynamics through the flyby, we present the range of possible post-flyby spin states. These spin state distributions will be valuable for planning Apophis observation campaigns and spacecraft missions, most notably OSIRIS-APEX. The simulations indicate that gravitationally induced changes to the asteroid's tumbling periods and rotational angular momentum direction (pole) will likely be significant and measurable. For the current spin state and inertia estimates and their uncertainties, Apophis is likely to remain in a short axis mode (SAM) tumbling state but its effective spin rate could halve or double. Its pole is likely to shift by 10 degrees or more and increase in longitude while moving closer to the ecliptic plane. These spin state changes are very sensitive to the asteroid's close approach attitude and mass distribution. With ground-based tracking of the asteroid's spin state through the encounter, this sensitivity will help refine mass distribution knowledge. We also discuss the implications of this abrupt spin state alteration for Apophis' Yarkovsky acceleration and geophysical properties, identifying possible pathways for surface and internal changes, most notably if Apophis is a contact binary. Comparison of the pre and post-flyby inertia estimates obtained from the ground-based observations will help assess the extent of possible geophysical changes.

Understanding and predicting the long-term spin state evolution of defunct satellites and rocket bodies is important for solar radiation pressure modeling, space domain awareness, and active debris removal (ADR). Dynamical modeling and observations indicate that defunct geosynchronous satellite spin states are primarily driven by solar radiation torques via the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. In our two recent papers, we uncovered dynamically rich YORP-driven behavior including cycling between uniform rotation and non-principal axis tumbling, angular momentum sun tracking, and tumbling period resonances. These papers only considered the YORP effect. However, tumbling satellites are also subject to energy dissipation from residual fuel slosh and flexure. Gravitational torques and other environmental perturbations may affect long-term evolution as well. In this paper, the third in our series, we develop semi-analytical tumbling-averaged models for internal energy dissipation and gravity gradient torques and combine them with the earlier YORP models. Accounting for YORP and dissipation, we find asymptotically stable tumbling states with constant angular momentum and kinetic energy and a pole fixed in the rotating sun-satellite orbit frame. With gravity gradients, these asymptotic states become stable limit cycles with yearly periodicity. We discuss the implications of these findings for the space debris population, ADR, and satellite decommission procedures.

Understanding and predicting the evolving spin states of defunct geosynchronous (GEO) satellites and rocket bodies is important for space situational awareness, active debris removal, satellite servicing, and anomaly resolution. There is clear evidence that many defunct GEO satellite spin states are predominantly driven by the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect. The YORP effect is spin state evolution due to solar radiation and thermal re-emission torques. Observations are crucial to understand how YORP drives spin states and to validate dynamical models. Unfortunately, GEO satellites are non-resolved from ground-based telescopes and extracting spin states (spin periods, rotational angular momentum vector, instantaneous attitude) from ubiquitous photometric light curve data is challenging. Even for well-known objects, light curve inversion often yields several or more well-fitting spin state solutions within the measurement noise and modeling uncertainty (i.e. detailed satellite geometry, reflective properties, etc.). Also, there is strong evidence that the YORP effect drives satellites from uniform rotation to non-principal axis tumbling. Such tumbling states further complicate the light curve inversion process because the motion is driven by two independent periods rather than one. To aid complete spin state analysis, particularly for the tumbling case, Doppler radar observations collected at NASA Goldstone Deep Space Communications Complex are incorporated. Observing the well-documented retired GOES 8–12 weather satellites, the radar data yielded unambiguous spin period estimates for all targets and greatly narrowed pole solutions, independent of light curve data. Significant changes in spin rates and pole directions were observed over a two month span. These findings are consistent with YORP-driven evolution.

Estimating and predicting the spin states of defunct satellites and rocket bodies is important for space situational awareness, active debris removal, and satellite servicing. Observations show that the spin states of defunct geosynchronous (GEO) satellites are diverse and can change significantly over time. Spin state evolution for many defunct GEO satellites is primarily driven by solar radiation torques via the Yarkovsky-O’Keefe-RadzievskiiPaddack (YORP) effect. To better understand the YORP-driven evolution of these objects we obtain spin state estimates from a combination of Deep Space Network (DSN) Doppler radar echoes and optical light curves. The resolved nature of Doppler radar echoes allows for clear identification of satellite spin periods and can greatly constrain possible spin pole directions. Observations of the defunct GOES 8-12 GEO weather satellites demonstrate ongoing spin period evolution and pole motion consistent with YORP theory. Observations of two spent upper stage rocket bodies yield spin periods, center of mass offsets, and constraints on spin pole directions.

