Atmospheric mass-loss from high-velocity giant impacts

ABSTRACT Using moving mesh hydrodynamic simulations, we determine the shock propagation and resulting ground velocities for a planet hit by a high-velocity impactor. We use our results to determine the atmospheric mass-loss caused by the resulting ground motion due to the impact shock wave. We find that there are two distinct shock propagation regimes. In the limit in which the impactor is significantly smaller than the target (Ri << Rt), the solutions are self-similar and the shock velocity at a fixed point on the target scale as $m_{\rm i}^{2/3}$, where mi is the mass of the impactor. In addition, the ground velocities follow a universal profile given by vg/vi = (14.2x2 − 25.3x + 11.3)/(x2 − 2.5x + 1.9) + 2ln Ri/Rt, where x = sin (θ/2), θ is the latitude on the target measured from the impact site, and vg and vi are the ground velocity and impact velocity, respectively. In contrast, in the limit in which the impactor is comparable to the size of the target (Ri ∼ Rt), we find that shock velocities decline with the mass of the impactor significantly more weakly than $m_{\rm i}^{2/3}$. We use the resulting surface velocity profiles to calculate the atmospheric mass-loss for a large range of impactor masses and impact velocities and apply them to the Kepler-36 system and the Moon forming impact. Finally, we present and generalize our results in terms of the vg/vi and the impactor to target size ratio (Ri/Rt) such that they can easily be applied to other collision scenarios.

Spectral Analysis of Impact Shock during Running

The purpose of this study was to determine the effects of increasing impact shock levels on the spectral characteristics of impact shock and impact shock wave attenuation in the body during treadmill running. Twelve male subjects ran at 2.0, 3.0, 4.0, and 5.0 m s−1on a treadmill. Axial accelerations of the shank and head were measured using low-mass accelerometers. The typical shank acceleration power spectrum contained two major components which corresponded to the active (5–8 Hz) and impact (12–20 Hz) phases of the time-domain ground reaction force. Both the amplitude and frequency of leg shock transients increased with increasing running speed. Greatest attenuation of the shock transmitted to the head occurred in the 15–50 Hz range. Attenuation increased with increasing running speed. Thus transmission of the impact shock wave to the head was limited, despite large increases in impact shock at the lower extremity.