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 . 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 (gravity-dominated cratering); and not less than 22-26 m diameter, formed in not less than 1-3 s, for the case of (strength-dominated cratering). At , 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 , 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 (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 (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.     

Observations of Comet 9P/Tempel 1 around the Deep Impact event by the OSIRIS cameras onboard Rosetta

The OSIRIS cameras on the Rosetta spacecraft observed Comet 9P/Tempel 1 from 5 days before to 10 days after it was hit by the Deep Impact projectile. The Narrow Angle Camera (NAC) monitored the cometary dust in 5 different filters. The Wide Angle Camera (WAC) observed through filters sensitive to emissions from OH, CN, Na, and OI together with the associated continuum. Before and after the impact the comet showed regular variations in intensity. The period of the brightness changes is consistent with the rotation period of Tempel 1. The overall brightness of Tempel 1 decreased by about 10% during the OSIRIS observations. The analysis of the impact ejecta shows that no new permanent coma structures were created by the impact. Most of the material moved with . Much of it left the comet in the form of icy grains which sublimated and fragmented within the first hour after the impact. The light curve of the comet after the impact and the amount of material leaving the comet ( of water ice and a presumably larger amount of dust) suggest that the impact ejecta were quickly accelerated by collisions with gas molecules. Therefore, the motion of the bulk of the ejecta cannot be described by ballistic trajectories, and the validity of determinations of the density and tensile strength of the nucleus of Tempel 1 with models using ballistic ejection of particles is uncertain.     

On the population, physical decay and orbital distribution of Jupiter family comets: Numerical simulations

We study the Jupiter family comet (JFC) population assumed to come from the Scattered Disk and transferred to the Jupiter’s zone through gravitational interactions with the Jovian planets. We shall define as JFCs those with orbital periods and Tisserand parameters in the range 2<T?3.1, while those comets coming from the same source, but that do not fulfill the previous criteria (mainly because they have periods ) will be called ‘non-JFCs’. We performed a series of numerical simulations of fictitious comets with a purely dynamical model and also with a more complete dynamical-physical model that includes besides nongravitational forces, sublimation and splitting mechanisms. With the dynamical model, we obtain a poor match between the computed distributions of orbital elements and the observed ones. However with the inclusion of physical effects in the complete model we are able to obtain good fits to observations. The best fits are attained with four splitting models with a relative weak dependence on q, and a mass loss in every splitting event that is less when the frequency is high and vice versa. The mean lifetime of JFCs with radii and is found to be of about 150-200 revolutions (∼. The total population of JFCs with radii within Jupiter’s zone is found to be of 450±50. Yet, the population of non-JFCs with radii in Jupiter-crossing orbits may be ∼4 times greater, thus leading to a whole population of JFCs + non-JFCs of ∼2250±250. Most of these comets have perihelia close to Jupiter’s orbit. On the other hand, very few non-JFCs reach the Earth’s vicinity (perihelion distances ) which gives additional support to the idea that JFCs and Halley-type comets have different dynamical origins. Our model allows us to define the zones of the orbital element space in which we would expect to find a large number of JFCs. This is the first time, to our knowledge, that a physico-dynamical model is presented that includes sublimation and different splitting laws. Our work helps to understand the role played by these erosion effects in the distribution of the orbital elements and lifetimes of JFCs.     

Radio OH observations of 9P/Tempel 1 before and after Deep Impact

We observed 18-cm OH emission in Comet 9P/Tempel 1 before and after Deep Impact. Observations using the Arecibo Observatory 305 m telescope took place between 8 April and 9 June, 2005, followed by post-impact observations using the National Radio Astronomy Observatory 100 m Green Bank Telescope 4-12 July, 2005. The resulting spectra were analyzed with a kinematic Monte Carlo model which allows estimation of the OH production rate, neutral gas outflow velocity, and distribution of the out-gassing from the nucleus. We detected typically 24% variability from the overall OH production rate trend in the two months leading up to the impact, and no dramatic increase in OH production in the days post-impact. Generally, the coma is well-described, within uncertainties, by a symmetric model with OH production rates from 1.6 to , and mean water outflow velocity of . At these low production rates, collisional quenching is expected to occur only within 20,000 km of the nucleus. However, our best-fit average quenching radius is 64,200 ± 22,000 km in April and May.     

