Astronomy and Computing 5 (2014) 57–69

Contents lists available at ScienceDirect

Astronomy and Computing

journal homepage: www.elsevier.com/locate/ascom

Full length article

Simulated measurements of 67P/Churyumov–Gerasimenko dustcoma at 3 AU by the Rosetta GIADA instrument using the GIPSI tool

V. Della Corte a,∗, S. Ivanovski b, F. Lucarelli a, A. Rotundi a, V. Zakharov c,d, M. Fulle e,A.V. Rodionov f, J.F. Crifo g, N. Altobelli h, E. Mazzotta Epifani ba Università Parthenope, Dip. Scienze Applicate, Centro Direzionale Isola C4, 80143 Naples, Italyb INAF - Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, 80131 Naples, Italyc Gordien Strato S. A. R. L., 11 Bd d’Alembert, 78280, Guyancourt, Franced LESIA, Observatoire de Paris, Place Janssen, F-92195 Meudon, Francee INAF - OsservatorioAstronomico di Trieste, via Tiepolo 11, 34143 Trieste, Italyf Russian Federal Nuclear Center - VNIIEF Sarov, NizhnyNovgorod Region, 607188, Russiag LATMOS, CNRS/UVSQ, 11 Bd d’Alembert, 78280 Guyancourt, Franceh ESA-ESAC, P.O. Box 78, E-28691 Villanueva de la Canada, Madrid, Spain

a r t i c l e i n f o

Article history:Received 2 October 2013Accepted 22 April 2014

Keywords:Space vehicles: instrumentsComets: 67P/Churyumov–GerasimenkoDust dynamicsNumerical simulations

a b s t r a c t

GIADA (Grain Impact Analyzer and Dust Accumulator) is an in situ instrument, on board the Rosettaspacecraft, designed to measure the dynamical properties of the dust grains emitted by the comet67P/Churiumov–Gerasimenko (hereafter 67P/C–G). It consists of three subsystems able to measure themass and speed of single dust grain and dust mass flux. Once the orbit and the attitude of a spacecraft aredefined, it is needed to simulate the performances of an in situ instrument. We present simulated GIADAperformances to evaluate its capability in fulfilling its scientific objectives along specific orbits. In orderto perform these simulations, because of the lack of real data on near-nucleus cometary environment, itis necessary to use a modeled dust coma along the spacecraft (S/C) orbits. We developed GIPSI (GIADAPerformance Simulator), a simulation tool conceived to replicate the GIADA capability in detecting comadust features through the dust abundances, mass and velocity dust distributions measurements. Usingstate-of-the-art comamodeling, we evaluated three different Rosetta orbit mission scenarios. We outlinethe optimal S/C orbit for GIADA by means of achievable dust coma evolution description, number ofcollected particles and grain velocity measurements. The quasi circular orbit with a 5 km peri-centerradius and a 10 km apo-center radius, during the pre-landing close observation phase is the best suitedfor the GIADA instrument.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Despite more than a century of ground-based observations ofcomets and the successful achievement of ten cometary flyby mis-sions during the last 25 years (Festou et al., 2004), the physicalcharacterization of cometary nuclei and their gas and dust envi-ronment remain rather primitive in many aspects. This is essen-tially due to the absence of adequate space and time resolutionof the nucleus vicinity because of the very brief duration of flyby

∗ Corresponding author. Tel.: +39 3286281835.E-mail address: vincenzo.dellacorte@uniparthenope.it (V. Della Corte).

http://dx.doi.org/10.1016/j.ascom.2014.04.0042213-1337/© 2014 Elsevier B.V. All rights reserved.

observations (less than one full rotation of the nucleus) and be-cause it is impossible to obtain this information through ground-based observations. The European Space Agency (ESA) Rosettamission (Glassmeier et al., 2007), launched in 2004, will start inmid-2014 its observations of comet 67P/Churyumov–Gerasimenko(67P/C–G) from orbit and will release a lander on its nucleus inNovember 2014. This is the first cometarymission to overcome theabove-mentioned limitations, by allowing observations from small(down to 5 km) distances of the target comet, along about one halfof its orbit (from3.6AUpre-perihelion to the 1.3 AUperihelion, andback to 1.6 AUpost-perihelion). The expected huge amount of highspace and time resolution data will require the usage of advanced3D + t dusty gasdynamical methods to build a comprehensivemodel of the nucleus activity. Several instruments onboardRosetta

