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. 2025 Apr 7;15:10284. doi: 10.1038/s41598-025-94574-1

Diverse evolutionary pathways of spheroidal asteroids driven by rotation rate

Yuta Shimizu 1, Hideaki Miyamoto 1,✉, Patrick Michel 1,2
PMCID: PMC11977021  PMID: 40195388

Abstract

Asteroids preserve a continuous record of evolutionary processes since the early solar system. They can take various shapes that represent the cumulative results of their evolution. However, for those showing common characteristics, this does not mean that they followed the same evolutionary path. Here, we show that (101955) Bennu and (162173) Ryugu, two near-Earth asteroids with spheroidal shapes, have evolved through distinct pathways despite their similar shapes. Using high-resolution imagery from NASA’s OSIRIS-REx and JAXA’s Hayabusa2 spacecraft, we map ~ 200,000 boulders and find latitudinal particle size sorting on both bodies. This represents opposite directions of surface material movements driven by their different rotation periods (4.3 h for Bennu and 7.6 h for Ryugu): toward the equator on Bennu and toward the poles on Ryugu. Furthermore, the spatial distribution of large boulders on Bennu suggests a prior slower rotation (> 5 h), implying a past shape evolution similar to that of Ryugu. Our findings demonstrate that small variations in rotation period, on the scale of a few hours, can drastically change the gravitational field on an asteroid, sometimes even reversing local gravity direction. This drives complex and diverse evolutionary pathways of asteroids, resulting in top-shaped bodies and binary systems observed today.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-94574-1.

Subject terms: Asteroids, comets and Kuiper belt; Geomorphology; Asteroids, comets and Kuiper belt; Geomorphology

Introduction

Spheroidal asteroids are commonly observed in the solar system1–3. Among them, top-shaped asteroids, characterized by their oblate spheroidal shapes with pronounced equatorial ridges, have been intensively studied through in situ observations by several missions, including the NASA’s Origins, Spectral Interpretation, Resource Identification and Security-Regolith Explorer (OSIRIS-REx) mission4, the Double Asteroid Redirect (DART) mission5, and the JAXA’s Hayabusa2 mission6. These missions have revealed that these asteroids are covered by dry, unconsolidated granular materials composed of both fine particles and meter-sized rocks. They are revealed to be highly mobile, as demonstrated by the sampling7,8 and artificial impact events9,10. The nature of these surface materials has allowed for their frequent movements (mass movements) on these bodies8,11–13, leading to the formation and alteration of their global shapes. Understanding these mass movement patterns is therefore fundamental to deciphering the evolutionary history and mechanisms of shape deformation of small asteroids.

Mass movement on an asteroid follows local gravity, which is determined by the gradient of the geopotential distribution that is controlled by the gravitational and centrifugal forces. The rotation rate, which can easily change due to the thermally driven torque known as the YORP (Yarkovsky–O’Keefe–Radzievskii–Paddack) effect14, changes this geopotential distribution and thus controls the direction of mass movement. For top-shaped asteroids, there exists a critical rotation period below which the lowest geopotential region shifts from the middle latitudes to the equator (Fig. 1a and b). Asteroids rotating faster than this threshold experience mass movement toward the equator (equatorward), while slower rotators have mass movement toward the poles (poleward), especially in low latitudes. Minor changes in rotation rate can even reverse the direction of mass movement when crossing this critical threshold (Fig. 1a and b). As a result, despite their similar shapes, top-shaped asteroids may have evolved along diverse evolutionary paths driven by variations in rotation rate. However, such phenomena have not been demonstrated with global geological evidence.

Fig. 1.

Fig. 1

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Average geopotential distribution as a function of latitude on spheroidal asteroids Bennu and Ryugu with different rotation periods. To calculate the geopotential, we use a shape model of Bennu and Ryugu with 49k facets, respectively. (a) Geopotential distribution on Bennu with the current and other rotation rates. At the current rotation rate (4.3 h) or lower, the equatorial region has the lowest geopotential, while when the rotation rate is higher than a critical rotation period threshold of ~ 5 h, the middle latitudes have the lowest geopotential. (b) Geopotential distribution on Ryugu. At the current rotation rate (7.6 h), the middle latitudes have the lowest geopotential, while at the rotation rate lower than ~ 5 h, which is a critical threshold of the rotation period, the equatorial region has the lowest geopotential.

