as to which impact angles produce which shapes or as to how far from the
primary centre-of-mass the merger occurs, $r_{\mathrm{merger}}$, which has
been plotted in the bottom right plot. Note, however, that the far-in
locations of the mergers for runs f60_R2 and Ryugu run 4 do not coincide with
their orbits by the final time step as each of these mergers is soon followed
by a migration outwards farther away from the primary.

Figure 23: The DEEVE axis ratio $a/b$ value before (grey) and after (coloured)
the critical merger which determines the final shape of the considered
secondaries at the final time step of our simulations, compared against
$\theta_{\mathrm{p}}$ which is the angle between the longest principal axis
and the relative velocity vector for the merger. A short-axis merger
corresponds to $\theta_{\mathrm{p}}\sim 90^{\circ}$ while a long-axis merger
would mean a value close to 0 or 180∘.

The reason why $\beta$ cannot directly predict the post-merger shape of the
body is due to the fact that it tells us nothing of how the asymmetric target
is rotated relative its trajectory and if it collides with the impactor at its
short-axis or long-axis. To verify this idea, we define the angle
$\theta_{\mathrm{p}}$ between the longest principal axis pre-merger, $a$, and
the relative velocity vector. An angle of $\theta_{\mathrm{p}}=0$ or
$180^{\circ}$ then corresponds to a relative velocity vector completely
aligned with $a$, while a value of $90^{\circ}$ tells us that the relative
velocity vector is parallel to the shortest axis, $b$. We plot this value
against the change in $a/b$ in figure 23. There is a correlation between a
reduction/increase in $a/b$ value of the largest remnant and the
$\theta_{\mathrm{p}}$ value of the merger, indicating that short-axis/long-
axis mergers indeed favour the creation of more oblate/prolate bodies. We
study the two outlier cases, Didymos runs 2 and 4 which are both long-axis
mergers per our definition but still show a reduction in $a/b$. The former
does not become an oblate spheroid, but rather a prolate, bilobate body where
the pre-merger axis $b$ instead is the longest axis. As for Didymos run 4, the
impactor is a highly elongated but low-mass aggregate on an eccentric orbit
that undergoes a close encounter with the primary, enters the Hill radius of
the target and is subsequently slowed down before it is tidally disrupted and
accreted, which makes it behave unlike any of the typical short- or long-axis
mergers we observe.

While the orientation and shape of the impactor will also affect the final
structure of the largest moon in our systems, the generally low mass ratio
between the two objects renders the orientation and initial shape of the
target far more important. This becomes evident when comparing figure 23 with
figure 24, where we instead have plotted the angle between the relative
velocity and the largest principal axis of the impactor. Only two of the
impactors have distinct short-axis mergers with $\theta_{\mathrm{p,impactor}}$
close to $90^{\circ}$ while five of the corresponding mergers generate more
oblate bodies. Instead, their orbits have the largest effect on the outcome of
the merger. Looking at the cases which generate more prolate bodies and
contact binaries such as Ryugu run 4, as well as Didymos runs 1 and 2, this
becomes evident when combining their distribution of impact angles with the
corresponding $\theta_{\mathrm{p}}$ values. Here we see that the long-axis
mergers Ryugu run 4 and Didymos run 1 have the largest impact angles as well,
showing that the impactor has a dissimilar trajectory to the target. Indeed,
investigating the merger in detail confirms that the impactor in Ryugu run 4
has a wider orbit than the target and approaches from the outside, while the
opposite is true for Didymos run 1 where the impactor instead has an orbit
closer to the primary and intersects the orbit of the target from inside.

Figure 24: Same as figure 23 but for the impactor in the merger.

From these results, there is an indication that a formation model more likely
to generate low-velocity, short-axis mergers is efficient at forming oblate
bodies. Tying this to the geometry of the disk, a wider initial radial
extension similar to those generated by giant impacts onto planets (e.g. Ida
et al., 1997; Kokubo et al., 2000) facilitate the fast formation of multiple
aggregates. Due to the hierarchical nature of the process, one aggregate will
quickly grow more massive than the other satellites in the system and often
becomes prolate and tidally locked on a synchronous orbit. Undergoing one or
more mergers with other satellites (depending on the mass ratios) under
favourable circumstances such as low impact velocity, similar trajectories and
$\theta_{\mathrm{p}}$ values close to 90∘ will then reduce the elongation of
the body significantly and can in some cases generate oblate spheroids.

####  5.2.1 Bilobate satellites

Further recalling our analysis from the section 5.1, the IDH, MDH and CDH
scenario outcomes are dependent on the position of the Roche limit relative to
the outer edge of the disk and are as a result system-specific. Because the
strength of the tidal forces largely affects the initial shape prior to
mergers, forming most aggregates farther away from this limit will generate
less prolate bodies that are less likely to have synchronous orbits, which is
the case for our Didymos-like systems. For the corresponding IDH cases where
growth is dominated by isotropic accretion of single grains and low-mass
aggregates, the moonlet will become more oblate over longer timescales.
However, for systems where there still are additional massive satellites, it
follows that the long-axis mergers will be likelier, which in turn increases
the probability of forming bilobate bodies. Hence, for our rotational failure
model, primaries with smaller radii and higher densities with Roche limits
closer to the surface should be more likely to have contact binary moons.

This is an important topic for further research, especially given the recent
discovery of the bilobate satellite Selam of the (152830) Dinkinesh system
(Levison et al., 2024) by the Lucy mission during a flyby (Levison et al.,
2021). Dinkinesh has a distinct top-shape indicative of rotational failure and
an effective diameter of $720\pm 24$ m making it smaller than both Didymos and
Ryugu. The satellite Selam is orbiting the primary at a distance of $\sim
9R_{\mathrm{main}}$ and has a distinct bilobate structure where the components
have diameters of $212\pm 21$ m and $234\pm 23$ m (Levison et al., 2024).
Despite the much greater separation between primary and secondary, the Lucy
images show that the lobes of Selam align radially with the primary,
indicative of a tidally locked orbit. In turn, there is a question of whether
or not Selam formed closer to the primary and then migrated outwards via
dynamical effects such as binary YORP (BYORP, Ćuk and Burns, 2005) or tidal
interaction (Jacobson and Scheeres, 2011b) or if it formed farther out in the
pyramidal regime according to the model of Madeira and Charnoz (2024).
Moreover, the analysis from Levison et al. (2024) also shows that the mass
ratio between the satellite and primary, assuming equal density for both
objects of $\rho=2400\pm 350\ \mathrm{kg/m}^{3}$, is 0.06 which is
significantly higher than any of the satellites we can form during the course
of our simulations (see table 3) as we assume a lower initial disk mass.
Nevertheless, judging from our spin-up simulations of Didymos in table 2 and
the work of similar studies (e.g. Sugiura et al., 2021; Hyodo and Sugiura,
2022), it is entirely possible for primaries with higher bulk densities to
shed such large masses via rotational failure when introducing some weak
cohesion to the primary. Hence, by performing follow-up SPH simulations with a
primary based on Dinkinesh with higher resolution, we can get a better
understanding of whether or not forming such a massive contact binary
satellite is achievable with the circumasteroidal disk model. Given the low
velocity of our impacts and the fact that our model can form weakly bilobate
bodies even with low-resolution simulations, we believe this to be the case.

With the pronounced equatorial ridge of Dinkinesh in mind, a history of
deformation and mass shedding due to rotational spin-up is very likely. In
turn, we expect that the existence of Selam cannot be explained with satellite
formation via giant impacts (Durda et al., 2004, 2007) alone. Yet, we can
imagine a scenario where a combination of rotational failure and a grazing
giant impact can lead to a similar type of debris disk investigated in this
work and Agrusa et al. (2024), especially since Dinkinesh displays
nonaxisymmetry and a significant concavity that could originate from a
collision.

###  5.3 Particle size distribution, shape and resolution

One important caveat of the SFD in our model and the low resolution of our
hand-off simulations is that it leads to unrealistically large boulders in the
system and an absence of smaller grains. As shown in a series of recent
publications related to the DART mission impact, the choice of boulder
packing, cohesion and SFD highly affects the dynamics of rubble piles and
whether or not they are disrupted or reshaped from high-energy collisions
(Raducan et al., 2022, 2024a, 2024b). Combining observations from the DART
mission (Li et al., 2023; Dotto et al., 2024) and SPH simulations of the DART
impact, Raducan et al. (2024b) found that Dimorphos is expected to be a
cohesionless rubble pile with a boulder packing of less than 40% on the
surface and slightly below it. This accounts for boulders with
$D_{\mathrm{p}}>2.5$ m, meaning most of the mass is constituted by smaller
grains and boulders, which aligns with observations of Dimorphos surface
(Pajola et al., 2023). The volume of boulders in Dimorphos, their packing and
SFD will be further constrained with the upcoming Hera mission (Michel et al.,
2022), which will revisit the binary system satellite once more post DART
impact and determine how the body was reshaped.

In our simulation, the presence of smaller particles has been omitted and
their mass is simply accounted for by using larger clusters of particles
represented by boulders with densities similar to the bulk density of the
primary for computational purposes. Including particles with diameters less
than 5 m would put a high computational strain on our simulations that cannot
currently be handled with the resources at our disposal as the number of
particles in each system would increase drastically, way above $10^{4}$.
Nevertheless, results from Raducan et al. (2024b) and previous studies such as
Zhang et al. (2017, 2021) show that large differences in particle sizes affect
the stability and structural dynamics of rubble pile asteroids. For our
purposes, excluding the small meter-sized particles from our simulations can
generate undesired behaviour in the contact mechanics and artificially high
mechanical strength for the inner structure from particle interlocking between
our large, highly angular particles. This becomes particularly important when
considering the high rate of tidal interactions and mergers we observe. While
our SFD is polydisperse for the standalone N-body simulations, it may be that
smaller grains with diameters below 5 m could smooth out contacts between
larger boulders, making the aggregates more fluid-like and thereby more
susceptible to tidal disruption and deformation during mergers. Further, a
more fluid-like behaviour would increase the time it takes for the newly
formed aggregates to settle in a specific shape as particle interlocking
effects would have less influence on the mechanical integrity of the body.
With weaker mechanical strength, dynamical effects such as tidal forces,
impacts, spin and self-gravity would have a more dominant role in the
determination of the final configuration of the constituents. Keeping these
potential caveats in mind, the specific shapes of the moons formed in our
simulations may be unphysical, which is why we have opted to solely rely on
DEEVE estimates for their geometrical properties. Moreover, another
consequence of altering our SFD in this manner could be that it facilitates
the creation of a distinct neck between two moonlets during the formation of a
bilobate object. The low impact velocities in our model would allow for longer
gravitational interactions prior to the contact and smaller loosely bound
grains could flow towards the other body, creating the characteristic neck
between them, seemingly present between the lobes of Selam (Levison et al.,
2024). However, if rubble piles get their mechanical strength from the
presence of larger boulders beneath their surfaces, interlocking effects
between granular particles could potentially also provide the cohesive effect
needed to keep structural integrity for the smaller constituent in contact
binaries (Meyer and Scheeres, 2024). We aim to investigate the validity of our
SFD and how it affects the stability of our aggregates in a follow-up study
using higher-resolution simulations of select mergers from our simulations and
tidal encounters with the primary.

With these model characteristics in mind, we also note that there are no
evident dissimilarities in outcomes and dynamical behaviour of the hand-off
and pure N-body systems in this work, which use drastically different SFDs.