58 V. Della Corte et al. / Astronomy and Computing 5 (2014) 57–69

Fig. 1. GIADA accommodation on the Rosetta spacecraft (courtesy of ESA, modified).

are dedicated to study various aspects of dust in the cometarycoma, all of which require a certain level of exposure to dust toachieve their goals. At the same time, impacts of dust particles canconstitute a hazard to payload-sensitive surfaces. To estimate thedust collection and analyze instrument performances, it is neces-sary to assess the optimal dust measuring scenario in the 67P/C–Gcoma by means of observation data coupled with advanced fluid-dynamics modeling: the so-called GIADA Performances Simula-tor (GIPSI; GIADA, Grain Impact Analyzer and Dust Accumulator)software was designed for this purpose. It is a tool simulating GI-ADA performances having as inputs the outputs of the presentlyavailable dust environments models. Here, we use the ‘‘Rodi-onov–Zakharov–Crifo’’ coma model (hereafter called RZC model),an ab initio dusty gasdynamical model using boundary conditionscompatiblewith the limited information available on the target nu-cleus and its activity is the only presently existing comamodel fea-turing the 3D + t capability absolutely needed to obtain adequaterepresentations of the vicinity of an active comet nucleus (Crifoet al., 2004a). When defining the gas and dust production rates, in-put parameters for the model, great care is taken to check that theresulting computed coma properties are fully compatible with theresults of all available nucleus activity observations. Still, becausethe observational information is very limited, the requirement ofcompatibility between model and astronomical data allows defin-ing possible ranges for the model input parameters. This results inthe definition of comapredictionswith significantly differing prop-erties. Only one of these possible coma configurations is consideredin the present work, for reasons given in detail below.

We focus our simulation work to conditions applicable in theearly phase of the mission, just before and after the RosettaLander release (heliocentric distances near 3 AU and nucleocentricdistances <50 km).

This article is aimed to check the capability and sensitivityof GIADA (see Fig. 1), one of the Rosetta orbiter’s instruments(Colangeli et al., 2007), to capture the features, and theirtime evolution, of a cometary dust environment along specificspacecraft (S/C) orbits. This aim is achieved using GIPSI.

2. The GIADA instrument

GIADA is an instrument with two systems devoted to the mea-surements of the physical properties of cometary dust grains, anda main electronics that manages the instrument and its commu-nication with the S/C . The first measurement system includes twosubsystems: the GrainDetection System (GDS) and underneath theImpact Sensor (IS); the second is the MicroBalance System (MBS).The GDS+ IS is designed to measure momentum and scalar veloc-ity (and hence mass) of single grains entering the instrument. TheGDS optically detects grains crossing a laser curtain of 10×10 cm2

and thickness of 3mm,measuring the scattered light by each singlegrain. The laser curtain is realized with four laser diodes (emittingat 915 nm) by means of their fore-optics. The lasers (numberedin sequence from #1 to #4) are pulsed at 100 kHz frequency incouples: when lasers #1 and #3 are on, lasers #2 and #4 are off,and vice versa. For each grain crossing the light curtain, the scat-tered/reflected light is detected by two series of detectors (four foreach series) placed at 90° with respect to the sources on oppositesides (left and right series). The signal of the photodiodes is treatedby the proximity electronics in order to reject the common modenoise. A dedicated collecting optic (Winston cone) is placed in frontof each photodiode in order to guarantee an uniform sensitivity inthe detection area. The amplitude of the signal is linked only to thephysical (shape and size, mainly) and chemical (through the opti-cal constants) properties of the detected grain (Epifani et al., 2002).The IS is formed by a 0.5-mm-thick aluminum square diaphragm(sensitive area of 100 cm2) equipped, in the center and at the cor-ners, with five piezoelectric sensors (PZTs). When a grain impactsthe sensing plate, the generated bendingwaves are detected by thePZTs (having a resonance frequency accorded to the plate-bendingwave frequency),whose output ismonotonically related to themo-mentum of the incident grain (Esposito et al., 2002). The GDS givesthe first estimate of the speed of the detected grain (light curtaincrossing time) and starts a time counter that is stoppedwhen the ISdetects the grain impact. Bymeans of the times-of-flight, the speedof the grain is measured (see Fig. 2). The coupled GDS + IS sys-tem, that has a field of view of 37°, determines the following for

