Planetary Dynamics: Shape, Gravity, Orbit, Tides, and Rotation from Observations and Models
Shape, gravity field, orbit, tidal deformation, and rotation state are fundamental geodetic parameters of any planetary object. Measurements of these parameters are prerequisites for e.g. spacecraft navigation and mapping from orbit, but also for modelling of the interior and evolution. This session welcomes contributions from all aspects of planetary geodesy, including the relevant theories, observations and models in application to planets, satellites, ring systems, asteroids, and comets.
Daniel Scheeres, Andrew French, Pasquale Tricarico, Steven Chesley, Yu Takahashi, Davide Farnocchia, Jay McMahon, Daniel Brack, Alex Davis, Ronald Ballouz, Erica Jawin, Benjamin Rozitis, Josh Emery, Andrew Ryan, Ryan Park, Brian Rush, Nick Mastrodemos, Brian Kennedy, Julie Bellerose, and Daniel Lubey and the OSIRIS-REx Team Members
Introduction: Estimates of asteroid (101955) Bennu’s gravity have been determined based on a series of independent solutions from different teams involved on the OSIRIS-REx mission. In addition to classical radio science techniques for estimating a body's gravity field coefficients, the discovery of particles ejected from Bennu that persist in orbit for multiple revolutions provides a unique opportunity to probe the gravity field to higher degree and order than possible by using conventional spacecraft tracking . However, the non-gravitational forces acting on these particles must also be characterized, and their impact on solution accuracy must be assessed, requiring the different gravity field estimates to be compared and reconciled.
Given the measured gravity field of Bennu, rigorous constraints on its internal density heterogeneity can be found by comparing the measured field with the constant density field computed from the asteroid shape. These results in turn provide unique insight into the global geophysical processes that drive the external and internal morphology of small rubble-pile asteroids such as Bennu.
Finally, definitive results on the surface and close-proximity force environment of Bennu can be derived and updated from the initial analysis based on the total mass and constant density shape. Several aspects of the environment are highly sensitive to the gravity field and have changed from earlier results [2, 3, 4].
We will present the current gravity field solutions and uncertainties, update the surface and proximity environment models, and provide the geophysical implications and interpretations of these measurements.
Geophysical Models: The estimated gravity field solutions are compared with the constant density shape model to constrain models of the internal density variation. We find that these differences are consistent with Bennu having an under-dense core and equatorial ridge. The degree to which these are under-dense cannot be specifically constrained, but feasible ranges for these values can be determined.
An under-dense equator could be consistent with transport of material to the equator without compaction. Given the slope transition at the Roche lobe, this would also be consistent with the ballistic transport of material into the equatorial region. Estimates of the rate of particle migration do not seem to be enough to account for the overall equatorial bulge of Bennu, however, implying that this feature could be older and not due to the more recent transport of material to the equator.
The lower-density interior is consistent with a period of rapid spin and failure of the interior of the body . This could also be consistent with the raised equatorial bulge. This interior failure could have occurred in an earlier epoch of YORP-induced rapid rotation or could trace to the initial formation of Bennu as a distinct rubble-pile body . Tests of this hypothesis require additional simulations of how rubble-pile asteroids coalesce after the catastrophic disruption of their parent body.
Acknowledgements: This material is based upon work supported by NASA under Contract NNM10AA11C issued through the New Frontiers Program. Part of this research was conducted at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. We are grateful to the entire OSIRIS-REx Team for making the encounter with Bennu possible.
References:  Lauretta D.S. & Hergenrother C.W. et al. (2019) Science 366, eaay3544.  Scheeres D.J. et al. (2019) Nature Astronomy 3, 352-361.  Barnouin O.S. et al. 2019. Nature Geoscience 12, 247-252.  Tricarico P. et al. (2019) EPSC-DPS Abstract #2019-547-1.  Scheeres D.J. et al. (2016) Icarus 276, 116-140.  Michel P. et al. (2018) AGU Fall Meeting 2018 Abstract #P33C-P33850.
