Sunao Hasegawa

The lifetime of weak porous boulders on main belt asteroids was experimentally investigated using their impact strength <mml:math altimg="si4.svg"><mml:msup><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub><mml:mo>∗</mml:mo></mml:msup></mml:math>. We conducted impact disruption experiments on weak porous targets to simulate the conditions of boulders found on C-type asteroids such as Ryugu and Bennu. Projectiles made of polycarbonate and nylon were impacted on spherical targets with the diameter from 30 to 120 mm at velocities ranging from 0.6 to 6.1 kms<SUP loc="post">‑1. The impact angle was normal to the target surface. We varied the target's tensile strength, denoted as <mml:math altimg="si7.svg"><mml:msub><mml:mi>Y</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:math>, and the mass of the target by more than one order of magnitude. Our findings revealed that <mml:math altimg="si4.svg"><mml:msup><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub><mml:mo>∗</mml:mo></mml:msup></mml:math> increased with increasing the tensile strength, and it slightly depended on the boulders' sizes. Additionally, we observed that <mml:math altimg="si4.svg"><mml:msup><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub><mml:mo>∗</mml:mo></mml:msup></mml:math> depended on impact velocity according to the scaling theory for catastrophic disruption, expressed as <mml:math altimg="si152.svg"><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">S</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:mn>0.15</mml:mn><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>‑</mml:mo><mml:mn>0.25</mml:mn></mml:mrow></mml:msup><mml:msubsup><mml:mi>v</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mn>0.53</mml:mn></mml:msubsup><mml:msup><mml:mfenced><mml:mfrac><mml:msub><mml:mi>Y</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub><mml:mi>ρ</mml:mi></mml:mfrac></mml:mfenced><mml:mn>0.74</mml:mn></mml:msup></mml:math>, where v<SUB loc="post">i, D and ρ represent impact velocity, target diameter and target density, respectively. We also investigated the momentum transfer efficiency, denoted as <mml:math altimg="si102.svg"><mml:mi>β</mml:mi></mml:math>, for monolithic asteroids with weak strength. <mml:math altimg="si102.svg"><mml:mi>β</mml:mi></mml:math> was determined for cratered targets with different tensile strengths and was found to be well scaled by a characteristic velocity, denoted as v*=<mml:math altimg="si155.svg"><mml:msqrt><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mi>ρ</mml:mi></mml:mrow></mml:msqrt></mml:math>, for the targets with a strength smaller than 283 kPa. The relationship obtained was <mml:math altimg="si156.svg"><mml:mi>β</mml:mi><mml:mo>‑</mml:mo><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>‑</mml:mo><mml:mn>3.3</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msup><mml:mi>v</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:mfenced><mml:mn>1.29</mml:mn></mml:msup></mml:math>. However, the β value for the strongest target with 731 kPa did not conform to this equation. Based on these results, we estimated the lifetime of boulders on main belt asteroids with various strength and sizes. Boulders with the strength between 200 kPa and 1.7 MPa, estimated for asteroids Ryugu and Bennu, are unlikely to be disrupted in less than 10 Ma for sizes larger than 4 m. However, boulders smaller than several 10 cm may not survive longer than 10 Ma, a duration almost corresponding to the surface age of Ryugu. The boulder with the size of 160 m on asteroid Ryugu could potentially survive longer than 90–183 Ma at the main belt if the strength exceeds 200 kPa....