###  5.4 Length of simulations and system stability

The heavy computational task of resolving contacts between polyhedra not only
limits the number of particles we can use, but also how long we can
realistically simulate a system, let alone several. Therefore, we had to
settle for resolving each system a maximum of ten days post rotational
failure. While we can capture and assess the main dynamical mechanisms
involved in generating oblate and bilobate shapes, we cannot speak for the
long-term stability of our aggregates and their orbits. There are many reasons
a potential moon could end up being deformed or even disrupted. Since a
majority of the debris disks in our systems have yet to be cleared of matter,
further mergers with aggregates still remaining in the system that migrate
over time and end up intercepting the orbit of the largest satellite can lead
to further growth and reshaping. Furthermore, while unlikely, a lower mass
object on an eccentric orbit that undergoes a close encounter with the primary
body can be scattered, directly collide with the largest remnant and disrupt
it or cause significant deformation due to the high-velocity impact. Orbit
decay through long-term tidal interactions with the primary or scattering
events with other aggregates could also lead to further mass shedding events
and deformation due to tidal disruption.

Despite the mass available in our systems and the number of aggregates that
interact gravitationally, most systems remain dynamically cold in the sense
that there the orbital inclinations are kept small, causing a large majority
of the close encounters to lead to mergers with low impact velocities. In
consequence, changes in orbits mainly occur through energy dissipation from
impacts, tidal effects and gravitational scattering with the primary. The
mergers also lead to breaking of the often initially synchronous orbits of the
largest remnant, leaving only a few of the satellites in such a state. One
possible result is that the perturbed aggregate then enters a state of non-
principal axis rotation, limiting or breaking any potential for migration via
BYORP (Ćuk and Burns, 2005; Quillen et al., 2022). Depending on the inertia
ratios of the satellite and its collisional history, it can also enter a state
of tumbling (Agrusa et al., 2021). For bodies that retain their synchronous
orbit, BYORP becomes important as a mechanism for migration and if multiple
satellites remain in the system, mean motion resonances can further affect the
orbital evolution. Long-term dynamical effects of binary asteroid systems are
complex and cannot be captured in a meaningful way over the course of just a
few days of dynamical evolution and we refer the interested reader to Agrusa
et al. (2024) who analysed the orbital stability and rotational state of 96
simulations lasting 100 days for a similar, debris disk based binary asteroid
formation model.

###  5.5 Comparison to Agrusa et al. (2024)

While there have been numerous previous studies on asteroid binary formation
(Walsh et al., 2008, 2012; Jacobson and Scheeres, 2011a; Tardivel et al.,
2018; Hyodo and Sugiura, 2022; Madeira et al., 2023; Madeira and Charnoz,
2024), the work most related to ours is Agrusa et al. (2024) (henceforth
referred to as A24). In this section, we summarise any differences and
similarities between the work brought up throughout the text with the previous
discussion in mind. The two models can consistently form oblate spheroid
satellites in wide debris disks around similar primary bodies over timescales
on the order of days, a few % of the cases in A24 and 3 out of 14 simulations
for this work. Judging from the distribution of DEEVE axis ratios for the
satellites formed in A24 (see their figure 12a), the simulations also seem to
have resulted in a few bilobate objects. The dynamical mechanisms that
determine the final shape are highly similar in both models as oblate
spheroids form in cases where the largest remnant in each system undergoes a
catastrophic re-shaping event due to a tidal encounter and/or a critical
merger. Therefore, the overall trends for the dynamical evolution of the disks
appear similar, independent of differing SFDs, particle shapes and contact
physics. However, while it is difficult to argue that our implementation, on
average, forms more oblate spheroids because of the low number of simulations
we could carry out, it would align with previous points made during the
discussion. Given how mergers and tidal encounters with the primary body are
the main mechanisms that determine the shape of a satellite in this regime,
this would mainly be attributed to the number of aggregates that
simultaneously can exist in the system throughout the evolution of the disk,
especially during the later stages. This number is governed by how efficiently
a given disk can create aggregates and their mechanical strength after
formation. With this in mind, we proceed to identify the main differences
between the models in our work and A24 that could cause our aggregates to form
more easily and survive for longer.

As mentioned in sections 2.2 and 2.5, the methods used to perform the spin-up
simulations are based on two distinct codes and setups, which accounts for the
variation in initial conditions for the subsequent dynamical evolution of the
resulting debris disks. Crucially, the disks simulated in A24 were symmetric,
less radially extended (by up to $1R_{\mathrm{main}}$), thinner and less
massive (max $0.04M_{\mathrm{main}})$. Hence, it is clear that the type of
mass-shedding event considered in A24 was less chaotic and more confined to
areas around the equator of their primary. As discussed in section 5.1, the
geometry of the debris disk appears to affect the number of aggregates
available in the system, as the ability of an aggregate to survive the tidal
forces depend on where they form in relation to the fluid Roche limit. The
thickness of the disk should also affect its efficiency at forming satellites,
as a thicker disk would let an aggregate accrete isotropically for longer
before it starts accreting only within the plane, which is less efficient
(analogous to 2D and 3D accretion rates in planet formation (e.g. Johansen and
Lambrechts, 2017)). Thus, a satellite forming in a thick disk would be more
efficient at clearing its vicinity of matter, reach higher masses and survive
for longer before it ultimately merges with another aggregate. The longevity
of a given aggregate is also dependent on its mechanical strength. Given that
the use of non-spherical particles, as compared to using spherical particles
with approximated granular behaviour, has been shown to increase the rigidity
of rubble pile objects (Ferrari and Tanga, 2020) and ability to withstand
tidal disruption (Marohnic et al., 2023), it is likely that our use of angular
particles with rich geometric diversity and non-linear contact mechanics also
contribute to a higher mechanical strength. This allows aggregates to more
easily survive under the influence of strong tidal forces in our model.

Another main difference between the two studies comes from the disk masses
considered. The satellites in A24 with masses similar to that of Dimorphos all
occur in cases where the disk mass is 0.03$M_{\mathrm{main}}$ or less, which
offers an explanation for why our model generates more massive largest
remnants. While the oblate spheroid satellites from our results all have lower
masses than their more prolate counterparts ($<0.02M_{\mathrm{main}}$), the
systems they form in are not fully resolved by the final time step as
mentioned above. Therefore, it would be meaningful to run additional SPH spin-
up simulations with a smaller effective friction angle to get initial
conditions for less massive debris disks. Moreover, by running standalone
N-body simulations with lower initial disk masses and altering their disk
geometry to be more similar to the disks in A24, we would be able to further
narrow down the driving factors that increase the frequency of systems with
atypically shaped satellites.

##  6 Conclusions

In light of recent close-up observations of satellites in binary asteroid
systems that diverge from the typical elongated shape, such as the oblate
spheroid Dimorphos targeted by the DART mission (Rivkin et al., 2021), or the
contact binary Selam of the Dinkinesh system detected by the Lucy mission
(Levison et al., 2021, 2024), we have aimed to narrow down the mechanisms
involved in the formation process of these objects in this work. In turn, we
performed short-term dynamical evolution of circumasteroidal debris disks
formed around rapidly spinning asteroids. Taking initial conditions obtained
from SPH simulations of mass shedding through rotational failure, we used a
newly developed tool based on geometrical algorithms to perform numerical
hand-off to a granular N-body code that captures complex contact mechanics and
gravitational interactions between irregularly shaped particles. Investigating
two different systems, based on the asteroids Ryugu and Didymos, we carried
out two hand-off simulations and five standalone N-body simulations for each
case. Out of the 14 simulations, we end up with three systems with oblate
spheroid secondaries and three systems with bilobate satellites by the final
time steps.

We find that a radially extended disk wider than 2 primary radii favours
mergers and deformation via tidal interactions with the primary body. Growth
is rapid, hierarchical and primarily driven by mergers, allowing satellites
between 0.014$M_{\mathrm{main}}$ and 0.032$M_{\mathrm{main}}$ to form in just
a few days. As most moonlets initially end up in orbits near the fluid Roche
limit, they are most often prolate and on synchronous orbits that are
subsequently perturbed by mergers and close encounters with the main asteroid.
In our model, only systems where the largest satellite undergoes mild or
catastrophic disruption (losing less or more than half its mass, respectively)
during close encounters with the primary, making it less prolate, are capable
of forming satellites with Dimorphos-like shapes.

Analysis of critical mergers during our simulations shows that the impact
velocities in this formation regime are below one mutual escape velocity,
which is significantly lower compared to previous studies which have mainly
been focused on merger-driven moon formation in planetary rings (e.g. Leleu et
al., 2018). This hints at the existence of a different regime for mergers
during the formation of asteroid moons which results in homogeneous bodies
without the significant ridges and deformations caused by high-velocity
impacts. The low-energy mergers facilitate the formation of bilobate
satellites with two lobes connected by a thin neck, which we expect to find
when performing higher-resolution simulations of some impacts. Moreover, we
find that the initial shape and the orientation of the longest principal axis
of the most massive body in the merger highly influence the post-merger shape.
Given the bodies are initially prolate before impact, mergers where the
relative velocity vector is parallel with the shortest axis lead to more
oblate shapes while mergers where the same vector is more closely aligned with
the longest axis result in more prolate bodies and bilobate objects.

Due to the heavy computational task of resolving contacts between irregularly
shaped particles, we had to settle for a shorter simulation time than desired
of at most 10 days and an SFD not allowing for particles smaller than 5 m in
diameter. In turn, we cannot draw any conclusions regarding the stability of
our systems and the potential presence of higher-order dynamical effects such
as BYORP, mean motion resonance between multiple satellites and tumbling.
Nevertheless, our results provide valuable insight into the formation
mechanisms that govern deformation of the initially prolate bodies asteroid
satellites that make up a majority of the population (Pravec et al., 2016).
Judging from the chaotic formation pathways in our simulations, oblate
spheroids and bilobate satellites may be more prevalent in asteroid binaries
than indicated by lightcurve measurements, which are biased against detecting
satellite shapes that are more oblate (Pravec et al., 2016; Agrusa et al.,
2024).

While computationally expensive, the added internal mechanic strength from the
contact mechanics in our N-body simulations caused by particle–particle
interlocking, dilatancy and complex random packing of the irregularly shaped
grains better our understanding of how granular aggregate satellites behave
during mergers and close encounters with their primaries. When complete tidal
disruption is more difficult, more aggregates will survive the earliest stages
of formation, allowing for more mergers and reshaping events. However, recent
studies such as Raducan et al. (2024b) have emphasised that the structural
integrity of aggregates is highly dependent on the distribution between large
boulders and smaller particles with diameters less than 2.5 m. Furthermore,
the observed boulder diameters on the surface of Dimorphos go down to 1 m and
up to 16 m, while we include much larger particles serving as clusters of
smaller constituents. Given that the presence of smaller particles can smooth
out contacts during deformation events such as mergers and tidal interactions,
making the body behave more like a fluid, we recognise that our aggregates may
be too rigid and will further investigate the effect of particle SFD choice
for our implementation. With upcoming missions such as Hera (Michel et al.,
2022), which will send a spacecraft to revisit the Didymos system in 2027
after the DART impact and determine the resulting shape of Dimorphos and its
internal structure, the boulder volume fraction and SFD can be further
constrained, allowing us to significantly improve our formation model.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported
in this paper.

## Acknowledgments

J.W. and F.F. acknowledge funding from the Swiss National Science Foundation
(SNSF) Ambizione grant No. 193346. M.J. and S.D.R. acknowledge support from
SNSF project No. 200021_207359. G.M. acknowledges the support of the European
Research Council, France (101001282, METAL). We thank the two anonymous
reviewers for their constructive feedback, as well as Harrison F. Agrusa and
Masatoshi Hirabayashi for helpful discussions and input during this project.

