Effects of DART impact on Dimorphos’ spin state and surface motion away from the impact point

<p><strong>INTRODUCTION</strong></p> <p>&#160; &#160; The NASA Double Asteroid Redirection Test (DART) mission is set to impact an asteroid of approximately 160 m in size, named Dimorphos (the secondary of the binary Near-Earth Asteroid (65803) Didymos) in September 2022. Little is known about the shape of the satellite, except available ground-based observations are compatible with a spherical to moderately elongated (b / a < 1.2) shape. Also, one primary goal of this mission is to improve our understanding of the impact momentum multiplication factor (&#8216;&#946;&#8217;). By checking the potentially antipodal escaping mass, it is possible to refine the estimation of the &#946; factor.</p> <p>&#160; &#160; In this work we investigate the possible reaction of Dimorphos to the DART collision, under the assumption that it is a spherical gravitational aggregate produced in the formation of the binary system [1][2]. The very structure of the target is unknown; therefore, we model it by (a) 100,550 mono-dispersed spherical particles in a close hexagonal packing (CHP) configuration; (b) multi-dispersed distribution of 100,000 spherical particles; (c) multi-dispersed distribution of only 13,600 particles.</p> <p><strong>METHODOLOGY</strong></p> <p>&#160; &#160; We perform numerical simulations of the collision event on a stand-alone Dimorphos by using a discrete-element N-body numerical code (PKDGRAV-SSDEM [3]). We do not perform simulations of the shattering phase, we instead concentrate on the effect of the collision on the target, once the shattering phase implying material damage (melting, vaporization, heating, and deformation) is over. Therefore, our synthetic projectile carries the same nominal momentum as the DART spacecraft does, but it delivers to the target only a small fraction of kinetic energy expected to survive once the shattering (non-elastic) phase has dissipated most of the impact kinetic energy [4]. We account for different center and off-center possible impact geometry compatible with DART nominal impact angle (20&#186;) with respect to the target orbital plane (Fig.1).</p> <p><img src="data:image/jpeg;base64, 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alt="" width="377" height="214" /></p> <p><strong>RESULTS</strong></p> <p>&#160; &#160; Here we report on results obtained so far on the effects of the DART impact on Dimorphos in the mono- and multi-dispersed distributions. In particular, we focussed on: a) Changes in spin period and direction of the spin axis, and tracking of their evolution in time. b) Energy distribution of surface particles capable to lift/move over the surface.&#160;&#160;</p> <p>&#160; &#160; Our model of the DART impact in the case of mono- and multi-dispersed distribution of spherical particles shows that:</p> <ul> <li>Spin period may be changed (decreased) by up to about -30 min in all impact configurations, except for the impact geometry R5 carrying in negative angular momentum. In this case to the system slows down its spin period to +10 min, depending on structure.</li> <li>The angular momentum vector may be tilted up to 3 deg with respect to initial direction.</li> <li>Spin vector is tilted with respect to angular momentum vector by about 0.1 deg with a precession motion about the latter.</li> </ul> <ul> <li>Negligible mass escaping from antipodal impact region does not substantially affect beta estimation.</li> <li>The energy and momentum wave reach the surface away from the impact area so that mass lift and displacement of sizeable particles over the surface are possible.</li> </ul> <p>&#160; &#160; Such predictions may be of interest in the study of the post-impact dynamics of the system&#8211; that will be determined by the Hera mission measurements.&#160; Finally, the results may contribute to the interpretation of (lack of) motion of boulders on the surface of Dimorphos away from the impact point. In fact, a comparison of DART- LICIACube and Hera images may show displacement of boulders. This in turn may give information on the internal structure of the body itself.</p> <p>&#160; &#160; We are currently modeling non-spherical shape for Dimorphos and the presence of the mass of Didymos primary in the system. On the other hand, instead of using spherical particles as the basic components (or &#8216;fragments&#8217;) of Dimorphos, we plan to apply irregular shapes and the corresponding mass distribution for the fragments. This refinement is expected to better reproduce the actual shear forces between the fragments.</p> <p><strong>REFERENCES:</strong></p> <p>[1] A. Campo Bagatin et al. (2001) Icarus, 149-1, 198.</p> <p>[2] A. Campo Bagatin et al. (2018) Icarus, Volume 302, 343.</p> <p>[3] Stephen R. Schwartz et al. (2012) Granular Matter 14, 263.</p> <p>[4] D. W. Walker (2013) Int. J. of Impact Engin. 56, 12.</p>