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

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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 1.8×10 kg (1.5 2.2×10 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 2.3×10 kg (1.5 2.9×10 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 (0.17 0.90 mm s-2), which corresponds to a comet mass of m=4.5×10 kg (2.3 12.0×10 kg) and a bulk density of ρ=400 kgm (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.

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