Modelling meteor ablation in the venusian atmosphere

A comparative study of meteor ablation in the atmospheres of the Earth and Venus is presented. The classical single body meteor ablation model is extended to incorporate a heat penetration depth estimate allowing the simulation of larger meteoroids, than would an isothermal model. The ablation of icy and rocky meteoroids, with densities of 1.0 and 3.4 g cm⁻³, respectively, and initial radii of up to for rock and for ice (equivalent to an initial mass of in both cases), was simulated in both atmospheres. In general venusian meteors are brighter than terrestrial equivalents. Large, slow, rocky objects may be up to 0.7 mag brighter on Venus, while small, icy particles with entry speeds in the range 30-60 km s⁻¹, are found to be upwards of 2.7 mag brighter than at the Earth. Venusian meteors reach maximum brightness at greater altitudes than would similar particles at the Earth. Rocky meteoroids have their points of maximum brightness some 15-35 km higher up at Venus, between 90 and 120 km, whereas, for icy particles this altitude difference is about 5-25 km higher up than at the Earth, in the range 100-125 km. These findings agree, for the most part, with recent analytical studies. Venusian meteors, which last from 100 ms to , tend to be shorter-lived than terrestrial meteors, with correspondingly shorter visible trails. Large (), slow () icy particles reach a maximum magnitude of ∼−2 at Venus and remain visible for about one second, with a large section of the smaller faster meteoroids simulated here remaining visible for several hundred milliseconds. In light of recent space-based meteor observations at the Earth [Jenniskens, P., Tedesco, E., Muthry, J., Laux, C.O., Price, S., 2002. Meteorit. Planet. Sci. 37, 1071-1078], such brightness, height and duration estimates as suggested in this work, may be used in developing future observational campaigns to be carried out from Venus orbit.     

Hubble Space Telescope observations of the nucleus fragment 73P/Schwassmann-Wachmann 3-C

The investigation of fragmented comets provides information on the physical properties and internal structure of cometary nuclei, as well as insights into the mechanisms responsible for cometary breakups. The Jupiter-family Comet 73P/Schwassmann-Wachmann 3 (73P/SW3) fragmented non-tidally into at least four components, and probably more, in the autumn of 1995. Fragment C was detected with the Wide Field Planetary Camera 2 (WFPC2) of the Hubble Space Telescope (HST) on 26 November 2001 when it was 3.26 AU from the Sun and 2.34 AU from the Earth. The high spatial resolution of the HST allowed us to separate the signal of the fragment from that of its coma, and to determine its R magnitude in the Johnson-Kron-Cousins photometric system from four images taken with the F675W filter. Assuming a spherical body with a geometric albedo of 0.04 and a linear phase coefficient of 0.04 mag deg⁻¹ for the R band, we derived an effective radius of . The pre-breakup radius of the original nucleus was estimated to be 1.1 km, which implies that the volume of fragment C is ∼25% of the total volume of the pre-breakup nucleus. The limited temporal coverage of our observations preclude deriving an accurate shape or rotational period; our measurements are consistent with a rather spherical body but an elongated shape cannot be excluded. Fragment C was very active despite its rather large heliocentric distance, with an estimated dust production rate of (∼130 metric tons day⁻¹). A very large fraction of the surface area of fragment C must have been sublimating to sustain such a high level of activity. Fragment C may be recovered at its next return in 2006, if it does not experience further fragmentation.     

Deep Impact: Optical spectroscopy and photometry obtained at MIRA

We present spectroscopic and photometric observations, spanning the optical UV to the far red, before, during, and after the NASA Deep Impact event of July 4, 2005. The inner 2000 km of the pre- and post-impact coma was about 0.3 magnitude redder in B-R than in the outer coma. The pre-impact spectrum was a faint reflected solar spectrum dominated by molecular emissions extending >40,000 km from the nucleus. The post-impact light curve in R and I showed a rapid rise consistent with an expanding optically thick cloud during the first 18 min after impact. During the next 8 min the cloud became optically thin. Sixty minutes after impact the impact R-band flux reached a plateau at , the comet brightening by a factor of ∼4.3 above its pre-impact value observed in a 15″ aperture. The mean expansion velocity of the grains during the first 49 min was . The spectrum became dominated by scattered sunlight during the first hour after impact. The volume scattering function (VSF) observed 32 min after impact shows strong reddening. At 49 min, however, the VSF shows an additional twofold increase in the blue but only a 20% increase at 5500 Å. Post-impact spectra and R-I photometry showed rapid reddening. The particle size distribution, dominated by 1-2.5 μm particles shortly after impact, changed dramatically during the first hour due to sublimation of water-ice particles of this size. On the night following impact the comet was still substantially brighter than before impact, but R-I had returned to its pre-impact value. B-R remained significantly redder. The ejecta 25 h after impact was fan-shaped subtending ∼180° roughly symmetrical about position angle 225°. The mean expansion velocity 90° from the direction to the Sun was .     