Recently, the two top-shaped, near-Earth asteroids (101955) Bennu and (162173) Ryugu have been successfully investigated and sampled by the OSIRIS-REx and Hayabusa2 missions, respectively. The high-resolution imageries from the OSIRIS-REx Camera Suite (OCAMS)15 and the Hayabusa2 Optical Navigation Camera Telescope (ONC-T)16 have provided an unique opportunity to compare them and revolutionized our understanding of top-shaped asteroids. Bennu and Ryugu share similarities in several aspects, such as a subkilometer-sized radius, a low bulk density, a low albedo and a carbonaceous surface17–20.

However, the evolutionary paths of Bennu and Ryugu remain uncertain. While a previous numerical study21 suggested possible different formation mechanisms for their top shapes during the early stages, the similarities and differences between their evolutionary pathways until today are still unknown. At their current rotation periods (Bennu at 4.3 h and Ryugu at 7.6 h17,18), they have different geopotential distributions (Fig. 2), suggesting equatorward mass movement on Bennu and poleward movement on Ryugu. This idea is consistent with the previous observational results finding the mass movement morphologies heterogeneously distributed on Bennu11 and the latitudinal color variations in the equatorial region of Ryugu8,13. Yet, whether the mass movement patterns on the two asteroids have been globally uniform throughout their evolutionary history remains poorly understood, making their history of shape deformation and evolutionary path unclear. Essentially, globally distributed, numerous fragmented rock particles (i.e., boulders) should contain critical geological records that are important for understanding active geological processes on small bodies, as demonstrated for asteroids Itokawa22 and Eros23. Despite this, no analysis has been performed based on all the available high-resolution images from the entire mission durations to examine all of the surface boulders observed on both asteroids12,13. Here, we present the first comprehensive global survey of boulders on Bennu and Ryugu, revealing that the shapes of these two asteroids have evolved differently due to distinct histories of rotation rate changes.

Fig. 2.

Fig. 2

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Geopotential distribution and local slope direction on Bennu and Ryugu. With their current rotation periods (4.3 h for Bennu and 7.6 h for Ryugu), the lowest geopotential region exists in the equatorial region for Bennu and in the middle latitudes for Ryugu. A slower rotation for Bennu moves its lowest geopotential toward middle latitudes, similar to the current state of Ryugu. A faster rotation for Ryugu moves its lowest geopotential toward the equator, similar to the current state of Bennu. The white arrows indicate the local slope directions with respect to the rotation rate: equatorward for faster rotations and poleward for slower rotations.

Results

Global boulder mappings on Bennu and Ryugu

For Bennu, we use a global image mosaic with a resolution of ~ 5 cm/pix24, which is currently the best observational condition for boulders. We identify 173,775 boulder profiles, which are then mapped onto a global three-dimensional shape model of Bennu that is derived from the OSIRIS-REx Laser Altimeter (OLA) data25 (Fig. 3a). For Ryugu, we use the ONC-T images taken in 2019 (~ 0.64 m/pix). We identify 20,714 boulders, which are also mapped onto a global three-dimensional shape model (Fig. 3b). We identify a smaller number of boulders on Ryugu because images of Ryugu have a much lower resolution than images of Bennu. Using these mapping results, we obtain essential parameters for each boulder, such as size, axial ratio (i.e., the ratio of the longest axis to the second longest axis), and position.

Fig. 3.

Fig. 3

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Global boulder mapping on Bennu and Ryugu. (a) Boulders on Bennu identified globally and mapped onto the shape model of Bennu. A total of 3,456,617 boulders were automatically identified, and the post-process unambiguously identified 173,775 boulder profiles. (b) Boulders on Ryugu identified globally and mapped on the shape model of Ryugu. We automatically identified 66,471 boulders, resulting in the final identifications of 20,714 boulder profiles. These panels also show close-up images, representing details of the boulder identification in local regions.

Distributions of boulder size and axial ratio

The cumulative size frequency distributions (CSFDs) of boulders on Bennu and Ryugu follow a similar power-law trend with a slope of Inline graphic and Inline graphic, respectively (Fig. 4a). These slopes are slightly different from previously reported values of Inline graphic for Bennu12 and Inline graphic for Ryugu26. Values close to -3.0 support the idea that the boulders on the two bodies are dominated by fragmented objects27. We find that the distributions of the axial ratios of the boulders on both bodies are similar to each other (Fig. 4b). The mean axial ratios for boulders on Bennu and Ryugu are Inline graphic and Inline graphic respectively. These ratios are in the same range as those on Itokawa (0.63) and Eros (0.72)27, further supporting the hypothesis that boulder formation on both bodies is closely related to impact events27.