How to cite:
Scheeres, D., French, A., Tricarico, P., Chesley, S., Takahashi, Y., Farnocchia, D., McMahon, J., Brack, D., Davis, A., Ballouz, R., Jawin, E., Rozitis, B., Emery, J., Ryan, A., Park, R., Rush, B., Mastrodemos, N., Kennedy, B., Bellerose, J., and Lubey, D. and the OSIRIS-REx Team Members: The Measured Gravity and Global Geophysical Properties of (101955) Bennu, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-929, https://doi.org/10.5194/epsc2020-929, 2020.
Yun Zhang, Patrick Michel, Olivier S. Barnouin, Michael G. Daly, Ronald-Louis Ballouz, Kevin J. Walsh, and Dante S. Lauretta
Previous studies have shown that material strength and density heterogeneity play important roles in asteroid reshaping processes through YORP spin-up (Holsapple 2010). The final shapes are also dependent on the magnitude and distribution of these intrinsic properties. In turn, material properties as well as the reshaping history of an asteroid could be revealed by examining its detailed morphology. The high-resolution shape, detailed surface characteristics, and internal density distribution of (101955) Bennu measured by the OSIRIS-REx mission (Barnouin et al. 2019; Walsh et al. 2019; Scheeres et al. 2019; Lauretta et al. 2019) now grant us an opportunity to decipher its material properties from its current state.
We use the Bennu shape model with a resolution of 1.68 m per facet derived from the data collected by the OSIRIS-REx Laser Altimeter (Seabrook et al. 2019; Barnouin et al. 2020) to construct rubble-pile models consisting of ~10,000 to ~100,000 spheres with different particle size distributions. The soft-sphere discrete element method is applied to simulate the spin-up process of these rubble piles (Schwartz et al., 2012; Zhang et al., 2017, 2018). The contact interactions between the constituent spheres are used to control the material shear and cohesive strengths. We study the behaviors of our simulated rubble piles against rotation as a function of frictional and cohesive properties.
In response to the rotational acceleration, we find that the contact-force networks adjust themselves to maintain the overall stability. The stress distributions in the Bennu rubble-pile models change with the spin rate. When no cohesion is included, the local regions subject to the highest shear stress are located near the surface at the slow spin state and shift to the interior during the subsequent spin-up. The critical spin period value of this transition decreases with a larger friction angle of the asteroid. For example, with a friction angle of ~20°, this transition occurs before achieving a spin period of ~ 5 hr and the Bennu rubble-pile model begins to fail internally and deform before achieving the current spin period of ~4.276 hr (Barnouin et al. 2019). With a friction angle of 30°, the rubble-pile Bennu is able to marginally keep its structure stable at 4.276 hr with an internal region subject to the highest shear stress. When the friction angle is larger than ~37°, the most sensitive region subject to the highest shear stress occurs at the surface at Bennu’s current spin rate. Since some recent surface mass movement is evidenced on Bennu (Jawin et al. 2020), Bennu’s material may have a high friction angle larger than 37° to promote surface movement. This friction-angle magnitude is common for terrestrial granular materials and is comparable to the maximum surface slope of Bennu (~40°).
The critical spin period to induce structural failure for Bennu modeled as a rubble pile with a friction angle of ~37° is ~3.4 hr, which is notably faster than its current spin period. If this is the case, Bennu might have been spun up to a spin period smaller than 3.4 hr in the past to induce some macroscopic reshaping effects. The critical spin period decreases to 2.6 hr if the rubble-pile material contains a small amount of cohesion ~ 3 Pa that is homogenously distributed. This fast critical spin state would lift any surface material that is not cohesively attached to the surface. This is inconsistent with the recent surface mass movement observed on Bennu. Furthermore, the structural failure is induced by surface cracking, preventing surface shedding from occurring. Therefore, our study suggests that Bennu should not have an overall cohesion larger than ~3 Pa.
However, if the cohesion distribution is highly heterogeneous, it is possible that some regions have a large material cohesion and some other regions are cohesionless. This inhomogeneous cohesion distribution is consistent with the estimated porosity and boulder distribution on Bennu, and could account for the formation of the observed features such as longitudinal ridges and internal heterogeneity.