## References

  * Agrusa et al. (2022) Agrusa, H.F., Ferrari, F., Zhang, Y., Richardson, D.C., Michel, P., 2022.  Dynamical Evolution of the Didymos-Dimorphos Binary Asteroid as Rubble Piles following the DART Impact.  PSJ 3, 158.  doi:10.3847/PSJ/ac76c1, arXiv:2207.06995.
  * Agrusa et al. (2021) Agrusa, H.F., Gkolias, I., Tsiganis, K., Richardson, D.C., Meyer, A.J., Scheeres, D.J., Ćuk, M., Jacobson, S.A., Michel, P., Karatekin, Ö., Cheng, A.F., Hirabayashi, M., Zhang, Y., Fahnestock, E.G., Davis, A.B., 2021.  The excited spin state of Dimorphos resulting from the DART impact.  Icarus 370, 114624.  doi:10.1016/j.icarus.2021.114624, arXiv:2107.07996.
  * Agrusa et al. (2024) Agrusa, H.F., Zhang, Y., Richardson, D.C., Pravec, P., Ćuk, M., Michel, P., Ballouz, R.L., Jacobson, S.A., Scheeres, D.J., Walsh, K., Barnouin, O., Daly, R.T., Palmer, E., Pajola, M., Lucchetti, A., Tusberti, F., DeMartini, J.V., Ferrari, F., Meyer, A.J., Raducan, S.D., Sánchez, P., 2024.  Direct N-body Simulations of Satellite Formation around Small Asteroids: Insights from DART’s Encounter with the Didymos System.  PSJ 5, 54.  doi:10.3847/PSJ/ad206b, arXiv:2401.09269.
  * Ballouz et al. (2019) Ballouz, R.L., Walsh, K.J., Richardson, D.C., Michel, P., 2019.  Using a geometrical algorithm to provide N-body initial conditions for the gravitational phase of asteroid family formation.  MNRAS 485, 697--707.  doi:10.1093/mnras/stz410.
  * Barnouin et al. (2023) Barnouin, O., Ballouz, R.L., Marchi, S., Vincent, J.B., Agrusa, H., Zhang, Y., Pajola, M., Tusberti, F., Daly, R.T., Ernst, C., Palmer, E., Michel, P., 2023.  The geology and evolution of the near-earth binary asteroid system (65803) didymos.  Nature Communications submitted.
  * Barnouin et al. (2019) Barnouin, O.S., Daly, M.G., Palmer, E.E., Gaskell, R.W., Weirich, J.R., Johnson, C.L., Al Asad, M.M., Roberts, J.H., Perry, M.E., Susorney, H.C.M., Daly, R.T., Bierhaus, E.B., Seabrook, J.A., Espiritu, R.C., Nair, A.H., Nguyen, L., Neumann, G.A., Ernst, C.M., Boynton, W.V., Nolan, M.C., Adam, C.D., Moreau, M.C., Rizk, B., Drouet D’Aubigny, C.Y., Jawin, E.R., Walsh, K.J., Michel, P., Schwartz, S.R., Ballouz, R.L., Mazarico, E.M., Scheeres, D.J., McMahon, J.W., Bottke, W.F., Sugita, S., Hirata, N., Hirata, N., Watanabe, S.I., Burke, K.N., Dellagiustina, D.N., Bennett, C.A., Lauretta, D.S., Osiris-Rex Team, Highsmith, D.E., Small, J., Vokrouhlický, D., Bowles, N.E., Brown, E., Donaldson Hanna, K.L., Warren, T., Brunet, C., Chicoine, R.A., Desjardins, S., Gaudreau, D., Haltigin, T., Millington-Veloza, S., Rubi, A., Aponte, J., Gorius, N., Lunsford, A., Allen, B., Grindlay, J., Guevel, D., Hoak, D., Hong, J., Schrader, D.L., Bayron, J., Golubov, O., Sánchez, P., Stromberg, J., Hirabayashi, M., Hartzell, C.M., Oliver, S., Rascon, M., Harch, A., Joseph, J., Squyres, S., Richardson, D., Emery, J.P., McGraw, L., Ghent, R., Binzel, R.P., Asad, M.M.A., Johnson, C.L., Philpott, L., Susorney, H.C.M., Cloutis, E.A., Hanna, R.D., Connolly, H.C., Ciceri, F., Hildebrand, A.R., Ibrahim, E.M., Breitenfeld, L., Glotch, T., Rogers, A.D., Clark, B.E., Ferrone, S., Thomas, C.A., Campins, H., Fernandez, Y., Chang, W., Cheuvront, A., Trang, D., Tachibana, S., Yurimoto, H., Brucato, J.R., Poggiali, G., Pajola, M., Dotto, E., Epifani, E.M., Crombie, M.K., Lantz, C., Izawa, M.R.M., de Leon, J., Licandro, J., Garcia, J.L.R., Clemett, S., Thomas-Keprta, K., van Wal, S., Yoshikawa, M., Bellerose, J., Bhaskaran, S., Boyles, C., Chesley, S.R., Elder, C.M., Farnocchia, D., Harbison, A., Kennedy, B., Knight, A., Martinez-Vlasoff, N., Mastrodemos, N., McElrath, T., Owen, W., Park, R., Rush, B., Swanson, L., Takahashi, Y., Velez, D., Yetter, K., Thayer, C., Adam, C., Antreasian, P., Bauman, J., Bryan, C., Carcich, B., Corvin, M., Geeraert, J., Hoffman, J., Leonard, J.M., Lessac-Chenen, E., Levine, A., McAdams, J., McCarthy, L., Nelson, D., Page, B., Pelgrift, J., Sahr, E., Stakkestad, K., Stanbridge, D., Wibben, D., Williams, B., Williams, K., Wolff, P., Hayne, P., Kubitschek, D., Barucci, M.A., Deshapriya, J.D.P., Fornasier, S., Fulchignoni, M., Hasselmann, P., Merlin, F., Praet, A., Bierhaus, E.B., Billett, O., Boggs, A., Buck, B., Carlson-Kelly, S., Cerna, J., Chaffin, K., Church, E., Coltrin, M., Daly, J., Deguzman, A., Dubisher, R., Eckart, D., Ellis, D., Falkenstern, P., Fisher, A., Fisher, M.E., Fleming, P., Fortney, K., Francis, S., Freund, S., Gonzales, S., Haas, P., Hasten, A., Hauf, D., Hilbert, A., Howell, D., Jaen, F., Jayakody, N., Jenkins, M., Johnson, K., Lefevre, M., Ma, H., Mario, C., Martin, K., May, C., McGee, M., Miller, B., Miller, C., Miller, G., Mirfakhrai, A., Muhle, E., Norman, C., Olds, R., Parish, C., Ryle, M., Schmitzer, M., Sherman, P., Skeen, M., Susak, M., Sutter, B., Tran, Q., Welch, C., Witherspoon, R., Wood, J., Zareski, J., Arvizu-Jakubicki, M., Asphaug, E., Audi, E., Ballouz, R.L., Bandrowski, R., Becker, K.J., Becker, T.L., Bendall, S., Bennett, C.A., Bloomenthal, H., Blum, D., Boynton, W.V., Brodbeck, J., Burke, K.N., Chojnacki, M., Colpo, A., Contreras, J., Cutts, J., D’Aubigny, C.Y.D., Dean, D., Dellagiustina, D.N., Diallo, B., Drinnon, D., Drozd, K., Enos, H.L., Enos, R., Fellows, C., Ferro, T., Fisher, M.R., Fitzgibbon, G., Fitzgibbon, M., Forelli, J., Forrester, T., Galinsky, I., Garcia, R., Gardner, A., Golish, D.R., Habib, N., Hamara, D., Hammond, D., Hanley, K., Harshman, K., Hergenrother, C.W., Herzog, K., Hill, D., Hoekenga, C., Hooven, S., Howell, E.S., Huettner, E., Janakus, A., Jones, J., Kareta, T.R., Kidd, J., Kingsbury, K., Balram-Knutson, S.S., Koelbel, L., Kreiner, J., Lambert, D., Lauretta, D.S., Lewin, C., Lovelace, B., Loveridge, M., Lujan, M., Maleszewski, C.K., Malhotra, R., Marchese, K., McDonough, E., Mogk, N., Morrison, V., Morton, E., Munoz, R., Nelson, J., Nolan, M.C., Padilla, J., Pennington, R., Polit, A., Ramos, N., Reddy, V., Riehl, M., Rizk, B., Roper, H.L., Salazar, S., Schwartz, S.R., Selznick, S., Shultz, N., Smith, P.H., Stewart, S., Sutton, S., Swindle, T., Tang, Y.H., Westermann, M., Wolner, C.W.V., Worden, D., Zega, T., Zeszut, Z., Bjurstrom, A., Bloomquist, L., Dickinson, C., Keates, E., Liang, J., Nifo, V., Taylor, A., Teti, F., Caplinger, M., Bowles, H., Carter, S., Dickenshied, S., Doerres, D., Fisher, T., Hagee, W., Hill, J., Miner, M., Noss, D., Piacentine, N., Smith, M., Toland, A., Wren, P., Bernacki, M., Munoz, D.P., Watanabe, S.I., Sandford, S.A., Aqueche, A., Ashman, B., Barker, M., Bartels, A., Berry, K., Bos, B., Burns, R., Calloway, A., Carpenter, R., Castro, N., Cosentino, R., Donaldson, J., Dworkin, J.P., Cook, J.E., Emr, C., Everett, D., Fennell, D., Fleshman, K., Folta, D., Gallagher, D., Garvin, J., Getzandanner, K., Glavin, D., Hull, S., Hyde, K., Ido, H., Ingegneri, A., Jones, N., Kaotira, P., Lim, L.F., Liounis, A., Lorentson, C., Lorenz, D., Lyzhoft, J., Mazarico, E.M., Mink, R., Moore, W., Moreau, M., Mullen, S., Nagy, J., Neumann, G., Nuth, J., Poland, D., Reuter, D.C., Rhoads, L., Rieger, S., Rowlands, D., Sallitt, D., Scroggins, A., Shaw, G., Simon, A.A., Swenson, J., Vasudeva, P., Wasser, M., Zellar, R., Grossman, J., Johnston, G., Morris, M., Wendel, J., Burton, A., Keller, L.P., McNamara, L., Messenger, S., Nakamura-Messenger, K., Nguyen, A., Righter, K., Queen, E., Bellamy, K., Dill, K., Gardner, S., Giuntini, M., Key, B., Kissell, J., Patterson, D., Vaughan, D., Wright, B., Gaskell, R.W., Le Corre, L., Li, J.Y., Molaro, J.L., Palmer, E.E., Siegler, M.A., Tricarico, P., Weirich, J.R., Zou, X.D., Ireland, T., Tait, K., Bland, P., Anwar, S., Bojorquez-Murphy, N., Christensen, P.R., Haberle, C.W., Mehall, G., Rios, K., Franchi, I., Rozitis, B., Beddingfield, C.B., Marshall, J., Brack, D.N., French, A.S., McMahon, J.W., Scheeres, D.J., Jawin, E.R., McCoy, T.J., Russell, S., Killgore, M., Bottke, W.F., Hamilton, V.E., Kaplan, H.H., Walsh, K.J., Bandfield, J.L., Clark, B.C., Chodas, M., Lambert, M., Masterson, R.A., Daly, M.G., Freemantle, J., Seabrook, J.A., Barnouin, O.S., Craft, K., Daly, R.T., Ernst, C., Espiritu, R.C., Holdridge, M., Jones, M., Nair, A.H., Nguyen, L., Peachey, J., Perry, M.E., Plescia, J., Roberts, J.H., Steele, R., Turner, R., Backer, J., Edmundson, K., Mapel, J., Milazzo, M., Sides, S., Manzoni, C., May, B., Delbo’, M., Libourel, G., Michel, P., Ryan, A., Thuillet, F., Marty, B., 2019.  Shape of (101955) Bennu indicative of a rubble pile with internal stiffness.  Nature Geoscience 12, 247--252.  doi:10.1038/s41561-019-0330-x.