Fig. 4.

Fig. 4

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Boulder analysis on Bennu and Ryugu. (a) Cumulative boulder size-frequency distributions. The cumulative number per Inline graphic is fitted with a cumulative power-law distribution, shown in dashed lines, with a completeness limit at boulder size of 2.34 m for Bennu and 6.02 m for Ryugu. The power-law exponent (alpha) of the cumulative power-law distribution is Inline graphic for Bennu and Inline graphic for Ryugu, suggesting that the boulders on both bodies are dominated by fragmented objects. (b) Axial ratio distributions of boulders. Similar trends are observed on both bodies, with mean axial ratios of Inline graphic for Bennu and Inline graphic for Ryugu, respectively. These ratios are in the same range as those of boulders on asteroids Itokawa and Eros, further suggesting similar boulder origins related to impact events. (c) Latitudinal average boulder size on Bennu and Ryugu. On Bennu, the average boulder size is the largest at the equator and decreases toward the poles, with some exceptions observed in the northern hemisphere. On Ryugu, the average boulder size is smallest at the equator and increases toward the poles. This represents the size sorting in the direction of local slopes, suggesting equatorward mass movements on Bennu and poleward mass movements on Ryugu, respectively. (d) Spatial distribution of boulders on Bennu. The number of boulders is normalized by the area of each latitude bin. The smaller boulders (Inline graphic5 m) are abundant in the middle latitudes, while the larger boulders (Inline graphic5 m) are abundant in the equatorial region. In addition, the secondary peaks of large boulders exist at middle latitudes. This suggests that Bennu may have recently experienced a change in rotation rate, leading to the reversal of the direction of mass movement. (e) Spatial distribution of boulders on Ryugu. Similar to Bennu, the smaller boulders (Inline graphic5 m) are abundant in the middle latitudes. However, the larger boulders (Inline graphic5 m) are abundant at the high latitudes. We do not observe any secondary concentrations for large boulders, unlike Bennu, suggesting that Ryugu may not have recently experienced the reversal of the direction of mass movement.

Boulder size sorting on both asteroids

Our mapping result shows a latitudinal size sorting of boulders on Bennu and Ryugu (Fig. 4c). On Bennu, the average boulder size is the largest at the equatorial region, and it gradually decreases toward the polar regions, although we observe some exceptions in the northern hemisphere. On Ryugu, the average boulder size is the smallest at the equatorial region and it increases toward the polar regions. The observed size sorting on both bodies is similar to the fall sorting often observed on the talus deposits28,29, a size sorting of rocks in the direction of the slope. Thus, the inverse trend of the longitudinal average boulder size on both asteroids suggests the opposite directions of mass movement: equatorward on Bennu and poleward on Ryugu.

The spatial distribution of boulders on both bodies shows consistent result (Fig. 4d and e). The small boulders (Inline graphic5 m) on Bennu and Ryugu are both abundant in the middle latitudes. We find the opposite trend for the large boulders (Inline graphic5 m) between the two asteroids; on Bennu, these boulders are abundant in the equatorial region, while on Ryugu, they are more abundant in the high latitudes. This result indicates a size sorting of boulders on both bodies in the opposite direction (i.e., equatorward or poleward), which is consistent with our result from the latitudinal average size distribution. Importantly, the estimated mass movement directions on both bodies are consistent with the local slope directions at their current rotation rates (Fig. 2). Therefore, although Bennu and Ryugu share similar properties in many aspects, they have experienced individual shape evolution due to their different rotation rates.

Note that on Ryugu, the lowest geopotential regions are currently at the middle latitudes (Fig. 1b), which could lead to mass movement from both the equatorial and polar regions toward the middle latitudes. However, the significantly larger surface area of the equatorial region (0.30 Inline graphic for Inline graphic in latitude) compared to the polar regions (0.045 Inline graphic for Inline graphic in latitude) implies that a greater volume of material could be transported from the equator than from the poles. Furthermore, once granular material is mobilized, it often requires significant momentum transfer, either through friction or collisions, to stop its movement. These dynamics can cause materials to pass through the lowest geopotential regions and reach higher potential regions. Therefore, while mass movement from the polar regions to the middle latitudes is plausible, the dominant flow from the equatorial region could overlay such movements. This could explain the size sorting of boulders on Ryugu, suggesting a dominant poleward mass movement.

