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Dynamical and Physical Properties of 65803 Didymos 47th Lunar and Planetary Science Conference (2016) 1501.pdf DYNAMICAL AND PHYSICAL PROPERTIES OF 65803 DIDYMOS. D. C. Richardson1, O. S. Barnouin2, L. A. M. Benner3, W. F. Bottke Jr.4, A. Campo Bagatin5, A. F. Cheng2, M. Hirabayashi6, C. Maurel7, J. W. McMahon6, P. Michel8, N. Murdoch7, S. P. Naidu3, P. Pravec9, A. S. Rivkin2, D. J. Scheeres6, P. Scheirich9, K. Tsiganis10, Y. Zhang1,11, and the AIDA Dynamical and Physical Properties of Didymos Working Group12, 1Department of Astron- omy, University of Maryland, College Park, MD 20742, [email protected], 2JHU/APL, 3JPL/Caltech, 4SwRI, 5U Alicante, 6U Colorado, 7ISAE, 8Obs. Côte d’Azur, 9Acad. Sci. Czech Rep., 10Aristotle U, 11Tsinghua U, 12various. Introduction: The near-Earth asteroid (NEA) Figure 1: Preliminary 65803 Didymos, a binary system, is the target of the shape model of the pri- proposed Asteroid Impact & Deflection Assessment mary from combined (AIDA) mission, which combines an orbiter [1] and a radar and lightcurve kinetic impactor experiment planned for fall 2022 [2]. data, diameter ~780 m. The Dynamical and Physical Properties of Didymos The secondary (not im- Working Group is supporting this mission by address- aged) is estimated to be ing the following broad questions: what is the dynam- more elongated. ical state of the Didymos system, how can the conse- quences of the impact best be measured, and how can System dynamics. We have constructed a model the physical properties of the system be inferred based for the short-term binary dynamics in which each on current knowledge? Below we outline our current component is represented by a rigid body composed of progress toward answering these questions. ~1,000 blocks that fit its shape. The secondary is as- Origin: Didymos is an Apollo-class NEA with sumed to be a triaxial ellipsoid, with axial ratios a/b semimajor axis, eccentricity, and inclination (a, e, i) of and b/c varying between 1.1 and 1.5. Almost all cases (1.64 AU, 0.384, 3.4°). Using a new NEA population appear to be stable for 500 orbits, in the absence of model [3], it likely reached its current orbit by exiting solar tides. The orbital period and semimajor axis the inner main belt near or within the ν6 resonance be- have very small variations (~1 m) and the eccentricity tween 2.1–2.5 AU (> 82%). Other possible source of the orbit stays < 0.018, increasing slightly with a/b regions are the Hungaria asteroids (8%) and the in- and b/c. The orbital plane oscillates minimally about ner/central main belt via the 3:1 mean-motion reso- the initial one (i < 0.003°). The rotation axes remain nance with Jupiter (7%). Remote observations [4] stable, as the obliquity stays < 0.02° and < 0.3° for the show Didymos is spectroscopically most consistent primary and secondary, respectively. While the rota- with ordinary chondrites, with an affinity for L/LL- tion period of the primary is extremely stable (δP1 ~ type meteorites. Didymos likely originated from a 0.1 s), the secondary shows secular oscillations— high-albedo family [5]; its geometric albedo, pv = 0.16 possibly librations—that depend on the axial ratios and ± 0.04 [6], matches the mean albedo of the prominent may range from δP2 ~ 0.2 to 1.5 h. A more complete Baptistina family in that zone. However, several addi- long-term analysis is currently underway. tional family candidates may also make plausible par- Internal Structure: The Didymos primary is ents (e.g., Flora, Nysa, Massalia, Lucienne). close to if not beyond the limit for loose material to Current Dynamical State: Table 1 gives basic remain on the surface at the equator. Weak cohesion data on the current dynamical and rotational state of (< 100 Pa) may be implied, although there is sufficient Didymos based on observations to date. The second- uncertainty in the shape model that zero cohesion can- ary is assumed to orbit in the equatorial plane of the not yet be ruled out. primary. Figure 1 shows the current shape model from Continuum analysis. Figure 2 shows the failure radar and lightcurve observations. Also see [7]. mode diagram of the primary (indicating the degree of cohesion needed to maintain its shape as a function of Table 1: Didymos System Basic Properties spin period), based on a continuum analysis [8], as- Primary Diameter 0.780 ± 10% km suming uniform internal structure and the nominal bulk Secondary Diameter 0.163 ± 0.018 km density. A Drucker-Prager model is used for the yield Total System Mass (5.278 ± 0.04) × 1011 kg condition, and the friction angle is fixed at 35°. We Component Bulk Density 2,100 km m−3 ± 30% find two distinct failure modes, if there is insufficient Primary Rotation Period 2.2600 ± 0.0001 h cohesion/friction. If Didymos fails at a spin period Component Separation 1.18 +0.04/−0.02 km longer than 3.0 h, only the equatorial region fails. Secondary Orbital Period 11.920 +0.004/−0.006 h Otherwise, the internal structure should fail first. 