  * Barzilai and Borwein (1988) Barzilai, J., Borwein, J.M., 1988.  Two-Point Step Size Gradient Methods.  IMA Journal of Numerical Analysis 8, 141--148.  URL: https://doi.org/10.1093/imanum/8.1.141, doi:10.1093/imanum/8.1.141, arXiv:https://academic.oup.com/imajna/article-pdf/8/1/141/2402762/8-1-141.pdf.
  * Benavidez et al. (2012) Benavidez, P.G., Durda, D.D., Enke, B.L., Bottke, W.F., Nesvorný, D., Richardson, D.C., Asphaug, E., Merline, W.J., 2012.  A comparison between rubble-pile and monolithic targets in impact simulations: Application to asteroid satellites and family size distributions.  Icarus 219, 57--76.  doi:10.1016/j.icarus.2012.01.015.
  * Benner et al. (2015) Benner, L.A.M., Busch, M.W., Giorgini, J.D., Taylor, P.A., Margot, J.L., 2015.  Radar Observations of Near-Earth and Main-Belt Asteroids, in: Asteroids IV, pp. 165--182.  doi:10.2458/azu_uapress_9780816532131-ch009.
  * Benz and Asphaug (1994) Benz, W., Asphaug, E., 1994.  Impact simulations with fracture. i. method and tests.  Icarus 107, 98--116.  URL: https://www.sciencedirect.com/science/article/pii/S0019103584710098, doi:https://doi.org/10.1006/icar.1994.1009.
  * Benz and Asphaug (1995) Benz, W., Asphaug, E., 1995.  Simulations of brittle solids using smooth particle hydrodynamics.  Computer Physics Communications 87, 253--265.  URL: https://www.sciencedirect.com/science/article/pii/0010465594001763, doi:https://doi.org/10.1016/0010-4655(94)00176-3. particle Simulation Methods.
  * Benz and Asphaug (1999) Benz, W., Asphaug, E., 1999.  Catastrophic Disruptions Revisited.  Icarus 142, 5--20.  doi:10.1006/icar.1999.6204, arXiv:astro-ph/9907117.
  * Boldrin et al. (2016) Boldrin, L.A.G., Scheeres, D.J., Winter, O.C., 2016.  Dynamics of rotationally fissioned asteroids: non-planar case.  MNRAS 461, 3982--3992.  doi:10.1093/mnras/stw1607.
  * Bottke et al. (2002) Bottke, W. F., J., Vokrouhlický, D., Rubincam, D.P., Broz, M., 2002.  The Effect of Yarkovsky Thermal Forces on the Dynamical Evolution of Asteroids and Meteoroids, in: Asteroids III, pp. 395--408.
  * Bottke et al. (2006) Bottke, William F., J., Vokrouhlický, D., Rubincam, D.P., Nesvorný, D., 2006.  The Yarkovsky and Yorp Effects: Implications for Asteroid Dynamics.  Annual Review of Earth and Planetary Sciences 34, 157--191.  doi:10.1146/annurev.earth.34.031405.125154.
  * Chabot et al. (2024) Chabot, N.L., Rivkin, A.S., Cheng, A.F., Barnouin, O.S., Fahnestock, E.G., Richardson, D.C., Stickle, A.M., Thomas, C.A., Ernst, C.M., Terik Daly, R., Dotto, E., Zinzi, A., Chesley, S.R., Moskovitz, N.A., Barbee, B.W., Abell, P., Agrusa, H.F., Bannister, M.T., Beccarelli, J., Bekker, D.L., Bruck Syal, M., Buratti, B.J., Busch, M.W., Campo Bagatin, A., Chatelain, J.P., Chocron, S., Collins, G.S., Conversi, L., Davison, T.M., DeCoster, M.E., Prasanna Deshapriya, J.D., Eggl, S., Espiritu, R.C., Farnham, T.L., Ferrais, M., Ferrari, F., Föhring, D., Fuentes-Muñoz, O., Gai, I., Giordano, C., Glenar, D.A., Gomez, E., Graninger, D.M., Green, S.F., Greenstreet, S., Hasselmann, P.H., Herreros, I., Hirabayashi, M., Husárik, M., Ieva, S., Ivanovski, S.L., Jackson, S.L., Jehin, E., Jutzi, M., Karatekin, O., Knight, M.M., Kolokolova, L., Kumamoto, K.M., Küppers, M., La Forgia, F., Lazzarin, M., Li, J.Y., Lister, T.A., Lolachi, R., Lucas, M.P., Lucchetti, A., Luther, R., Makadia, R., Mazzotta Epifani, E., McMahon, J., Merisio, G., Merrill, C.C., Meyer, A.J., Michel, P., Micheli, M., Migliorini, A., Minker, K., Modenini, D., Moreno, F., Murdoch, N., Murphy, B., Naidu, S.P., Nair, H., Nakano, R., Opitom, C., Ormö, J., Michael Owen, J., Pajola, M., Palmer, E.E., Palumbo, P., Panicucci, P., Parro, L.M., Pearl, J.M., Penttilä, A., Perna, D., Petrescu, E., Pravec, P., Raducan, S.D., Ramesh, K.T., Ridden-Harper, R., Rizos, J.L., Rossi, A., Roth, N.X., Rożek, A., Rozitis, B., Ryan, E.V., Ryan, W.H., Sánchez, P., Santana-Ros, T., Scheeres, D.J., Scheirich, P., Senel, C.B., Snodgrass, C., Soldini, S., Souami, D., Statler, T.S., Street, R., Stubbs, T.J., Sunshine, J.M., Tan, N.J., Tancredi, G., Tinsman, C.L., Tortora, P., Tusberti, F., Walker, J.D., Waller, C.D., Wünnemann, K., Zannoni, M., Zhang, Y., 2024.  Achievement of the Planetary Defense Investigations of the Double Asteroid Redirection Test (DART) Mission.  PSJ 5, 49.  doi:10.3847/PSJ/ad16e6.
  * Charnoz et al. (2010) Charnoz, S., Salmon, J., Crida, A., 2010.  The recent formation of Saturn’s moonlets from viscous spreading of the main rings.  Nature 465, 752--754.  doi:10.1038/nature09096.
  * Cotto-Figueroa et al. (2015) Cotto-Figueroa, D., Statler, T.S., Richardson, D.C., Tanga, P., 2015.  Coupled Spin and Shape Evolution of Small Rubble-pile Asteroids: Self-limitation of the YORP Effect.  ApJ 803, 25.  doi:10.1088/0004-637X/803/1/25, arXiv:1411.1114.
  * Crida and Charnoz (2012) Crida, A., Charnoz, S., 2012.  Formation of Regular Satellites from Ancient Massive Rings in the Solar System.  Science 338, 1196.  doi:10.1126/science.1226477, arXiv:1301.3808.
  * Ćuk and Burns (2005) Ćuk, M., Burns, J.A., 2005.  Effects of thermal radiation on the dynamics of binary NEAs.  Icarus 176, 418--431.  doi:10.1016/j.icarus.2005.02.001.
  * Da et al. (2023) Da, T.K.F., Loriot, S., Yvinec, M., 2023.  3D alpha shapes, in: CGAL User and Reference Manual. 5.5.2 ed.. CGAL Editorial Board.  URL: https://doc.cgal.org/5.5.2/Manual/packages.html#PkgAlphaShapes3.
  * Daly et al. (2023a) Daly, R.T., Ernst, C.M., Barnouin, O.S., Chabot, N.L., Rivkin, A.S., Cheng, A.F., Adams, E.Y., Agrusa, H.F., Abel, E.D., Alford, A.L., Asphaug, E.I., Atchison, J.A., Badger, A.R., Baki, P., Ballouz, R.L., Bekker, D.L., Bellerose, J., Bhaskaran, S., Buratti, B.J., Cambioni, S., Chen, M.H., Chesley, S.R., Chiu, G., Collins, G.S., Cox, M.W., DeCoster, M.E., Ericksen, P.S., Espiritu, R.C., Faber, A.S., Farnham, T.L., Ferrari, F., Fletcher, Z.J., Gaskell, R.W., Graninger, D.M., Haque, M.A., Harrington-Duff, P.A., Hefter, S., Herreros, I., Hirabayashi, M., Huang, P.M., Hsieh, S.Y.W., Jacobson, S.A., Jenkins, S.N., Jensenius, M.A., John, J.W., Jutzi, M., Kohout, T., Krueger, T.O., Laipert, F.E., Lopez, N.R., Luther, R., Lucchetti, A., Mages, D.M., Marchi, S., Martin, A.C., McQuaide, M.E., Michel, P., Moskovitz, N.A., Murphy, I.W., Murdoch, N., Naidu, S.P., Nair, H., Nolan, M.C., Ormö, J., Pajola, M., Palmer, E.E., Peachey, J.M., Pravec, P., Raducan, S.D., Ramesh, K.T., Ramirez, J.R., Reynolds, E.L., Richman, J.E., Robin, C.Q., Rodriguez, L.M., Roufberg, L.M., Rush, B.P., Sawyer, C.A., Scheeres, D.J., Scheirich, P., Schwartz, S.R., Shannon, M.P., Shapiro, B.N., Shearer, C.E., Smith, E.J., Steele, R.J., Steckloff, J.K., Stickle, A.M., Sunshine, J.M., Superfin, E.A., Tarzi, Z.B., Thomas, C.A., Thomas, J.R., Trigo-Rodríguez, J.M., Tropf, B.T., Vaughan, A.T., Velez, D., Waller, C.D., Wilson, D.S., Wortman, K.A., Zhang, Y., 2023a.  Successful kinetic impact into an asteroid for planetary defence.  Nature 616, 443--447.  doi:10.1038/s41586-023-05810-5.
  * Daly et al. (2023b) Daly, R.T., Ernst, C.M., Barnouin, O.S., Gaskell, R.W., Nair, H., Agrusa, H.F., Chabot, N.L., Cheng, A.F., Dotto, E., Mazzotta Epifani, E., Espiritu, R.C., Farnham, T.L., Palmer, E.E., Pravec, P., Rivkin, A.S., Waller, C.D., Zinzi, A., the DART and LICIACube teams, 2023b.  An updated shape model of dimorphos from dart data.  The Planetary Science Journal submitted.
  * Davis and Scheeres (2020) Davis, A.B., Scheeres, D.J., 2020.  High-fidelity Modeling of Rotationally Fissioned Asteroids.  PSJ 1, 25.  doi:10.3847/PSJ/ab9a39.
  * DeMartini et al. (2019) DeMartini, J.V., Richardson, D.C., Barnouin, O.S., Schmerr, N.C., Plescia, J.B., Scheirich, P., Pravec, P., 2019.  Using a discrete element method to investigate seismic response and spin change of 99942 Apophis during its 2029 tidal encounter with Earth.  Icarus 328, 93--103.  doi:10.1016/j.icarus.2019.03.015.
  * Dotto et al. (2024) Dotto, E., Deshapriya, J., Gai, I., Hasselmann, P., Mazzotta Epifani, E., Poggiali, G., Rossi, A., Zanotti, G., Zinzi, A., Bertini, I., Brucato, J., Dall’Ora, M., Della Corte, V., Ivanovski, S., Lucchetti, A., Pajola, M., Amoroso, M., Barnouin, O., Campo Bagatin, A., Capannolo, A., Caporali, S., Ceresoli, M., Chabot, N., Cheng, A., Cremonese, G., Fahnestock, E., Farnham, T., Ferrari, F., Gomez Casajus, L., Gramigna, E., Hirabayashi, M., Ieva, S., Impresario, G., Jutzi, M., Lasagni Manghi, R., Lavagna, M., Li, J.Y., Lombardo, M., Modenini, D., Palumbo, P., Perna, D., Pirrotta, S., Raducan, S., Richardson, D., Rivkin, A., Stickle, A., Tortora, P., Tusberti, F., Zannoni, M., 2024.  The dimorphos ejecta plume properties revealed by liciacube.  Nature doi:10.1038/s41586-023-06998-2.