Discussion

We observe a notable trend in the spatial distribution of large boulders on Bennu (Fig. 4d), suggesting a reversal of the mass movement direction on the asteroid. As discussed, the primary concentration is in the equatorial region, but there are secondary concentrations at middle latitudes. Importantly, the location of these middle latitude peaks on Bennu matches that of the primary peaks on Ryugu. This suggests that Bennu’s rotation rate may have been slower in the past, similar to the current situation for Ryugu. The rotation rate of Bennu is accelerating at a rate of Inline graphic30 due to the YORP effect. Assuming that this acceleration has remained constant, Bennu would have experienced the reversal of mass movement directions within the past ~ 0.3 Myr when its rotation period became faster than the critical threshold of 5 h (Fig. 1a). This reversal could account for the observed secondary peaks in the middle latitudes in the spatial distribution of large boulders on Bennu.

On Ryugu, we do not observe such secondary peaks in the spatial distribution of large boulders (Fig. 4e). This suggests the absence of recent reversal in the direction of mass movement. Ryugu is estimated to have rotated more rapidly (~ 3.5 h) in the past17,31. During this period, its lowest geopotential region was likely at the equator, similar to the current state of Bennu (Fig. 2). In this situation, mass movement could be equatorward, possibly forming the equatorial ridge17,31. Similar to Bennu, the geopotential distribution on Ryugu would change dramatically at the critical rotation period threshold of ~ 5 h (Fig. 1b). The thermal simulation32 suggests that Ryugu is slowing down at a rate of Inline graphic, requiring ~ 0.2–3 Myr for the deacceleration from the past rotation period of 5 h to the current 7.6 h. Assuming that the deacceleration rate of Ryugu has been closer to the lower bound of the estimated values, Ryugu may not have recently experienced the reversal of the mass movement direction, compared to Bennu. This could explain the different trend in the spatial distributions of large boulders between the two asteroids.

Our results suggest that asteroids currently rotating rapidly, such as Bennu, may have previously rotated more slowly. They may have experienced a shape evolution similar to what slower-rotating objects, like Ryugu, are experiencing today. The opposite scenario could also be true for asteroids currently rotating slowly. These scenarios may occur in the future due to the changes in their rotation rate. Importantly, small changes in the rotation period in the order of a few hours can significantly change the gravitational field on an asteroid, driving diverse evolutionary pathways. This mechanism explains the distinct geological features and boulder distributions observed on spheroidal asteroids such as Bennu and Ryugu. Note that the finding presented in this work represents the accumulated results of evolution of an asteroid. It shows that, while spheroidal asteroids may have evolved similarly during the early stages, when they formed a top shape33,34, these bodies subsequently followed diverse evolutionary pathways, driven by their unique spin rate histories. This is demonstrated for the first time through our comprehensive boulder dataset for both Bennu and Ryugu.

The unconsolidated nature of the surface material is the key to this diverse evolution of asteroids. Sampling events at Ryugu and Bennu7,8, as well as numerical simulations35, reveal a significantly low cohesive nature of the surface material. The safety assessment36 shows that even a very low cohesion (> 0.6 Pa) can prevent surface materials from initiating mass movement. Thus, if these materials had even slightly higher cohesion up to several Pa, which is not the case for Bennu and Ryugu, the inferred surface motions and diverse evolutionary processes would not be achieved.

Two other asteroids with spheroidal shapes have been imaged by spacecraft, although with less detail, for which the rotation rate also plays an important role in surface mass movement and evolution (Fig. 5). The asteroid (65803) Didymos and its moon Dimorphos were recently observed by the DART mission9, and will be further studied by the ESA’s Hera mission37. Didymos exhibits a spheroidal shape, while the shape is flatter compared to those of Bennu and Ryugu38. Its rapid rotation rate of 2.26 h39 suggests an equatorward direction of mass movement on the body. This is evidenced by the DART imagery that reveals several boulder tracks and terminal boulders existing on the tails of tracks near the equator40. The asteroid (152830) Dinkinesh and its moon Selam were also recently observed by NASA’s Lucy mission41. The rotation rate of Dinkinesh is 3.73 h, which also suggests an equatorward mass movement. In both cases, such an equatorward mass movement led to the ejection of surface materials and the formation of a secondary38,41,42, showing the important role of the rotation rate and mass movement direction in asteroid evolution. Thus, asteroids with similar shapes can follow different evolutionary pathways, depending on the history of their rotation rate and resulting surface material behavior.