Acknowledgements: Y. Z. acknowledges funding from the Université Côte d’Azur “Individual grants for young researchers” program of IDEX JEDI. Y.Z. and P.M. acknowledge funding support from the French space agency CNES and from the European Union's Horizon 2020 research and innovation programme under grant agreement no. 870377 (project NEO-MAPP). This material is based upon work supported by NASA under Contract NNM10AA11C issued through the New Frontiers Program. We are grateful to the entire OSIRIS-REx Team for making the encounter with Bennu possible.
Barnouin, O. S., Daly, M. G., Palmer, E. E., et al. 2019, Nat. Geosci., 12, 247.
Barnouin, O. S., Daly, M. G., Palmer, E. E., et al. 2020, Planet. Space Sci., 180, 104764.
Holsapple, K. A. 2010, Icarus 205, 430.
Jawin, E. R., Walsh, K. J., McCoy, T. J., et al. 2020, LPSC, 2326, 1201.
Lauretta, D. S., DellaGiustina, D. N., Bennett, C. A., et al. 2019, Nature, 568, 55.
Scheeres, D. J., McMahon, J. W., French, A. S., et al. 2019, Nat. Astron., 3, 352.
Seabrook, J. A., Daly, M. G., Barnouin, O. S., et al. 2019, Planet. Space Sci. 177, 104688.
Schwartz, S. R., Richardson, D. C., & Michel, P. 2012, Granular Matter, 14(3), 363–380.
Walsh, K. J., Jawin E. R., Ballouz, R.-L., et al. 2019, Nat. Geosci. 12, 242–246.
Zhang, Y., Richardson, D. C., Barnouin, O. S., et al. 2017, Icarus, 294, 98–123.
Zhang, Y., Richardson, D. C., Barnouin, O. S., et al. 2018, Astrophys. J., 857(1), 15.
How to cite:
Zhang, Y., Michel, P., Barnouin, O. S., Daly, M. G., Ballouz, R.-L., Walsh, K. J., and Lauretta, D. S.: Numerical modeling of Bennu’s structural stability and implications for its internal and surface properties, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-722, https://doi.org/10.5194/epsc2020-722, 2020.
Stefania Soldini, Takanao Saiki, Hitoshi Ikeda, Koji Wada, Masahiko Arakawa, and Yuichi Tsuda
Abstract: A sphere cluster (SPH-Mas) based gravity model allows a semi-analytic expression of the linearised equations around the equilibrium points. Depending on the sphere packing distribution, the SPH-Mas model can retrieve the same dynamical objects common to others gravity models (i.e. spherical harmonics and polyhedron) or for non-uniform density objects. This model has the advantage to define the same particles mesh distribution for both astrophysical and astrodynamics tools. The Hayabusa2’s Small Carry-on Impactor operation is used as a scenario to study the ejecta particle dynamics around an irregular body. The goNEAR (gravitational orbit Near Earth Asteroid Regions) tool was used to simulate the impact operation in a non-linear sense when the effect of the solar radiation pressure perturbation is taken into account for particles size of 10 cm, 5 cm, 1 cm and 1 mm in diameter.
Introduction: In November 2019, the Japanese Hayabusa2 spacecraft completed an 18 months mission exploration around the asteroid Ryugu  and it is expected to return to Earth late this year (2020). JAXA’s Hayabusa2 and NASA’s OSIRIS-Rex missions  are contributing to answer fundamental questions related to the formation of our solar system and the origin of Life . After a successful touchdown in March 2019, Japan has set a new first when in April 2019 the Hayabusa2 spacecraft deployed and activated the explosive Small Carry-on Impactor (SCI) to successfully form an artificial crater .
We propose a genearlised methodology to study the dynamics around Equilibrium Points (EPs) of irregular bodies with application to the asteroid Ryugu . To the core of our study, we aim to gain a general insight on the dynamics around irregular shape bodies for studying the dynamics of ejecta particles. Moreover, we are looking into a generalised gravity model of celestial bodies that can be easily extended not only to any irregular shape bodies but also to arbitrary density distributions . The selected generalised gravity model provides a mass distribution that can be used for both hydrodynamics impact simulations and orbital dynamics around EPs.