  * Durda et al. (2004) Durda, D.D., Bottke, W.F., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C., Leinhardt, Z.M., 2004.  The formation of asteroid satellites in large impacts: results from numerical simulations.  Icarus 167, 382--396.  doi:10.1016/j.icarus.2003.09.017.
  * Durda et al. (2007) Durda, D.D., Bottke, W.F., Nesvorný, D., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C., 2007.  Size-frequency distributions of fragments from SPH/ N-body simulations of asteroid impacts: Comparison with observed asteroid families.  Icarus 186, 498--516.  doi:10.1016/j.icarus.2006.09.013.
  * Edelsbrunner and Mücke (1994) Edelsbrunner, H., Mücke, E., 1994.  Three-dimensional alpha shapes.  URL: https://arxiv.org/abs/math/9410208, doi:10.48550/ARXIV.MATH/9410208.
  * Ester et al. (1996) Ester, M., Kriegel, H.P., Sander, J., Xu, X., et al., 1996.  A density-based algorithm for discovering clusters in large spatial databases with noise.
  * Ferrari et al. (2020) Ferrari, F., Lavagna, M., Blazquez, E., 2020.  A parallel-GPU code for asteroid aggregation problems with angular particles.  MNRAS 492, 749--761.  doi:10.1093/mnras/stz3458, arXiv:1912.04197.
  * Ferrari et al. (2022) Ferrari, F., Raducan, S.D., Soldini, S., Jutzi, M., 2022.  Ejecta Formation, Early Collisional Processes, and Dynamical Evolution after the DART Impact on Dimorphos.  PSJ 3, 177.  doi:10.3847/PSJ/ac7cf0.
  * Ferrari and Tanga (2020) Ferrari, F., Tanga, P., 2020.  The role of fragment shapes in the simulations of asteroids as gravitational aggregates.  Icarus 350, 113871.  doi:10.1016/j.icarus.2020.113871, arXiv:2005.14032.
  * Ferrari and Tanga (2022) Ferrari, F., Tanga, P., 2022.  Interior of top-shaped asteroids with cohesionless surface.  Icarus 378, 114914.  doi:10.1016/j.icarus.2022.114914.
  * Ferrari et al. (2017) Ferrari, F., Tasora, A., Masarati, P., Lavagna, M., 2017.  N-body gravitational and contact dynamics for asteroid aggregation.  Multibody System Dynamics 39, 3--20.
  * Fleischmann et al. (2016) Fleischmann, J., Serban, R., Negrut, D., Jayakumar, P., 2016.  On the importance of displacement history in soft-body contact models.  Journal of Computational and Nonlinear Dynamics 11, 044502.
  * Harris et al. (2009) Harris, A.W., Fahnestock, E.G., Pravec, P., 2009.  On the shapes and spins of “rubble pile” asteroids.  Icarus 199, 310--318.  doi:10.1016/j.icarus.2008.09.012.
  * Hirabayashi (2015) Hirabayashi, M., 2015.  Failure modes and conditions of a cohesive, spherical body due to YORP spin-up.  MNRAS 454, 2249--2257.  doi:10.1093/mnras/stv2017, arXiv:1508.06913.
  * Hirabayashi et al. (2015) Hirabayashi, M., Sánchez, D.P., Scheeres, D.J., 2015.  Internal Structure of Asteroids Having Surface Shedding Due to Rotational Instability.  ApJ 808, 63.  doi:10.1088/0004-637X/808/1/63, arXiv:1506.03354.
  * Hirabayashi and Scheeres (2015) Hirabayashi, M., Scheeres, D.J., 2015.  Stress and Failure Analysis of Rapidly Rotating Asteroid (29075) 1950 DA.  ApJ 798, L8.  doi:10.1088/2041-8205/798/1/L8, arXiv:1411.5926.
  * Ho et al. (2022) Ho, A., Wold, M., Poursina, M., Conway, J.T., 2022.  Dynamics of asteroid systems post-rotational fission.  A&A 665, A43.  doi:10.1051/0004-6361/202243706, arXiv:2206.11570.
  * Holsapple (2010) Holsapple, K.A., 2010.  On YORP-induced spin deformations of asteroids.  Icarus 205, 430--442.  doi:10.1016/j.icarus.2009.08.014.
  * Holsapple and Michel (2006) Holsapple, K.A., Michel, P., 2006.  Tidal disruptions: A continuum theory for solid bodies.  Icarus 183, 331--348.  doi:10.1016/j.icarus.2006.03.013.
  * Holsapple and Michel (2008) Holsapple, K.A., Michel, P., 2008.  Tidal disruptions. II. A continuum theory for solid bodies with strength, with applications to the Solar System.  Icarus 193, 283--301.  doi:10.1016/j.icarus.2007.09.011.
  * Huchra and Geller (1982) Huchra, J.P., Geller, M.J., 1982.  Groups of Galaxies. I. Nearby groups.  ApJ 257, 423--437.  doi:10.1086/160000.
  * Hyodo and Sugiura (2022) Hyodo, R., Sugiura, K., 2022.  Formation of Moons and Equatorial Ridge around Top-shaped Asteroids after Surface Landslide.  ApJ 937, L36.  doi:10.3847/2041-8213/ac922d, arXiv:2209.07045.
  * Ida et al. (1997) Ida, S., Canup, R.M., Stewart, G.R., 1997.  Lunar accretion from an impact-generated disk.  Nature 389, 353--357.  doi:10.1038/38669.
  * Jacobson et al. (2016) Jacobson, S.A., Marzari, F., Rossi, A., Scheeres, D.J., 2016.  Matching asteroid population characteristics with a model constructed from the YORP-induced rotational fission hypothesis.  Icarus 277, 381--394.  doi:10.1016/j.icarus.2016.05.032, arXiv:1605.06157.
  * Jacobson and Scheeres (2011a) Jacobson, S.A., Scheeres, D.J., 2011a.  Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems.  Icarus 214, 161--178.  doi:10.1016/j.icarus.2011.04.009, arXiv:1404.0801.
  * Jacobson and Scheeres (2011b) Jacobson, S.A., Scheeres, D.J., 2011b.  Long-term Stable Equilibria for Synchronous Binary Asteroids.  ApJ 736, L19.  doi:10.1088/2041-8205/736/1/L19, arXiv:1104.4671.
  * Johansen and Lambrechts (2017) Johansen, A., Lambrechts, M., 2017.  Forming Planets via Pebble Accretion.  Annual Review of Earth and Planetary Sciences 45, 359--387.  doi:10.1146/annurev-earth-063016-020226.
  * Jutzi (2014) Jutzi, M., 2014.  Sph calculations of asteroid disruptions: The role of pressure dependent failure models.  Planetary and Space Science 107.  doi:10.1016/j.pss.2014.09.012.
  * Jutzi (2015) Jutzi, M., 2015.  Sph calculations of asteroid disruptions: The role of pressure dependent failure models.  Planetary and Space Science 107, 3--9.  URL: https://www.sciencedirect.com/science/article/pii/S0032063314002931, doi:https://doi.org/10.1016/j.pss.2014.09.012. vIII Workshop on Catastrophic Disruption in the Solar System.
  * Jutzi and Asphaug (2015) Jutzi, M., Asphaug, E., 2015.  The shape and structure of cometary nuclei as a result of low-velocity accretion.  Science 348, 1355--1358.  doi:10.1126/science.aaa4747.
  * Jutzi et al. (2008) Jutzi, M., Benz, W., Michel, P., 2008.  Numerical simulations of impacts involving porous bodies: I. implementing sub-resolution porosity in a 3d sph hydrocode.  Icarus 198, 242--255.  URL: https://www.sciencedirect.com/science/article/pii/S0019103508002558, doi:https://doi.org/10.1016/j.icarus.2008.06.013.
  * Jutzi et al. (2022) Jutzi, M., Raducan, S.D., Zhang, Y., Michel, P., Arakawa, M., 2022.  Constraining surface properties of asteroid (162173) ryugu from numerical simulations of hayabusa2 mission impact experiment.  Nature Communications 13, 7134.  URL: https://doi.org/10.1038/s41467-022-34540-x, doi:10.1038/s41467-022-34540-x.
  * Kokubo et al. (2000) Kokubo, E., Ida, S., Makino, J., 2000.  Evolution of a Circumterrestrial Disk and Formation of a Single Moon.  Icarus 148, 419--436.  doi:10.1006/icar.2000.6496.
  * Korycansky and Asphaug (2006) Korycansky, D.G., Asphaug, E., 2006.  Low-speed impacts between rubble piles modeled as collections of polyhedra.  Icarus 181, 605--617.  doi:10.1016/j.icarus.2005.10.028.
  * Korycansky and Asphaug (2009) Korycansky, D.G., Asphaug, E., 2009.  Low-speed impacts between rubble piles modeled as collections of polyhedra, 2.  Icarus 204, 316--329.  doi:10.1016/j.icarus.2009.06.006.
  * Leisner et al. (2020) Leisner, A., Richardson, D., Statler, T., Nichols, W., Zhang, Y., 2020.  An extended parameter space study of the effect of cohesion in gravitational aggregates through spin-up simulations.  Planetary and Space Science 182.  URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85078214335&doi=10.1016%2fj.pss.2020.104845&partnerID=40&md5=a72106a33ba22b58f228f3620eb534c9, doi:10.1016/j.pss.2020.104845. cited by: 4; All Open Access, Bronze Open Access.
  * Leleu et al. (2018) Leleu, A., Jutzi, M., Rubin, M., 2018.  The peculiar shapes of Saturn’s small inner moons as evidence of mergers of similar-sized moonlets.  Nature Astronomy 2, 555--561.  doi:10.1038/s41550-018-0471-7, arXiv:1805.08682.