V. Della Corte et al. / Astronomy and Computing 5 (2014) 57–69 59

Fig. 2. GIADA combined GDS-IS working principle: a dust grain entering in GIADAis detected first by the GDS and then by the IS, for this dust grain GIADA obtainsthe optical cross section, the momentum and the time of flight between the 2subsystems.

Table 1Lower and upper detection limits of quantities measured by GIADA subsystems.

Subsystem Physical quantity Lower limit Upper limit

GDS Radius (Silicate) (µm) 15 200GDS Radius (Carbon) (µm) 60 500GDS IS MBS Scalar velocity (m s−1) 1 180GDS + IS Momentum (kg m s−1) 6.5 × 10−10 4.0 × 10−4

Cumulative mass (g) 1 × 10−10 1 × 10−4

Scalar velocity (m s−1) 1 180

each detected grain: speed, time-of-flight, momentum, and mass.The MBS system is a network of five quartz crystal microbalances(QCMs) positioned on the top plate of GIADA. In order to cover thewidest range ofmeasurements, the QCMs, eachwith a field of viewof 40°, point along the +Z, +X, −X, +Y , and −Y directions of theS/C coordinate system. Each QCM is equipped with a pair of sens-ing quartz crystals, characterized by a small temperature depen-dence frequency to obtain a good signal stability. One crystal isexposed to dust deposition whereas the second works as a refer-ence for the vibrating frequency. The addition, or removal, of smallmass depositions on the exposed quartz crystal induces a change inthe resonating frequency of the quartz crystal. Measuring the beatfrequency of the two crystals, the dust flux and fluence are derived.In fact, the output signal is proportional to the mass deposited onthe QCM (Palomba et al., 2002). The sensitivities and the upper de-tection limits are reported in Table 1 for each GIADA subsystem.

3. Observational data on the comet 67P/C–G

The most critical information needed to build a circumnuclearmodel is, evidently, information on the nucleus itself. Unfortu-nately, due to its exceedingly small size (kilometric), only coarseand uncertain approximations of the nucleus shape can be derivedfrom on-ground observations (actually, from the orbiting Hubbletelescope). Two 67P/C–G nucleus shapes have been derived on thetwo successive perihelion passes of the comet of 2002 (Lamy et al.,2003) and 2007 (Lamy et al., 2007). These shape determinationssubstantially differ between them; in addition, they cannot revealsmall topographic details (hectometric or less).

As to the gas production – driver of the dust production – onlythe total production of H2O near the perihelion and at 1.84 AUwas measured. The derived values are, however, averages over

several nucleus rotation periods. It is believed that, as all comets,67P/C–G also produces CO, CO2, and awealth of tracemolecules. Anestimate of the production rates of CO and/or CO2 – assuming thesemolecules to be the most abundant ones irrespective of H2O – wasderived from photometric IR observations by Bauer et al. (2012),yielding at 3.4 AU 8×1026 mol/s if CO dominates, or 8×1025 mol/sif CO2 dominates. On the other hand, Ootsubo et al. (2012) estimateCO < 1.35 × 1026 mol/s at 1.8 AU. So the interval of uncertaintyon CO production is at least 1 × 1026–8 × 1026 mol/s at 3 AU.

The grainmass spectrum, shape spectrum, and total productionrates can be derived from the spatial characteristics of the dust tailobserved from the Earth; the solar radiation pressure acting on thegrains far from the nucleus performs some kind of mass spectrom-etry of the grains (the ratio between solar radiation pressure andsolar gravity forces places grains of different mass along differentorbits); thus, the dust images can be inverted into total mass fluxand ejection velocity. In Fulle et al. (2004), a comprehensive sum-mary of the dust environment of 67P/C–G from 3.6 AU to the peri-helion, consistent with the available astronomical observations in2004, is given.