Fig. 5.

Fig. 5

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Rotation rate and evolution of spheroidal asteroids. Four asteroids with different rotation periods are shown: Ryugu (7.6 h), Bennu (4.3 h), Dinkinesh (3.7 h) and Didymos (2.3 h). Spheroidal asteroids have a critical threshold for their rotation period, beyond which the lowest geopotential moves from the equator to middle latitudes. Asteroids rotating faster than this threshold (current Bennu) experience equatorward mass movement, while slower rotators (current Ryugu) experience poleward mass movement. Due to the YORP effect, rotation period of asteroids can easily exceed or fall below the critical threshold, causing a reversal of the direction of mass movement, as we show the evidence on Bennu. With a faster rotation rate, asteroids can lose surface material from the equator, forming a secondary, as in the case of Dinkinesh-Selam and Didymos-Dimorphos systems. In this manner, the rotation rate can drive diverse evolutionary pathways of spheroidal asteroids. Image ids: hyb2_onc_20190221_065642_tvf (Ryugu), 20181213T010148S790_map_iofL2pan (Bennu), lor_0752129707_03631_00001_1 × 1_sci_03 and lor_0752129962_03682_00001_1 × 1_sci_03 (Dinkinesh-Selam system), dart_0401929893_44487_02 and dart_0401930040_12262_02 (Dimorphos-Didymos system).

Methods

Automatic rock identification

Mapping of rock particles on asteroids can be extremely challenging for several reasons. To achieve meaningful statistical analysis, thousands of particles must be correctly identified. More importantly, each particle should be observed using multiple images with distinct photometric conditions to yield distinct mapping results. This means that a particle may be identified multiple times in multiple images. Such duplicate counts significantly affect the statistical properties of rock distributions, so the exact locations of mapped rocks should be carefully handled to remove duplicates. As a result, the conventional manual analysis of rock particles is usually extremely time consuming and impractical to perform on multiple bodies. Furthermore, particle profiles are often blurred and difficult to distinguish from the background due to irregular particle shapes, overlapping/buried particles, and limited image resolution. This leads to the inconclusive criterion for boundaries of particles from different observers27,43, and as a result, the manual analysis often contains subjective uncertainties. A similar situation is often discussed in the crater analysis44, but the situation for rock particles is much more complicated due to the above reasons. Even trained professionals can produce inconsistent mapping results as observed in the case of the global survey of Itokawa45,46. Therefore, a fast, reliable, and reproducible technique for mapping rock particles is essential. Our solution is to map rock particles using an automated rock identification technique that can overcome the limitations of the conventional manual analysis.

In order to identify rock particles, previous studies have employed various strategies, such as polylines43,47, bounding boxes48, ellipses26,27, and polygons49,50 (Supplementary Fig. S1). Overall, polygons provide relatively accurate information on particle size, position, and shape, but at the cost of increased time consumption. Therefore, we develop an automatic algorithm that identifies particles from the background at the pixel level, and distinguishes each individual particle. This strategy is technically referred to as instance segmentation. To perform this task, we use the cascade R-CNN (Region-based Convolutional Neural Networks) model51, which has proven to be one of the most successful and widely used models for instance segmentation. We convert the results of the algorithm into the polygons representing each profile of a particle, as the identification result.

We employ the public implementation of Cascade R-CNN, based on the MMDetection toolbox52. We select 30 OCAMS and ONC-T images (Supplementary Table S1) and prepare more than 60,000 profiles of rock particles, as there is currently no conventional or public data available for profiles of rock particles on small bodies. Using this dataset, we perform the fine tuning of the model, with computational resources equipped with Intel Xeon Platinum 8360Y CPUs, 512 GB RAM, and 8 NVIDIA A100 GPUs.