  * Levison et al. (2024) Levison, H.F., Marchi, S., Noll, K.S., Spencer, J.R., Statler, T.S., Bell, J.F., Bierhaus, E.B., Binzel, R., Bottke, W.F., Britt, D., Brown, M.E., Buie, M.W., Christensen, P.R., Dello Russo, N., Emery, J.P., Grundy, W.M., Hahn, M., Hamilton, V.E., Howett, C., Kaplan, H., Kretke, K., Lauer, T.R., Manzoni, C., Marschall, R., Martin, A.C., May, B.H., Mottola, S., Olkin, C.B., Pätzold, M., Parker, J.W., Porter, S., Preusker, F., Protopapa, S., Reuter, D.C., Robbins, S.J., Salmon, J., Simon, A.A., Stern, S.A., Sunshine, J.M., Wong, I., Weaver, H.A., Adam, C., Ancheta, S., Andrews, J., Anwar, S., Barnouin, O.S., Beasley, M., Berry, K.E., Birath, E., Bolin, B., Booco, M., Burns, R., Campbell, P., Carpenter, R., Crombie, K., Effertz, M., Eifert, E., Ellis, C., Faiks, P., Fischetti, J., Fleming, P., Francis, K., Franco, R., Freund, S., Gallagher, C., Geeraert, J., Gobat, C., Gorgas, D., Granat, C., Gray, S., Haas, P., Harch, A., Hegedus, K., Isabelle, C., Jackson, B., Jacob, T., Jennings, S., Kaufmann, D., Keeney, B.A., Kennedy, T., Lauffer, K., Lessac-Chenen, E., Leonard, R., Levine, A., Lunsford, A., Martin, T., McAdams, J., Mehall, G., Merkley, T., Miller, G., Montanaro, M., Montgomery, A., Murphy, G., Myers, M., Nelson, D.S., Ocampo, A., Olds, R., Pelgrift, J.Y., Perkins, T., Pineau, J., Poland, D., Ramanan, V., Rose, D., Sahr, E., Short, O., Solanki, I., Stanbridge, D., Sutter, B., Talpas, Z., Taylor, H., Treiu, B., Vermeer, N., Vincent, M., Wallace, M., Weigle, G., Wibben, D.R., Wiens, Z., Wilson, J.P., Zhao, Y., 2024.  A contact binary satellite of the asteroid (152830) Dinkinesh.  Nature 629, 1015--1020.  doi:10.1038/s41586-024-07378-0, arXiv:2406.19337.
  * Levison et al. (2021) Levison, H.F., Olkin, C.B., Noll, K.S., Marchi, S., Bell, James F., I., Bierhaus, E., Binzel, R., Bottke, W., Britt, D., Brown, M., Buie, M., Christensen, P., Emery, J., Grundy, W., Hamilton, V.E., Howett, C., Mottola, S., Pätzold, M., Reuter, D., Spencer, J., Statler, T.S., Stern, S.A., Sunshine, J., Weaver, H., Wong, I., 2021.  Lucy Mission to the Trojan Asteroids: Science Goals.  PSJ 2, 171.  doi:10.3847/PSJ/abf840.
  * Li et al. (2021) Li, D., Mustill, A.J., Davies, M.B., 2021.  Accretion of tidally disrupted asteroids on to white dwarfs: direct accretion versus disc processing.  MNRAS 508, 5671--5686.  doi:10.1093/mnras/stab2949, arXiv:2106.00441.
  * Li et al. (2023) Li, J.Y., Hirabayashi, M., Farnham, T.L., Sunshine, J.M., Knight, M.M., Tancredi, G., Moreno, F., Murphy, B., Opitom, C., Chesley, S., Scheeres, D.J., Thomas, C.A., Fahnestock, E.G., Cheng, A.F., Dressel, L., Ernst, C.M., Ferrari, F., Fitzsimmons, A., Ieva, S., Ivanovski, S.L., Kareta, T., Kolokolova, L., Lister, T., Raducan, S.D., Rivkin, A.S., Rossi, A., Soldini, S., Stickle, A.M., Vick, A., Vincent, J.B., Weaver, H.A., Bagnulo, S., Bannister, M.T., Cambioni, S., Bagatin, A.C., Chabot, N.L., Cremonese, G., Daly, R.T., Dotto, E., Glenar, D.A., Granvik, M., Hasselmann, P.H., Herreros, I., Jacobson, S., Jutzi, M., Kohout, T., Forgia, F.L., Lazzarin, M., Lin, Z.Y., Lolachi, R., Lucchetti, A., Makadia, R., Epifani, E.M., Michel, P., Migliorini, A., Moskovitz, N.A., Ormö, J., Pajola, M., Sánchez, P., Schwartz, S.R., Snodgrass, C., Steckloff, J., Stubbs, T.J., Trigo-Rodríguez, J.M., 2023.  Ejecta from the DART-produced active asteroid dimorphos.  Nature 616, 452--456.  doi:10.1038/s41586-023-05811-4.
  * Liu et al. (2015) Liu, B., Zhang, X., Lin, D.N.C., Aarseth, S.J., 2015.  Migration and Growth of Protoplanetary Embryos. II. Emergence of Proto-Gas-Giant Cores versus Super Earth Progenitors.  ApJ 798, 62.  doi:10.1088/0004-637X/798/1/62, arXiv:1410.7952.
  * Madeira and Charnoz (2024) Madeira, G., Charnoz, S., 2024.  Revisiting Dimorphos formation: A pyramidal regime perspective and application to Dinkinesh’s satellite.  Icarus 409, 115871.  doi:10.1016/j.icarus.2023.115871, arXiv:2311.07271.
  * Madeira et al. (2023) Madeira, G., Charnoz, S., Hyodo, R., 2023.  Dynamical origin of Dimorphos from fast spinning Didymos.  Icarus 394, 115428.  doi:10.1016/j.icarus.2023.115428, arXiv:2301.02121.
  * Madeira et al. (2024) Madeira, G., Charnoz, S., Rambaux, N., Robutel, P., 2024.  Long-term dust dynamics in Didymos and Dimorphos system: Production, stability, and transport.  Icarus 412, 115997.  doi:10.1016/j.icarus.2024.115997, arXiv:2402.03943.
  * Madeira et al. (2022) Madeira, G., Giuliatti Winter, S.M., Ribeiro, T., Winter, O.C., 2022.  Dynamics around non-spherical symmetric bodies - I. The case of a spherical body with mass anomaly.  MNRAS 510, 1450--1469.  doi:10.1093/mnras/stab3552, arXiv:2112.01817.
  * Margot et al. (2002) Margot, J.L., Nolan, M.C., Benner, L.A.M., Ostro, S.J., Jurgens, R.F., Giorgini, J.D., Slade, M.A., Campbell, D.B., 2002.  Binary Asteroids in the Near-Earth Object Population.  Science 296, 1445--1448.  doi:10.1126/science.1072094.
  * Marohnic et al. (2023) Marohnic, J.C., DeMartini, J.V., Richardson, D.C., Zhang, Y., Walsh, K.J., 2023.  An Efficient Numerical Approach to Modeling the Effects of Particle Shape on Rubble-pile Dynamics.  PSJ 4, 245.  doi:10.3847/PSJ/ad0467, arXiv:2311.11322.
  * Meyer and Scheeres (2024) Meyer, A.J., Scheeres, D.J., 2024.  The Strength and Shapes of Contact Binary Objects.  ApJ 963, L14.  doi:10.3847/2041-8213/ad2853, arXiv:2402.07760.
  * Michel et al. (2003) Michel, P., Benz, W., Richardson, D.C., 2003.  Disruption of fragmented parent bodies as the origin of asteroid families.  Nature 421, 608--611.  doi:10.1038/nature01364.
  * Michel et al. (2004) Michel, P., Benz, W., Richardson, D.C., 2004.  Catastrophic disruption of pre-shattered parent bodies.  Icarus 168, 420--432.  doi:10.1016/j.icarus.2003.12.011.
  * Michel et al. (2001) Michel, P., Benz, W., Tanga, P., Richardson, D.C., 2001.  Collisions and Gravitational Reaccumulation: Forming Asteroid Families and Satellites.  Science 294, 1696--1700.  doi:10.1126/science.1065189.
  * Michel et al. (2022) Michel, P., Küppers, M., Bagatin, A.C., Carry, B., Charnoz, S., de Leon, J., Fitzsimmons, A., Gordo, P., Green, S.F., Hérique, A., Juzi, M., Karatekin, Ö., Kohout, T., Lazzarin, M., Murdoch, N., Okada, T., Palomba, E., Pravec, P., Snodgrass, C., Tortora, P., Tsiganis, K., Ulamec, S., Vincent, J.B., Wünnemann, K., Zhang, Y., Raducan, S.D., Dotto, E., Chabot, N., Cheng, A.F., Rivkin, A., Barnouin, O., Ernst, C., Stickle, A., Richardson, D.C., Thomas, C., Arakawa, M., Miyamoto, H., Nakamura, A., Sugita, S., Yoshikawa, M., Abell, P., Asphaug, E., Ballouz, R.L., Bottke, W.F., Lauretta, D.S., Walsh, K.J., Martino, P., Carnelli, I., 2022.  The ESA Hera Mission: Detailed Characterization of the DART Impact Outcome and of the Binary Asteroid (65803) Didymos.  PSJ 3, 160.  doi:10.3847/PSJ/ac6f52.
  * Michel et al. (2002) Michel, P., Tanga, P., Benz, W., Richardson, D.C., 2002.  Formation of Asteroid Families by Catastrophic Disruption: Simulations with Fragmentation and Gravitational Reaccumulation.  Icarus 160, 10--23.  doi:10.1006/icar.2002.6948.
  * Monteiro et al. (2023) Monteiro, F., Lazzaro, D., Rondón, E., Arcoverde, P., Evangelista-Santana, M., Michimani, J., Pereira, W., Mesquita, W., Medeiros, H., Corrêa, T., Silva-Cabrera, J., Rodrigues, T., 2023.  Lightcurve analysis of near-Earth objects from the IMPACTON project: Evidence of binary systems and cohesion strength.  Icarus 390, 115297.  doi:10.1016/j.icarus.2022.115297.
  * Movshovitz et al. (2012) Movshovitz, N., Asphaug, E., Korycansky, D., 2012.  Numerical Modeling of the Disruption of Comet D/1993 F2 Shoemaker-Levy 9 Representing the Progenitor by a Gravitationally Bound Assemblage of Randomly Shaped Polyhedra.  ApJ 759, 93.  doi:10.1088/0004-637X/759/2/93, arXiv:1207.3386.
  * Naidu et al. (2023) Naidu, S.P., Chesley, S.R., Moskovitz, N., Thomas, C., Meyer, A.J., Pravec, P., Scheirich, P., Farnocchia, D., Brozovic, M., Benner, L.A., Rivkin, A.S., Chabot, N.L., 2023.  Orbital and physical characterization of dimorphos following the dart impact.  The Planetary Science Journal submitted.
  * Pajola et al. (2023) Pajola, M., Tusberti, F., Liucchetti, A., Barnouin, O., Cambioni, S., Ernst, C.M., Dotto, E., Poggiali, G., Hirabayashi, M., Nakano, R., Mazzotta Epifani, E., Chabot, N.L., Della Corte, V., Rivkin, A., Agrusa, H., Zhang, Y., 2023.  Evidence for multi-fragmentation and mass shedding of boulders on rubble-pile binary asteroids.  Nature Communications submitted.
  * Porco et al. (2007) Porco, C.C., Thomas, P.C., Weiss, J.W., Richardson, D.C., 2007.  Saturn’s Small Inner Satellites: Clues to Their Origins.  Science 318, 1602.  doi:10.1126/science.1143977.