Spin state predictions for defunct satellites in geosynchronous earth orbit (GEO) are valuable for active debris removal and servicing missions as well as material shedding studies and attitude-dependent solar radiation pressure (SRP) modeling. Previous studies have shown that solar radiation torques can explain the observed spin state evolution of some GEO objects via the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. These studies have focused primarily on uniform rotation. Nevertheless, many objects are in non-principal axis rotation (i.e. tumbling). Recent exploration of the tumbling regime for the family of retired GOES 8-12 satellites has shown intriguing YORP-driven behavior including spin-orbit coupling, tumbling cycles, and tumbling period resonances. To better explore and understand the tumbling regime, we develop a semi-analytical tumbling-averaged rotational dynamics model. The derivation requires analytically averaging over the satellite's torque-free rotation, defined by Jacobi elliptic functions. Averaging is facilitated by a second order Fourier series approximation of the facet illumination function. The averaged model is found to capture and explain the general long-term behavior of the full dynamics while reducing computation time by roughly three orders of magnitude. This improved computation efficiency promises to enable rapid exploration of general long-term rotational dynamics for defunct satellites and rocket bodies.

The growing number of defunct satellites in geosynchronous earth orbit (GEO) motivates continued development of active debris removal (ADR) and satellite servicing missions. These missions will benefit greatly from detailed target spin state information and accurate future predictions. The spin rates of defunct GEO satellites are diverse with uniform rotators and non-principal axis tumblers. For some satellites, observations show that these spin rates can change significantly over time includ-ing transitions between uniform rotation and tumbling. Modeling and observations have shown that some defunct GEO satellite spin states are largely driven by solar torques via the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect. Recent studies of the tumbling YORP regime with full Euler dynamics models have uncovered dynamically rich behaviors that are consistent with satellite observations. Unfortunately, the full dynamics do not explain the fundamental mechanisms driving these behaviors. Furthermore, their computational overhead greatly hinders broad, long-term (i.e. multi-year) dynamical studies. To remedy these issues, we present tumbling averaged dynamics models that accurately capture and explain the behavior observed in the full dynamics while reducing computation times by up to three orders of magnitude. These averaged models promise to facil-itate broad studies of long-term rotational dynamics for defunct satellites and rocket bodies.

Observations indicate that the spin states of retired and otherwise defunct satellites are diverse and can change significantly over time. Understanding defunct satellite spin state evolution is important for solar radiation pressure modeling, active debris removal, satellite servicing, and space situational awareness. Research has shown that many defunct satellites in geosynchronous earth orbit (GEO) are primarily driven by solar radiation torques via the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. Recent exploration of YORP-driven nonprincipal axis tumbling has uncovered rich dynamic behavior, including tumbling cycles, spin-orbit coupling, and tumbling period resonances. Radar and optical observations of the defunct Geostationary Operational Environmental Satellite (GOES) 8 strongly suggest that it has been captured in a tumbling resonance at least once since 2018. Motivated by these findings, we develop a numerical resonance-averaged dynamic model to understand YORP-driven resonance capture, building on our earlier nonresonant averaging framework. This resonance-averaged model illuminates resonance capture mechanisms. Also, by averaging over the satellite's rotation, this model is roughly 20 times faster to propagate than the full (Euler) dynamics. Overall, this allows for rapid, broad exploration to determine resonance capture durations, spin states changes, and the influence of initial spin rate and resonance order on resonance strength. This resonance-averaged model can be easily applied to other environmental perturbations.

On February 15, 2013 asteroid (367943) Duende, provisionally named 2012 DA14, experienced an extremely close earth encounter, passing within 27,700 km altitude. An observation campaign was made possible by one year's notice of the flyby. This campaign, discussed in detail in the companion paper by Moskovitz et al. (2019), yielded visible-wavelength photometry before and after closest approach. Post-flyby Goldstone Doppler-delay radar data were also obtained. These data indicated a roughly 40 m x 20 m object in non-principal axis rotation. Leveraging light curve frequency analysis from the Moskovitz et al. companion paper, dynamical and inertia constraints from the rough radar-derived elongations, and simulated photometry, only two post-flyby states were deemed viable. These were a long axis mode (LAM) with long axis convention periods P-(phi) over bar = 6.36 h and P-psi = 8.73 h and a short axis mode (SAM) with P-(phi) over bar = 8.71 h and P-psi = 23.7 h (each with nominal long-intermediate and long-short ellipsoid axis ratios of 1.7:1 and 2.3:1 respectively). The SAM solution was more consistent with the post-flyby photometry and radar data. Nevertheless, there were differences between the amplitude and phase of the post-flyby and best-fit simulated SAM light curves at some epochs. These discrepancies may be due to a non-ellipsoidal shape, non-uniform albedo, and/or incorrect spin state solution (attitude, inertias, tumbling periods, or rotation mode). Analysis of the sparse pre-flyby photometry by Moskovitz et al. yielded poor Fourier series solutions for all principal axis states and different peaks in the pre and post-flyby WindowCLEAN power spectra. This suggests the asteroid was tumbling before the encounter and that its spin state changed. Propagating the best-fitting LAM and SAM solutions backwards through the flyby with terrestrial tidal torques resulted in significant dispersion of the rotation states. The pre-flyby SAM states coincided with the notable Moskovitz et al. Fourier solution P-1 = 8.37 h and P-2 = 24.2 h. Overall, we propose Duende was tumbling before the 2013 flyby and that its spin state may have changed during the flyby. Furthermore, our analysis suggests Duende is currently in SAM with P-(phi) over bar = 8.71 h and P-psi= 23.7 h with pole J2000 ecliptic longitude and obliquity of roughly 70 degrees and 95 degrees or 245 degrees and 90 degrees respectively. The spin state characterization approach outlined in this paper could be used for future analyses with inertia, dynamical, and observational constraints.