Boulder identification on Bennu

For the dataset, we use Global PAN Mosaic having a global resolution of 5 cm/pix24. This mosaic is orthorectified and photometrically normalized, which offers appropriate observation conditions for a comprehensive global boulder survey on Bennu. We first convert the global mosaic by using the sinusoidal projection, where the distortion of the image is minimized along the center line of the image. We crop the global mosaic into Inline graphic pixel images along the center line of the mosaic, and repeated this process, changing the center of the sinusoidal projection by every Inline graphic longitudes in order to cover the whole surface area of Bennu. Note that each cropped image has overlapping areas with other cropped images both vertically and horizontally, so that no rock particles positioning at the edge of an image are analyzed in images. In this manner, we obtain a total of 7,080 cropped images.

We then identify boulders on Bennu in each image, resulting in a total of 3,456,617 boulder profiles. We convert each rock profile from the body-fixed coordinate systems expressed in x, y, and z to the geographic coordinate system expressed in latitude, longitude, and radius by using the backplanes. Those are evaluated whether they overlap other profiles. If the overlapping is confirmed, we adopt the results of particles with larger areas as the identification results. Note that backplanes have some errors in certain regions, such as boundaries of shadowed and non-shadowed areas. Those errors can lead to uncertainties during the conversion of the result of automatic identification. Also, particles that are geometrically unsuitable for analysis, such as those that are partially buried or significantly overlapped by other particles, can yield unreliable size measurements. Therefore, these particles should be excluded from the identification results. Thus, the result is checked by multiple observers, and some errors and outliers are omitted or modified manually. In this manner, we omit duplicated identifications and obtain the global identification result having 173,775 profiles of boulders (Supplementary Table S2).

Boulder identification on Ryugu

For the global mapping of boulders on Ryugu, we prepare 425 ONC-T images (~ 0.64 m/pix; Supplementary Table S3), which cover the global surface of Ryugu, and generate a three-dimensional shape model of Ryugu with Metashape (ver. 1.6.4) that is a commercial software for creating shape models with Structure from Motion (SfM) method. Based on the shape model, we generate a global mosaic image, which is also converted by using the sinusoidal projection. Similar to the analysis on Bennu, we crop the global mosaic into Inline graphic pixel images along the center line, and repeated this process, changing the center of the sinusoidal projection by every Inline graphic longitudes to cover the global surface of Ryugu. As a result, we obtain a total of 1,620 images, and automatically identify 66,471 boulders on Ryugu. Then, each boulder profile is projected onto the global shape model, evaluating duplicate identifications and removing them.

Note that although the OSIRIS-REx mission performed multiple close proximity operations to Bennu, including orbits around the asteroid as well as close surface fly-bys, allowing a more detailed and global coverage of its surface, the Hayabusa2 mission relied on a hovering strategy to study Ryugu. As a result, Ryugu was observed at a lower resolution and higher emission angles compared to Bennu. This led to increased errors and reduced reliability in the identification results, particularly for small particles, which were also fewer in number than those for Bennu. Therefore, we correct the identifications by reviewing each profile from different observation directions in a three-dimensional space with the Small Body Mapping Tool (ver. 0.8.1)53 and CloudCompare (ver. 2.12.0). Particles that are geometrically unsuitable for analysis are excluded from the results in this process, as in the case of the analysis for Bennu. Note that the resolution of the ONC-T images remains sufficient to observe meter-sized boulders on Ryugu, thereby supporting the identification results shown in this work. In this manner, we result in a total of 20,714 boulders on the global surface of Ryugu (Supplementary Table S4).

Determining the size and axial ratio of particles

To accurately measure the sizes of particles existing on a rocky asteroid with an irregular shape, we design a procedure to obtain sizes of particles not from individual images but from three-dimensional coordinates projected on the surface of the shape model of Bennu and Ryugu. Supplementary Fig. S2 shows the overall concept of the measurement. A profile automatically identified and expressed in the body-fixed coordinate system is used to determine the longest axis of each particle by finding the longest dimension of the profile. The best-fitting plane of this profile is also calculated, and the profile is projected on the plane for the following processes. Previous work27 shows that the mean lengths of the longest and second longest dimensions are the best parameter to characterize the size of a particle reflecting its volume. Thus, we obtain the best-fitting ellipse of the projected rock profile on the best-fitting plane and the size of particles by calculating the mean length of the semi-major and semi-minor axes of the ellipse. In this manner, we record the sizes, and the lengths of the semi-major and semi-minor axes. Note that in the analysis of CSFD, we use the method proposed by previous work54 as the fitting function of the power-law distribution.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary Material 1 (2.9MB, docx)
Supplementary Material 2 (11.8KB, xlsx)
Supplementary Material 3 (11.5MB, xlsx)
Supplementary Material 4 (27.5KB, xlsx)
Supplementary Material 5 (1.4MB, xlsx)