  * Pravec et al. (2019) Pravec, P., Fatka, P., Vokrouhlický, D., Scheirich, P., Ďurech, J., Scheeres, D.J., Kušnirák, P., Hornoch, K., Galád, A., Pray, D.P., Krugly, Y.N., Burkhonov, O., Ehgamberdiev, S.A., Pollock, J., Moskovitz, N., Thirouin, A., Ortiz, J.L., Morales, N., Husárik, M., Inasaridze, R.Y., Oey, J., Polishook, D., Hanuš, J., Kučáková, H., Vraštil, J., Világi, J., Gajdoš, Š., Kornoš, L., Vereš, P., Gaftonyuk, N.M., Hromakina, T., Sergeyev, A.V., Slyusarev, I.G., Ayvazian, V.R., Cooney, W.R., Gross, J., Terrell, D., Colas, F., Vachier, F., Slivan, S., Skiff, B., Marchis, F., Ergashev, K.E., Kim, D.H., Aznar, A., Serra-Ricart, M., Behrend, R., Roy, R., Manzini, F., Molotov, I.E., 2019.  Asteroid pairs: A complex picture.  Icarus 333, 429--463.  doi:10.1016/j.icarus.2019.05.014, arXiv:1901.05492.
  * Pravec and Harris (2000) Pravec, P., Harris, A.W., 2000.  Fast and Slow Rotation of Asteroids.  Icarus 148, 12--20.  doi:10.1006/icar.2000.6482.
  * Pravec and Harris (2007) Pravec, P., Harris, A.W., 2007.  Binary asteroid population. 1. Angular momentum content.  Icarus 190, 250--259.  doi:10.1016/j.icarus.2007.02.023.
  * Pravec et al. (2002) Pravec, P., Harris, A.W., Michalowski, T., 2002.  Asteroid Rotations.  pp. 113--122.
  * Pravec et al. (2016) Pravec, P., Scheirich, P., Kušnirák, P., Hornoch, K., Galád, A., Naidu, S.P., Pray, D.P., Világi, J., Gajdoš, Š., Kornoš, L., Krugly, Y.N., Cooney, W.R., Gross, J., Terrell, D., Gaftonyuk, N., Pollock, J., Husárik, M., Chiorny, V., Stephens, R.D., Durkee, R., Reddy, V., Dyvig, R., Vraštil, J., Žižka, J., Mottola, S., Hellmich, S., Oey, J., Benishek, V., Kryszczyńska, A., Higgins, D., Ries, J., Marchis, F., Baek, M., Macomber, B., Inasaridze, R., Kvaratskhelia, O., Ayvazian, V., Rumyantsev, V., Masi, G., Colas, F., Lecacheux, J., Montaigut, R., Leroy, A., Brown, P., Krzeminski, Z., Molotov, I., Reichart, D., Haislip, J., LaCluyze, A., 2016.  Binary asteroid population. 3. Secondary rotations and elongations.  Icarus 267, 267--295.  doi:10.1016/j.icarus.2015.12.019.
  * Pravec et al. (2006) Pravec, P., Scheirich, P., Kušnirák, P., Šarounová, L., Mottola, S., Hahn, G., Brown, P., Esquerdo, G., Kaiser, N., Krzeminski, Z., Pray, D.P., Warner, B.D., Harris, A.W., Nolan, M.C., Howell, E.S., Benner, L.A.M., Margot, J.L., Galád, A., Holliday, W., Hicks, M.D., Krugly, Y.N., Tholen, D., Whiteley, R., Marchis, F., DeGraff, D.R., Grauer, A., Larson, S., Velichko, F.P., Cooney, W.R., Stephens, R., Zhu, J., Kirsch, K., Dyvig, R., Snyder, L., Reddy, V., Moore, S., Gajdoš, Š., Világi, J., Masi, G., Higgins, D., Funkhouser, G., Knight, B., Slivan, S., Behrend, R., Grenon, M., Burki, G., Roy, R., Demeautis, C., Matter, D., Waelchli, N., Revaz, Y., Klotz, A., Rieugné, M., Thierry, P., Cotrez, V., Brunetto, L., Kober, G., 2006.  Photometric survey of binary near-Earth asteroids.  Icarus 181, 63--93.  doi:10.1016/j.icarus.2005.10.014.
  * Quillen et al. (2022) Quillen, A.C., LaBarca, A., Chen, Y., 2022.  Non-principal axis rotation in binary asteroid systems and how it weakens the BYORP effect.  Icarus 374, 114826.  doi:10.1016/j.icarus.2021.114826, arXiv:2107.14789.
  * Raducan et al. (2024a) Raducan, S.D., Jutzi, M., Cheng, A.F., Zhang, Y., Barnouin, O., Collins, G.S., Daly, R.T., Davison, T.M., Ernst, C.M., Farnham, T.L., Ferrari, F., Hirabayashi, M., Kumamoto, K.M., Michel, P., Murdoch, N., Nakano, R., Pajola, M., Rossi, A., Agrusa, H.F., Barbee, B.W., Syal, M.B., Chabot, N.L., Dotto, E., Fahnestock, E.G., Hasselmann, P.H., Herreros, I., Ivanovski, S., Li, J.Y., Lucchetti, A., Luther, R., Ormö, J., Owen, M., Pravec, P., Rivkin, A.S., Robin, C.Q., Sánchez, P., Tusberti, F., Wünnemann, K., Zinzi, A., Epifani, E.M., Manzoni, C., May, B.H., 2024a.  Physical properties of asteroid dimorphos as derived from the dart impact.  Nature Astronomy URL: http://dx.doi.org/10.1038/s41550-024-02200-3, doi:10.1038/s41550-024-02200-3.
  * Raducan et al. (2024b) Raducan, S.D., Jutzi, M., Merrill, C.C., Michel, P., Zhang, Y., Hirabayashi, M., Mainzer, A., 2024b.  Lessons learned from nasa’s dart impact about disrupting rubble-pile asteroids.  arXiv:2403.00683.
  * Raducan et al. (2022) Raducan, S.D., Jutzi, M., Zhang, Y., Ormö, J., Michel, P., 2022.  Reshaping and ejection processes on rubble-pile asteroids from impacts.  A&A 665, L10.  doi:10.1051/0004-6361/202244807, arXiv:2209.02677.
  * Ribeiro et al. (2023) Ribeiro, T., Winter, O.C., Madeira, G., Giuliatti Winter, S.M., 2023.  Dynamics around non-spherical symmetric bodies: II. The case of a prolate body.  MNRAS 525, 44--56.  doi:10.1093/mnras/stad2362.
  * Richardson et al. (2024) Richardson, D.C., Agrusa, H.F., Barbee, B., Cueva, R.H., Ferrari, F., Jacobson, S.A., Makadia, R., Meyer, A.J., Michel, P., Nakano, R., Zhang, Y., Abell, P., Merrill, C.C., Campo Bagatin, A., Barnouin, O., Chabot, N.L., Cheng, A.F., Chesley, S.R., Daly, T.R., Eggl, S., Ernst, C.M., Fahnestock, E.G., Farnham, T.L., Fuentes-Muñoz, O., Gramigna, E., Hamilton, D.P., Hirabayashi, M., Jutzi, M., Lyzhoft, J., Lasagni Manghi, R., McMahon, J., Moreno, F., Murdoch, N., Naidu, S., Palmer, E.E., Panicucci, P., Pou, L., Pravec, P., Raducan, S.D., Rivkin, A.S., Rossi, A., Sánchez, P., Scheeres, D.J., Scheirich, P., Schwartz, S.R., Souami, D., Tancredi, G., Tanga, P., Tortora, P., Trigo-Rodríguez, J.M., Tsiganis, K., Wimarsson, J., Zannoni, M., 2024.  The Dynamical State of the Didymos System Before and After the DART Impact.  PSJ, submitted .
  * Richardson et al. (1998) Richardson, D.C., Bottke, W.F., Love, S.G., 1998.  Tidal Distortion and Disruption of Earth-Crossing Asteroids.  Icarus 134, 47--76.  doi:10.1006/icar.1998.5954.
  * Richardson et al. (2000) Richardson, D.C., Quinn, T., Stadel, J., Lake, G., 2000.  Direct Large-Scale N-Body Simulations of Planetesimal Dynamics.  Icarus 143, 45--59.  doi:10.1006/icar.1999.6243.
  * Rivkin et al. (2021) Rivkin, A.S., Chabot, N.L., Stickle, A.M., Thomas, C.A., Richardson, D.C., Barnouin, O., Fahnestock, E.G., Ernst, C.M., Cheng, A.F., Chesley, S., Naidu, S., Statler, T.S., Barbee, B., Agrusa, H., Moskovitz, N., Terik Daly, R., Pravec, P., Scheirich, P., Dotto, E., Della Corte, V., Michel, P., Küppers, M., Atchison, J., Hirabayashi, M., 2021.  The Double Asteroid Redirection Test (DART): Planetary Defense Investigations and Requirements.  PSJ 2, 173.  doi:10.3847/PSJ/ac063e.
  * Robin et al. (2023) Robin, C.Q., Murdoch, N., Duchene, A., Vincent, J.B., Lucchetti, A., Pajola, M., Ernst, C.M., Daly, R.T., Barnouin, O.S., Raducan, S.D., Michel, P., Hirabayashi, M., Stott, A., Cuervo, G., Jawin, E.R., Trigo-Rodriguez, J.M., Parro, L.M., Sunday, C., Vivet, D., Mimoun, D., Rivkin, A.S., Chabot, N.L., 2023.  Mechanical properties of rubble pile asteroids: insights from a morphological analysis of surface boulders.  Nature Communications submitted.
  * Roche (1847) Roche, E., 1847.  Memoirs divers sur l’equilibre d’une mass fluide.  Acad. Sci. Lett. Montpelier. Mem. Section Sci. 1, 243.
  * Rollin et al. (2021) Rollin, G., Shevchenko, I.I., Lages, J., 2021.  Dynamical environments of MU69 and similar objects.  Icarus 357, 114178.  doi:10.1016/j.icarus.2020.114178, arXiv:2012.02814.
  * Rubincam (2000) Rubincam, D.P., 2000.  Radiative spin-up and spin-down of small asteroids.  Icarus (New York, N.Y. 1962) 148, 2--11.
  * Sakong et al. (2019) Sakong, J., Woo, S., Kim, T., 2019.  Determination of impact fragments from particle analysis via smoothed particle hydrodynamics and k-means clustering.  International Journal of Impact Engineering 134.  doi:10.1016/j.ijimpeng.2019.103387. publisher Copyright: © 2019 Elsevier Ltd Copyright: Copyright 2019 Elsevier B.V., All rights reserved.
  * Salmon et al. (2010) Salmon, J., Charnoz, S., Crida, A., Brahic, A., 2010.  Long-term and large-scale viscous evolution of dense planetary rings.  Icarus 209, 771--785.  doi:10.1016/j.icarus.2010.05.030, arXiv:1006.0633.
  * Sánchez and Scheeres (2012) Sánchez, D.P., Scheeres, D.J., 2012.  DEM simulation of rotation-induced reshaping and disruption of rubble-pile asteroids.  Icarus 218, 876--894.  doi:10.1016/j.icarus.2012.01.014.
  * Sánchez and Scheeres (2011) Sánchez, P., Scheeres, D.J., 2011.  Simulating Asteroid Rubble Piles with A Self-gravitating Soft-sphere Distinct Element Method Model.  ApJ 727, 120.  doi:10.1088/0004-637X/727/2/120.
  * Sánchez and Scheeres (2014) Sánchez, P., Scheeres, D.J., 2014.  The strength of regolith and rubble pile asteroids.  Meteoritics and Planetary Science 49, 788--811.  doi:10.1111/maps.12293, arXiv:1306.1622.
  * Sánchez and Scheeres (2016) Sánchez, P., Scheeres, D.J., 2016.  Disruption patterns of rotating self-gravitating aggregates: A survey on angle of friction and tensile strength.  Icarus 271, 453--471.  doi:10.1016/j.icarus.2016.01.016.