Background: The mascons (“mas”s “con” centrations) has been mainly used for explaining the Lunar gravity anomalies originally detected in 1968 . Conversely, Smooth Particles Hydrodynamics (SPH) codes are often used to simulate asteroid impact events and share the problem to handle the transition between a SPH simulation and N-body simulations . Since the SPH and Mascons make use of the same mass conservation law and we are interested to interface the SPH simulations with the N-Body simulations, we will rename the selected gravity model as the SPH-Mascons (SPH-Mas) model.
Figure 1: Sphere packing and the equilibrium points .
SPH-Mas Gravity Model: The gravity of an irregular shape body is modelled with a cluster of spheres, SPH-Mas. Each spherical particle contributes in the overall gravity field of the body. The exterior gravity potential of each sphere behaves as a single point mass. The potential of the irregular body is the result of the summation of each point mass’s potential that contributes to the overall potential field such that:
where mi (i = 1, ..., Nsph) is the mass of each SPH-Mas for a total of Nsph masses. r is the distance from the field point and the center of the asteroid. ri is the distance of each masses with respect to the center of the asteroid. The total mass of the asteroid is conserved and given by mb = ∑(i = 1,.., Nsph) mi.
Figure 2: Shape model  and the equilibrium points.
Sphere Packing: We consider Ryugu’s polyhedron model published in  as our “high fidelity” gravity model. We distribute the SPH-Mas within the asteroid shape such that we can approximate Ryugu’s “high fidelity” gravity field. For the scope of testing our semi-analytic formula, we compared a uniform sphere packing approach with a random packing approach for different numbers of SPH-Mas. Fig. 1 shows the comparison between the uniform distribution in the left panel and the random distribution in the right panel for Nsph = 19, 58, 1,605 and 1,406,146. By comparing the location of the EPs between Fig 1 and Fig 2, it is clear that under the assumption of uniform density polyhedron, the uniform sphere packing is preferable to the random sphere packing even for the case of Nsph major to the order of million spheres. Indeed, the random sphere packing does not necessarily preserve the geometry of the EPs that affects the ejecta dynamics.
Effect of SPH-Mas Packing onto Particles Dynamics: The derived semi-analytical formula based on an SPH-Mas gravity model is a direct function of the sphere packing distribution (density), their position (ri) and the asteroid’s spin axis angular velocity (7.6 h for Ryugu) which allows to find families of periodic orbits for ejecta particles around an non-uniform irregular shaped asteroid as shown in Fig 3.
Fate of Ryugu’s Ejecta: We made use of goNEAR tool to simulate the dynamics of 10 cm, 5 cm, 1 cm and 1mm in diameter size particles under the effect of the solar radiation pressure perturbation. In the numerical experiment, few particles seemed to survive in orbit for diameter of 5–10 cm (Fig 4). The search for evidence of particles in Ryugu orbit is still unconfirmed however the stability of EPs can be linked to long survival particles in orbit.
Figure 3: Family of periodic orbits as function of sphere packing .
Figure 4: SCI’s ejecta dynamics with the goNEAR tool .
References:  Watanabe et al. (2019) Science, 364, 268–272.  Lauretta et al. (2015) Meteoritics & Planet. Sci., 50, 834–849.  Sugita et al. (2019) Science, 364, 6437.  Arakawa et al. (2019) Science, under review  Soldini et al, (2019) PSS, (2020) 180  Melosh et al., (2013) Science, 340,1552–1555  Ballouz et al., (2018) 49th LPSC.
How to cite:
Soldini, S., Saiki, T., Ikeda, H., Wada, K., Arakawa, M., and Tsuda, Y.: The effect of "MASCONS" Sphere Packing onto the Dynamical Environment around Rubble-Pile Asteroids: Application to Ryugu, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-808, https://doi.org/10.5194/epsc2020-808, 2020.