Submillimeter Wave Astronomy Satellite observations of Comet 9P/Tempel 1 and Deep Impact

On 4 July 2005 at 5:52 UT the Deep Impact mission successfully completed its goal to hit the nucleus of 9P/Tempel 1 with an impactor, forming a crater on the nucleus and ejecting material into the coma of the comet. NASA's Submillimeter Wave Astronomy Satellite (SWAS) observed the ₁₁₀-₁₀₁ ortho-water ground-state rotational transition in Comet 9P/Tempel 1 before, during, and after the impact. No excess emission from the impact was detected by SWAS and we derive an upper limit of 1.8×¹⁰⁷ kg on the water ice evaporated by the impact. However, the water production rate of the comet showed large natural variations of more than a factor of three during the weeks before and after the impact. Episodes of increased activity with alternated with periods with low outgassing (). We estimate that 9P/Tempel 1 vaporized a total of N∼4.5×¹⁰³⁴ water molecules (∼1.3×¹⁰⁹ kg) during June-September 2005. Our observations indicate that only a small fraction of the nucleus of Tempel 1 appears to be covered with active areas. Water vapor is expected to emanate predominantly from topographic features periodically facing the Sun as the comet rotates. We calculate that appreciable asymmetries of these features could lead to a spin-down or spin-up of the nucleus at observable rates.     

Gravitational tidal waves in Titan's upper atmosphere

Tidal waves driven by Titan's orbital eccentricity through the time-dependent component of Saturn's gravitational potential attain nonlinear, saturation amplitudes (|T^′|>10 K, , and ) in the upper atmosphere (?500 km) due to the approximate exponential growth as the inverse square root of pressure. The gravitational tides, with vertical wavelengths of ∼100-150 km above 500 km altitude, carry energy fluxes sufficient in magnitude to affect the energy balance of the upper atmosphere with heating rates in the altitude range of 500-900 km.     

Saturn eddy momentum fluxes and convection: First estimates from Cassini images

We apply an automated cloud feature tracking algorithm to estimate eddy momentum fluxes in Saturn's southern hemisphere from Cassini Imaging Science Subsystem near-infrared continuum image sequences. Voyager Saturn manually tracked images had suggested no conversion of eddy to mean flow kinetic energy, but this was based on a small sample of <1000 wind vectors. The automated procedure we use for the Cassini data produces an order of magnitude more usable wind vectors with relatively unbiased sampling. Automated tracking is successful in and around the westward jet latitudes on Saturn but not in the vicinity of most eastward jets, where the linearity and non-discrete nature of cloud features produces ambiguous results. For the regions we are able to track, we find peak eddy fluxes and a clear positive correlation between eddy momentum fluxes and meridional shear of the mean zonal wind, implying that eddies supply momentum to eastward jets and remove momentum from westward jets at a rate . The behavior we observe is similar to that seen on Jupiter, though with smaller eddy-mean kinetic energy conversion rates per unit mass of atmosphere (). We also use the appearance and rapid evolution of small bright features at continuum wavelengths, in combination with evidence from weak methane band images where possible, to diagnose the occurrence of moist convective storms on Saturn. Areal expansion rates imply updraft speeds of over the convective anvil cloud area. As on Jupiter, convection preferentially occurs in cyclonic shear regions on Saturn, but unlike Jupiter, convection is also observed in eastward jet regions. With one possible exception, the large eddy fluxes seen in the cyclonic shear latitudes do not seem to be associated with convective events.     

Coring experiments with cryogenic water and carbon dioxide ices—toward planetary surface operations

As a prelude to the design of sampling devices able to extract materials from the icy surfaces of comets, outer-planet satellites, and the martian poles, it is necessary to understand some of the physical properties of these ices. To this end we have investigated the mechanical resistance displayed by two ices subjected to coring operations at low temperatures and under vacuum. The ices used in this study were water ice, frozen from liquid water, and carbon dioxide ice grown from its vapour. The coring tool employed had dimensions and required power levels that were comparable to a sample extraction system designed for a present-day spacecraft lander. The specific cutting strength, a parameter that measures the toughness of the material, has been measured while coring these two ices. For water ice this property rose from at an ice temperature of , to at . At the lower temperature of , pore-free carbon dioxide ice has also been measured to have a specific cutting strength approximately half that of water ice at the same temperature. These laboratory-based measurements may be used as guides for the power levels needed to core solid water and CO₂ ices at certain rates.     