47th Lunar and Planetary Science Conference (2016) 1501.pdf 100 −1 ] 50 Figure 2: Didy- ± 1.66 cm yr . This translates to a mean quadratic Pa [ Internal Surface failure −2 failure mos failure mode anomaly drift rate of ± 2.8° yr , or a very small period −1 10 Current plot. The current drift of 0.91 s yr . If the BYORP effect is working to 5 spin period is 2.26 shrink the binary orbit, intercomponent tidal forces can spin 1 h; the boundary oppose the effect, resulting in a constant orbit size 0.5 Cohesive Strength between surface [13], as is hypothesized for 1996 FG3 [14]. Further 1.5 2.0 2.5 3.0 3.5 4.0 failure and inter- details about these processes and the resulting dynam- Spin period [hr] nal failure is ~3 h. ical evolution for Didymos are discussed in [15]. Deploying a Lander: Using the ISAE-SUPAERO Discrete-element analysis. Using a soft-sphere ap- drop tower, we are performing low-speed collisions proach [9,10] we are exploring the conditions needed into granular material in low gravity to model a possi- for a rubble-pile model of the primary made up of ble lander deployment on the Didymos secondary. The monodisperse spheres to hold its shape. We find that aim is to understand the acceleration profile upon im- gravel-like material properties (friction angle 40°) to- pact and to quantify the coefficient of restitution if the gether with a spring-dashpot rolling friction model lander bounces. Reduced gravity is simulated by re- give a stable outcome without cohesion for bulk densi- leasing a free-falling projectile into a surface container ty > 2,500 kg m−3 when the spheres are packed ran- with a downward acceleration less than that of Earth's domly, and at even lower densities for hexagonal- gravity, controlled using an Atwood machine (a system close-pack configurations. The relative internal pres- of pulleys and counterweights). The projectile, sample sure distribution for a stable random-packed case is container, release mechanism, and deceleration system shown in Fig. 3. Analysis of this case shows that it is are custom designed for the 5.5 m drop tower [16] and everywhere below the Drucker-Prager yield condition. provide collision speeds and accelerations < 0.2 m s−1 and 0.1–1.0 m s−2, respectively, lower than in previous Figure 3: Relative experiments [17,18], and thus closer to the conditions pressure distribution that may be encountered during the AIDA mission. in a stable discrete Orbiting Debris: Due to the fast rotation of the model of the spinning primary and given the nominal physical parameters, primary (cross sec- centrifugal force may overcome gravitational force at tion). Material repose low latitudes. That allows regolith material of any size angle ~37°, packing to go through take-off/landing cycles and cause loss of efficiency ~62%. fines due to solar radiation pressure. Analysis of this effect accounting for the current shape model is ongo- Long-term Perturbations: The impact is ex- ing to estimate the effective mass density of floating pected to change the orbital period of the Didymos material in the neighbourhood of the primary. secondary by several minutes (~1%). It is necessary to References: [1] Michel P. et al. (2016), ASR, sub- understand any natural perturbative effects that may mitted. [2] Cheng, A. F. et al. (2016) P&SS, accepted. mask the impact signal. [3] Granvik et al. (2015) AAS/DPS, mtg. #47, id. Effect of solar and Earth tides. The Sun will con- #214.07. [4] Dunn et al. (2013) LPS XLIV, Abstract tribute the largest tidal effect on the system, but at a #1197. [5] Nesvorný et al. (2015) arXiv, 1502.01628. level 10 times below that anticipated for the impact [6] Pravec et al. (2006) Icarus, 181, 63–93. [7] Rivkin, itself. Formally, Earth tides can be slightly stronger A. S. (2016) LPS XLVII, submitted. [8] Hirabayashi M. than solar tides, but the necessary orbital configuration and Scheeres D. J. (2015) IAU Proc., 318, accepted. will not occur before or during encounter. [9] Schwartz et al. (2012) Gran. Matt., 14, 363–380. Thermal radiation forces. Thermal re-radiation [10] Barnouin O. S. et al. (2015) AAS/DPS, mtg. #47, from the Didymos secondary will lead to the binary- id. #402.09. [11] Ćuk M. and Burns J. A. YORP (BYORP) effect [11], which can cause a long- (2005) Icarus, 176, 418–431. [12] McMahon J. W. and term secular change to the binary semimajor axis.
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