Many defunct satellites in geosynchronous earth orbit (GEO) spin rapidly or have highly evolving spin states, with some transitioning between uniform and non-principal axis rotation (tumbling). It is hypothesized that the observed evolution of some defunct GEO satellites is caused by the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect and internal energy dissipation. YORP torques are generated by the absorption, reflection, and thermal re-emission of solar radiation and are known to cause secular changes in asteroid spin rates and obliquities. The defunct GOES 8 satellite is particularly notable. This satellite's uniform spin rate rapidly decreased in 2014 and it began tumbling. In this paper, newly analyzed light curve observations of the five nearly identical defunct GOES 8-12 satellites obtained between 2014 and 2018 are presented. The observations show large diversity in evolutionary time histories, with several satellites in consistent slow tumbling, GOES 10 in fast uniform rotation, and GOES 8 transitioning between both. To better understand this diversity, YORP dynamical models are investigated. They reveal that YORP driven spin state evolution is strongly dictated by end of life appendage orientations, which differ among the five satellites. The known end of life configurations are consistent with the observed evolution of GOES 8 and GOES 10. This provides a plausible explanation for the observed spin state diversity. Implications of the observed and simulated evolution for GEO debris mitigation are discussed.

— The growing inactive satellite population near geosynchronous Earth orbit (GEO) motivates improved understanding of these satellites’ dynamical evolution. Proposed active debris removal and servicing missions will require accurate spin state knowledge and predictions to capture and de-spin these large, inactive satellites. Spin state estimation from ubiquitous non-resolved ground-based optical measurements is very challenging due to complex satellite geometry and reflections. In this paper, we investigate how spin state estimates can be achieved through radar observations of inactive GEO satellites by the Deep Space Network (DSN). Leveraging time-varying viewing geometry due to Earth’s rotation and limited satellite geometry knowledge, we find that we can greatly constrain a satellite’s inertial spin pole. Analysis of 2017 Doppler echoes for the Echostar 2 satellite yielded pole solutions consistent with earlier optical studies. In addition, we have developed a radar observation model and unscented batch filter for radar-based spin state estimation.

On 15 February 2013, the asteroid 367943 Duende (2012 DA14) experienced a near-Earth encounter at an altitude of 27,700 km or 4.2 Earth radii. We present here the results of an extensive, multi-observatory campaign designed to probe for spectral and/or rotational changes to Duende due to gravitational interactions with the Earth during the flyby. Our spectral data reveal no changes within the systematic uncertainties of the data. Post-flyby lightcurve photometry places strong constraints on the rotation state of Duende, showing that it is in non-principal axis rotation with fundamental periods of P_1 = 8.71 +/- 0.03 and P_2 = 23.7 +/- 0.2 hours. Multiple lightcurve analysis techniques, coupled with theoretical considerations and delay-doppler radar imaging, allows us to assign these periods to specific rotational axes of the body. In particular we suggest that Duende is now in a non-principal, short axis mode rotation state with a precessional period equal to P_1 and oscillation about the symmetry axis at a rate equal to P_2. Temporal and signal-to-noise limitations inherent to the pre-flyby photometric dataset make it difficult to definitively diagnose whether these periods represent a change imparted due to gravitational torques during the flyby. However, based on multiple analysis techniques and a number of plausibility arguments, we suggest that Duende experienced a rotational change during the planetary encounter with an increase in its precessional rotation period. Our preferred interpretation of the available data is that the precession rate increased from 8.4 hours prior to the flyby to 8.7 hours afterwards. A companion paper by Benson et al. (2019) provides a more detailed dynamical analysis of this event and compares the data to synthetic lightcurves computed from a simple shape model of Duende. (abbreviated abstract)

Fourier transform analysis and Fourier series fitting methods for extracting the fundamental rotation periods of tumbling bodies from simulated light-curves are discussed and expanded. Methods leveraging the analytical dynamics and information about the body's moments of inertia, shape, and orientation are then explored for assigning extracted periods to the rotation and precession motion. These methods are then tested on simulated tumbling light-curves with all parameters known a priori for verification. While extraction was found to be challenging, dynamical relationships and body information helped significantly constrain the possible period solutions and in some cases the fundamental periods were conclusively determined. Applications for these methods include light-curve analysis for asteroids and defunct satellites with known or estimated moments of inertia and geometries. These methods provide initial rotation state estimates which can then be used in the full light-curve inversion process to obtain a complete rotation state solution.