CCD photometry of 23 minor planets

We present CCD photometric observations of 23 main-belt asteroids, of which 8 have never been observed before; thus, the data of these objects are the first in the literature. The majority showed well-detectable light variations, exceeding 0^m1. We have determined synodic periods for 756 Lilliana (936), 1270 Datura (34), 1400 Tirela (1336), 1503 Kuopio (998), 3682 Welther (359), 7505 Furushu (414) and 11436 1969 QR (123), while uncertain period estimates were possible for 469 Argentina (123), 546 Herodias (104) and 1026 Ingrid (53). The shape of the lightcurves of 3682 Welther changed on a short time-scale and showed dimmings that might be attributed to eclipses in a binary system. For the remaining objects, only lower limits of the periods and amplitudes were concluded.     

Interaction between eddies and mean flow in Jupiter's atmosphere: Analysis of Cassini imaging data

Beebe et al. [Beebe, R.F., et al., 1980. Geophys. Res. Lett. 17, 1-4] and Ingersoll et al. [Ingersoll, A.P., et al., 1981. J. Geophys. Res. 86, 8733-8743] used images from Voyagers 1 and 2 to analyze the interaction between zonal winds and eddies in Jupiter's atmosphere. They reported a high positive correlation between Jupiter's eddy momentum flux, , and the variation of zonal velocity with latitude, . This correlation implied a surprisingly high rate of conversion of energy from eddies to zonal flow: , a value more than 10% of Jupiter's thermal flux emission. However, Sromovsky et al. [Sromovsky, L.A., et al., 1982. J. Atmos. Sci. 39, 1413-1432] argued that possible biases in the analysis could have caused an artificially high correlation. In addition, significant differences in the derived eddy flux between datasets put into question the robustness of any one result. We return to this long-standing puzzle using images of Jupiter from the Cassini flyby of December 2000. Our method is similar to previous analyses, but utilizes an automatic feature tracker instead of the human eye. The number of velocity vectors used in this analysis is over 200,000, compared to the 14,000 vectors used by Ingersoll et al. We also find a positive correlation between and and derive a global average power per unit mass, , ranging from . Utilizing Ingersoll et al.'s estimate of the mass per unit area involved in the transport, this would imply a rate of energy conversion of . We discuss the implications of this result and employ several tests to demonstrate its robustness.     

A global solution for the Mars static and seasonal gravity, Mars orientation, Phobos and Deimos masses, and Mars ephemeris

With the collection of six years of MGS tracking data and three years of Mars Odyssey tracking data, there has been a continual improvement in the JPL Mars gravity field determination. This includes the measurement of the seasonal changes in the gravity coefficients (e.g., , , , , , ) caused by the mass exchange between the polar ice caps and atmosphere. This paper describes the latest gravity field MGS95J to degree and order 95. The improvement comes from additional tracking data and the adoption of a more complete Mars orientation model with nutation, instead of the IAU 2000 model. Free wobble of the Mars' spin axis, i.e. polar motion, has been constrained to be less than 10 mas by looking at the temporal history of and . A strong annual signature is observed in , and this is a mixture of polar motion and ice mass redistribution. The Love number solution with a subset of Odyssey tracking data is consistent with the previous liquid outer core determination from MGS tracking data [Yoder et al., 2003. Science 300, 299-303], giving a combined solution of k₂=0.152±0.009 using MGS and Odyssey tracking data. The solutions for the masses of the Mars' moons show consistency between MGS, Odyssey, and Viking data sets; Phobos GM=(7.16±0.005)×¹⁰⁻⁴ km³/s² and Deimos GM=(0.98±0.07)×¹⁰⁻⁴ km³/s². Average MGS orbit errors, determined from differences in the overlaps of orbit solutions, have been reduced to 10-cm in the radial direction and 1.5 m along the spacecraft velocity and normal to the orbit plane. Hence, the ranging to the MGS and Odyssey spacecraft has resulted in position measurements of the Mars system center-of-mass relative to the Earth to an accuracy of one meter, greatly reducing the Mars ephemeris errors by several orders of magnitude, and providing mass estimates for Asteroids 1 Ceres, 2 Pallas, 3 Juno, 4 Vesta, and 324 Bamberga.     

Detection of CH3D on Titan

We report the detection of ¹³CH₃D in Titan's stratosphere from Cassini/CIRS infrared spectra near 8.7 μm. Fitting simultaneously the ν₆ bands of both ¹³CH₃D and ¹²CH₃D and the ν₄ band of CH₄, we derive a D/H ratio equal to and a ¹²C/¹³C ratio in deuterated methane of , consistent with that measured in normal methane.