A ballistics analysis of the Deep Impact ejecta plume: Determining Comet Tempel 1ʹs 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 × 10 7  kg ( 1.5 – 2.2 × 10 7  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 5  kg ( 1.5 – 2.9 × 10 5  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 cometʹs mean surface gravity of g ¯ = 0.34  mm s −2 (0.17–0.90 mm s−2), which corresponds to a comet mass of m t = 4.5 × 10 13  kg ( 2.3 – 12.0 × 10 13  kg ) and a bulk density of ρ t = 400  kg m −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.