  * Sánchez and Scheeres (2018) Sánchez, P., Scheeres, D.J., 2018.  Rotational evolution of self-gravitating aggregates with cores of variable strength.  Planet. Space Sci. 157, 39--47.  doi:10.1016/j.pss.2018.04.001.
  * Sánchez and Scheeres (2020) Sánchez, P., Scheeres, D.J., 2020.  Cohesive regolith on fast rotating asteroids.  Icarus 338, 113443.  doi:10.1016/j.icarus.2019.113443, arXiv:1909.11270.
  * Sasaki and Hosono (2018) Sasaki, T., Hosono, N., 2018.  Particle Number Dependence of the N-body Simulations of Moon Formation.  ApJ 856, 175.  doi:10.3847/1538-4357/aab369, arXiv:1802.10287.
  * Scheeres (2007) Scheeres, D.J., 2007.  Rotational fission of contact binary asteroids.  Icarus 189, 370--385.  doi:10.1016/j.icarus.2007.02.015.
  * Scheeres (2009) Scheeres, D.J., 2009.  Minimum energy asteroid reconfigurations and catastrophic disruptions.  Planet. Space Sci. 57, 154--164.  doi:10.1016/j.pss.2008.03.009.
  * Scheeres (2015) Scheeres, D.J., 2015.  Landslides and Mass shedding on spinning spheroidal asteroids.  Icarus 247, 1--17.  doi:10.1016/j.icarus.2014.09.017, arXiv:1409.4015.
  * Scheeres et al. (2010) Scheeres, D.J., Hartzell, C.M., Sánchez, P., Swift, M., 2010.  Scaling forces to asteroid surfaces: The role of cohesion.  Icarus 210, 968--984.  doi:10.1016/j.icarus.2010.07.009, arXiv:1002.2478.
  * Schunová et al. (2014) Schunová, E., Jedicke, R., Walsh, K.J., Granvik, M., Wainscoat, R.J., Haghighipour, N., 2014.  Properties and evolution of NEO families created by tidal disruption at Earth.  Icarus 238, 156--169.  doi:10.1016/j.icarus.2014.05.006, arXiv:1405.4090.
  * Schwartz et al. (2013) Schwartz, S.R., Michel, P., Richardson, D.C., 2013.  Numerically simulating impact disruptions of cohesive glass bead agglomerates using the soft-sphere discrete element method.  Icarus 226, 67--76.  doi:10.1016/j.icarus.2013.05.007.
  * Schwartz et al. (2012) Schwartz, S.R., Richardson, D.C., Michel, P., 2012.  An implementation of the soft-sphere discrete element method in a high-performance parallel gravity tree-code.  Granular Matter 14, 363--380.
  * Sharma (2009) Sharma, I., 2009.  The equilibrium of rubble-pile satellites: The Darwin and Roche ellipsoids for gravitationally held granular aggregates.  Icarus 200, 636--654.  doi:10.1016/j.icarus.2008.11.027.
  * Sicardy (2020) Sicardy, B., 2020.  Resonances in Nonaxisymmetric Gravitational Potentials.  AJ 159, 102.  doi:10.3847/1538-3881/ab6d06, arXiv:2001.06382.
  * Stadel (2001) Stadel, J.G., 2001.  Cosmological N-body simulations and their analysis.  Ph.D. thesis. University of Washington, Seattle.
  * Statler (2009) Statler, T.S., 2009.  Extreme sensitivity of the YORP effect to small-scale topography.  Icarus 202, 502--513.  doi:10.1016/j.icarus.2009.03.003, arXiv:0903.1119.
  * Sugiura et al. (2018) Sugiura, K., Kobayashi, H., Inutsuka, S., 2018.  Toward understanding the origin of asteroid geometries. Variety in shapes produced by equal-mass impacts.  A&A 620, A167.  doi:10.1051/0004-6361/201833227, arXiv:1804.11039.
  * Sugiura et al. (2021) Sugiura, K., Kobayashi, H., Watanabe, S.i., Genda, H., Hyodo, R., Inutsuka, S.i., 2021.  SPH simulations for shape deformation of rubble-pile asteroids through spinup: The challenge for making top-shaped asteroids Ryugu and Bennu.  Icarus 365, 114505.  doi:10.1016/j.icarus.2021.114505, arXiv:2104.13516.
  * Takeda and Ida (2001) Takeda, T., Ida, S., 2001.  Angular Momentum Transfer in a Protolunar Disk.  ApJ 560, 514--533.  doi:10.1086/322406, arXiv:astro-ph/0108133.
  * Tardivel et al. (2018) Tardivel, S., Sánchez, P., Scheeres, D.J., 2018.  Equatorial cavities on asteroids, an evidence of fission events.  Icarus 304, 192--208.  doi:10.1016/j.icarus.2017.06.037.
  * Tasora et al. (2016) Tasora, A., Serban, R., Mazhar, H., Pazouki, A., Melanz, D., Fleischmann, J., Taylor, M., Sugiyama, H., Negrut, D., 2016.  Chrono: An open source multi-physics dynamics engine, in: Kozubek, T. (Ed.), High Performance Computing in Science and Engineering – Lecture Notes in Computer Science. Springer, pp. 19--49.
  * The CGAL Project (2023) The CGAL Project, 2023.  CGAL User and Reference Manual.  5.5.2 ed., CGAL Editorial Board.  URL: https://doc.cgal.org/5.5.2/Manual/packages.html.
  * Tiscareno et al. (2013) Tiscareno, M.S., Hedman, M.M., Burns, J.A., Castillo-Rogez, J., 2013.  Compositions and Origins of Outer Planet Systems: Insights from the Roche Critical Density.  ApJ 765, L28.  doi:10.1088/2041-8205/765/2/L28, arXiv:1302.1253.
  * Vokrouhlický and Čapek (2002) Vokrouhlický, D., Čapek, D., 2002.  YORP-Induced Long-Term Evolution of the Spin State of Small Asteroids and Meteoroids: Rubincam’s Approximation.  Icarus 159, 449--467.  doi:10.1006/icar.2002.6918.
  * Walsh (2018) Walsh, K.J., 2018.  Rubble Pile Asteroids.  ARA&A 56, 593--624.  doi:10.1146/annurev-astro-081817-052013, arXiv:1810.01815.
  * Walsh and Richardson (2006) Walsh, K.J., Richardson, D.C., 2006.  Binary near-Earth asteroid formation: Rubble pile model of tidal disruptions.  Icarus 180, 201--216.  doi:10.1016/j.icarus.2005.08.015.
  * Walsh et al. (2008) Walsh, K.J., Richardson, D.C., Michel, P., 2008.  Rotational breakup as the origin of small binary asteroids.  Nature 454, 188--191.  doi:10.1038/nature07078.
  * Walsh et al. (2012) Walsh, K.J., Richardson, D.C., Michel, P., 2012.  Spin-up of rubble-pile asteroids: Disruption, satellite formation, and equilibrium shapes.  Icarus 220, 514--529.  doi:10.1016/j.icarus.2012.04.029.
  * Watanabe et al. (2019) Watanabe, S., Hirabayashi, M., Hirata, N., Hirata, N., Noguchi, R., Shimaki, Y., Ikeda, H., Tatsumi, E., Yoshikawa, M., Kikuchi, S., Yabuta, H., Nakamura, T., Tachibana, S., Ishihara, Y., Morota, T., Kitazato, K., Sakatani, N., Matsumoto, K., Wada, K., Senshu, H., Honda, C., Michikami, T., Takeuchi, H., Kouyama, T., Honda, R., Kameda, S., Fuse, T., Miyamoto, H., Komatsu, G., Sugita, S., Okada, T., Namiki, N., Arakawa, M., Ishiguro, M., Abe, M., Gaskell, R., Palmer, E., Barnouin, O.S., Michel, P., French, A.S., McMahon, J.W., Scheeres, D.J., Abell, P.A., Yamamoto, Y., Tanaka, S., Shirai, K., Matsuoka, M., Yamada, M., Yokota, Y., Suzuki, H., Yoshioka, K., Cho, Y., Tanaka, S., Nishikawa, N., Sugiyama, T., Kikuchi, H., Hemmi, R., Yamaguchi, T., Ogawa, N., Ono, G., Mimasu, Y., Yoshikawa, K., Takahashi, T., Takei, Y., Fujii, A., Hirose, C., Iwata, T., Hayakawa, M., Hosoda, S., Mori, O., Sawada, H., Shimada, T., Soldini, S., Yano, H., Tsukizaki, R., Ozaki, M., Iijima, Y., Ogawa, K., Fujimoto, M., Ho, T.M., Moussi, A., Jaumann, R., Bibring, J.P., Krause, C., Terui, F., Saiki, T., Nakazawa, S., Tsuda, Y., 2019.  Hayabusa2 arrives at the carbonaceous asteroid 162173 Ryugu—A spinning top-shaped rubble pile.  Science 364, 268--272.  doi:10.1126/science.aav8032.
  * Wimarsson et al. (2020) Wimarsson, J., Liu, B., Ogihara, M., 2020.  Promoted mass growth of multiple, distant giant planets through pebble accretion and planet-planet collision.  MNRAS 496, 3314--3325.  doi:10.1093/mnras/staa1708, arXiv:2006.06451.
  * Yu et al. (2019) Yu, Y., Michel, P., Hirabayashi, M., Richardson, D.C., 2019.  The expansion of debris flow shed from the primary of 65803 Didymos.  MNRAS 484, 1057--1071.  doi:10.1093/mnras/sty3515.
  * Zhang and Michel (2020) Zhang, Y., Michel, P., 2020.  Tidal distortion and disruption of rubble-pile bodies revisited. Soft-sphere discrete element analyses.  A&A 640, A102.  doi:10.1051/0004-6361/202037856, arXiv:2006.14030.
  * Zhang et al. (2021) Zhang, Y., Michel, P., Richardson, D.C., Barnouin, O.S., Agrusa, H.F., Tsiganis, K., Manzoni, C., May, B.H., 2021.  Creep stability of the DART/Hera mission target 65803 Didymos: II. The role of cohesion.  Icarus 362, 114433.  doi:10.1016/j.icarus.2021.114433.
  * Zhang et al. (2017) Zhang, Y., Richardson, D.C., Barnouin, O.S., Maurel, C., Michel, P., Schwartz, S.R., Ballouz, R.L., Benner, L.A.M., Naidu, S.P., Li, J., 2017.  Creep stability of the proposed AIDA mission target 65803 Didymos: I. Discrete cohesionless granular physics model.  Icarus 294, 98--123.  doi:10.1016/j.icarus.2017.04.027, arXiv:1703.01595.
  * Zhang et al. (2018) Zhang, Y., Richardson, D.C., Barnouin, O.S., Michel, P., Schwartz, S.R., Ballouz, R.L., 2018.  Rotational Failure of Rubble-pile Bodies: Influences of Shear and Cohesive Strengths.  ApJ 857, 15.  doi:10.3847/1538-4357/aab5b2.
  * Zhou et al. (2022) Zhou, W.H., Zhang, Y., Yan, X., Michel, P., 2022.  The crater-induced YORP effect.  A&A 668, A70.  doi:10.1051/0004-6361/202244386, arXiv:2210.15802.