Angular momentum transfer in low velocity oblique impacts: Implications for asteroids

Abstract

The efficiency of angular momentum transfer ζ in low velocity oblique impacts was studied experimentally. ζ is defined as the fraction of incident angular momentum transferred to the rotation of the target. Plaster, mortar, cement, and one granite target were studied. Lead and aluminum projectiles were used. Only cratering impacts were considered. ζ was found to decrease with increasing incidence angle φ (relative to the surface normal). For example, for impacts into cylindrical mortar targets a least-squares fit of the form ζ = A(cos φ) β with A = 0.9 and β = 1.7 was found to match the data points reasonably well. In addition, β decreased from 1.9 to 1.4 as the kinetic energy density ϵ (= kinetic energy of the projectile/projectile volume) increased from 0.5 to 1.8 × 10 9 J m −3. This suggests that more energetic impacts transfer angular momentum more efficiently. ζ decreased as the indentation hardness H of the target increased: at φ ∼ 35°, ζ = 0.07 for granite ( H = 850 kg mm −2 and ζ = 0.7 for plaster ( H = 7.5 kg mm −2). Cement and mortar ( H = 76 kg mm −2) yielded intermediate values, although the values for cement ( ζ ∼ 0.3) were appreciably lower than for mortar ( ζ ∼ 0.6). In all cases where the velocity of the ricochetted projectile was determined, the fraction of angular momentum carried away by ejecta was found to be less than 30%. Finally, the results were only weakly dependent on the material of the projectile. If asteroid spin rates are the result of mutual noncatastrophic collisions and the taxonomic classes are indicative of the bulk properties (C asteroids being weaker than S asteroids and the latter weaker than M objects), then the differences between the corresponding spin rates are predicted to be smaller on the basis of our results than what could be expected from a consideration of the relative strength and density only. This conclusion is based on our finding for semirigid targets and ∼1-g projectiles impacting at <1 km sec −1 that hard targets are harder to spin up, i.e., exhibit smaller values of ζ in small-scale experiments. This would bring the predicted spin rates into a better agreement with observations. Moreover, on the basis of our experiments the equilibrium nutation angles should be smaller than the values previously obtained assuming ζ = 1, especially for strong asteroids for which ζ ⪡ 1 are expected from this work. This would make the detection of freely precessing asteroids even more difficult.