A ballistics analysis of the Deep Impact ejecta plume: Determining Comet Tempel 1's gravity, mass, and density

In July of 2005, the Deep Impact mission collided a 366 kg impactor with the nucleus of Comet 9P/Tempel 1, at a closing speed of 10.2 km s−1. In this work, we develop a first-order, three-dimensional, forward model of the ejecta plume behavior resulting from this cratering event, and then adjust the model parameters to match the flyby-spacecraft observations of the actual ejecta plume, image by image. This modeling exercise indicates Deep Impact to have been a reasonably “well-behaved” oblique impact, in which the impactor-spacecraft apparently struck a small, westward-facing slope of roughly 1/3-1/2 the size of the final crater produced (determined from initial ejecta plume geometry), and possessing an effective strength of not more than Y¯=1-10 kPa. The resulting ejecta plume followed well-established scaling relationships for cratering in a medium-to-high porosity target, consistent with a transient crater of not more than 85-140 m diameter, formed in not more than 250-550 s, for the case of Y¯=0 Pa (gravity-dominated cratering); and not less than 22-26 m diameter, formed in not less than 1-3 s, for the case of Y¯=10 kPa (strength-dominated cratering). At Y¯=0 Pa, an upper limit to the total ejected mass of 1.8×107 kg (1.5-2.2×107 kg) is consistent with measurements made via long-range remote sensing, after taking into account that 90% of this mass would have stayed close to the surface and then landed within 45 min of the impact. However, at Y¯=10 kPa, a lower limit to the total ejected mass of 2.3×105 kg (1.5-2.9×105 kg) is also consistent with these measurements. The expansion rate of the ejecta plume imaged during the look-back phase of observations leads to an estimate of the comet's mean surface gravity of g¯=0.34 mms−2 (0.17-0.90 mm s−2), which corresponds to a comet mass of mt=4.5×1013 kg (2.3-12.0×1013 kg) and a bulk density of ρt=400 kgm−3 (200-1000 kg m−3), where the large high-end error is due to uncertainties in the magnitude of coma gas pressure effects on the ejecta particles in flight.