Acknowledgements

We are grateful to the entire OSIRIS-REx team for making the encounter with Bennu possible, and to all the members of Hayabusa2 mission for their contributions to the successful encounter with Ryugu. We thank R. Hemmi for insights and technical support. Y.S. acknowledges JSPS KAKENHI (number JP21J21798, JP24K22896), H.M. acknowledges JSPS KAKENHI (JP23H00279) and partial support from DigitalBlast, and P.M. acknowledges support from the French space agency CNES and from the University of Tokyo.

Author contributions

Y.S. and H.M. conceived the idea for the study. Y.S. was responsible for preparing the data, developping the algorithm, conducting global mapping of boulders on Bennu and Ryugu, and processing the measurement results of the boulders. Y.S., H.M., and P.M. contributed to the interpretation of the results. Y.S. and H.M. drafted the original manuscript, P.M helped in its finalization. H.M. supervised the study. All authors have reviewed and approved the final manuscript.

Data availability

Image dataset used in this study from the OSIRIS-REx and the Hayabusa2 missions are available via the Planetary Data System (PDS, https://sbn.psi.edu/pds/resource/orex/) and the DARTS database (https://darts.isas.jaxa.jp/planet/project/hayabusa2/). The Global PAN Mosaic of Bennu and its backplanes can be downloaded from the United States Geological Survey (USGS, https://astrogeology.usgs.gov/search/map/Bennu/OSIRIS-REx/OCAMS/Bennu_OSIRIS-REx_OCAMS_Global_PAN _Mosaic_5cm_v1). The Small Body Mapping Tool (SBMT; https://sbmt.jhuapl.edu/) developed by Johns Hopkins Applied Physics Laboratory contains the shape models of asteroids used in this study. Other data including the boulder measurements (size, axial ratio, and position) on Bennu and Ryugu will be available with this publication via Supplementary Information.

Code availability

The code associated with this study is available at https://github.com/AstroYuta/automatic-rock-identification, and the code for calculating the geopotential of the shape models can be downloaded via https://data.darts.isas.jaxa.jp/pub/hayabusa2/paper/Watanabe_2019/. Metashape is available at https://www.agisoft.com/, and CloudCompare can be downloaded from https://www.danielgm.net/cc/.

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Material 1 (2.9MB, docx)
Supplementary Material 2 (11.8KB, xlsx)
Supplementary Material 3 (11.5MB, xlsx)
Supplementary Material 4 (27.5KB, xlsx)
Supplementary Material 5 (1.4MB, xlsx)

Data Availability Statement

Image dataset used in this study from the OSIRIS-REx and the Hayabusa2 missions are available via the Planetary Data System (PDS, https://sbn.psi.edu/pds/resource/orex/) and the DARTS database (https://darts.isas.jaxa.jp/planet/project/hayabusa2/). The Global PAN Mosaic of Bennu and its backplanes can be downloaded from the United States Geological Survey (USGS, https://astrogeology.usgs.gov/search/map/Bennu/OSIRIS-REx/OCAMS/Bennu_OSIRIS-REx_OCAMS_Global_PAN _Mosaic_5cm_v1). The Small Body Mapping Tool (SBMT; https://sbmt.jhuapl.edu/) developed by Johns Hopkins Applied Physics Laboratory contains the shape models of asteroids used in this study. Other data including the boulder measurements (size, axial ratio, and position) on Bennu and Ryugu will be available with this publication via Supplementary Information.

The code associated with this study is available at https://github.com/AstroYuta/automatic-rock-identification, and the code for calculating the geopotential of the shape models can be downloaded via https://data.darts.isas.jaxa.jp/pub/hayabusa2/paper/Watanabe_2019/. Metashape is available at https://www.agisoft.com/, and CloudCompare can be downloaded from https://www.danielgm.net/cc/.

Articles from Scientific Reports are provided here courtesy of Nature Publishing Group

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