4. Dust model

4.1. General considerations

In the absence of 67P/C–G flyby observations, the real distribu-tion of gas and dust around the nucleus, and the nucleus itself, re-mains unaccessible. Only ground-based images of the distributionof the emitted cometary dust are available, that is, on spatial scalescompared towhich the nucleus can be considered to be a point-likesource of grains released (isotropically or not) at mass-dependent‘‘initial velocities’’ (also isotropically or not). These images involveflight times order of magnitudes larger than the nucleus rotationperiods, so that the nucleus rotation can in general be ignored. Fi-nally, such observations blend all sizes together. Fortunately, how-ever, the grainmotion in these regions is relativelywell understood(Keplerian orbits) so that it is possible, by trial and error fits, to de-rive ‘‘effective’’ mass spectra and initial velocities from model fitsto the data (Fulle et al., 2010). These are only averages over the ro-tation of the nucleus of the real velocities, fluxes, mass spectra, andvelocity distributions (at each mass).

In ab initio physical modeling, where the nucleus shape androtation are duly considered, a model for the distribution of gasfluxes over the nucleus surface is postulated, hydrodynamicalmethods are used to derive the resulting 3D + t structure of thenear-nucleus gas outflow, and, finally, dust is seeded in the flowand the density and the velocity vectors acquired by the grains arecomputed (Crifo et al., 2004b). Of course, the ‘‘dust seeding’’ mustbe based on the results from the mentioned dust-tail analysis.

4.2. Fulle 67P/C–G dust-tail analysis

Fulle’s dust-tail model (Fulle, 1987, 1989) derives for each dustmass an ejection flux and an ejection velocity (Fulle, 1992). Thegrains are assumed to be spherical. According to the derived dustejection velocity, the mass able to escape the nucleus gravityfield at a distance of 20 nucleus radii, assuming a bulk density of1000 kg/m3, is checked. Due to the nucleus asphericity and possi-bly lower bulk density, the escape velocity is probably well lowerthan the assumed value of 0.5 m/s (Fulle et al., 2010). The methodalso requires the value of grain-specific mass to be postulated. Thelowest values of the dust mass loss rate are 0.1 kg/s at 3.4 AU andbetween 10 and 40 kg/s at 3 AU, derived by the assumed specificmass. The reported maximum dust mass loss rate at 3.4 AU is 0.24and 112 kg/s at 3 AU.

60 V. Della Corte et al. / Astronomy and Computing 5 (2014) 57–69

Fig. 3. Reference frame used to introduce anisotropy in Fulle’s 67P/C–Gmodeled dust environment: Z-axis is along the nucleus spin axis, the Sun direction is in the XZ-plane(_SUN = 71° at 3 AU). Six sectors are considered, each one centered on the six main axes +X, −X, +Y , −Y , +Z , and −Z . Sector 1 is always in the nightside and the subsolarpoint is in Sector 0.

Fig. 4. Comparison of the dust coma fits of the 67P/C–G VLT images, taken on June 1st 2008 at 3 AU, obtained with the isotropic model (left) with no night dust ejection, thatis, all weights = 20% but −X = 0, and anisotropic model (right), showing a good reproduction of the anti-sunward coma extension and of the left–right coma asymmetry.

The fits obtained by Fulle et al. (2010) are here slightly improvedintroducing an anisotropy in the dust ejection (Fig. 3). In fact, asa consequence of the short time occurring between actual dustejection (set as starting at 3.4 AU) and coma observation (at 3 AU),the isotropy ejection assumption yielded the dust coma isophotesfits in Fulle et al. (2010) be much more circular than the observedones.

Introducing the anisotropic dust ejection requires a referenceframe partly linked to the nucleus; see Fig. 3: the Z axis coincideswith the nucleus spin axis (pointing towards the northern ecliptichemisphere) and the X axis is oriented such as to have the subsolarpoint always in the XZ plane. The whole space surrounding the nu-cleus is divided into six squared angular sectors, each one centeredon the six main directions +X, −X, +Y , −Y , +Z , and −Z .

Each anisotropic sector is characterized by a specific dust lossrate obtained by multiplying the total dust loss rate by a weight w(the percentage of the total dust loss rate for the specific sector).The anisotropic and isotropic models are identical when all theseweights are equal to 16.67%. In the anisotropic dust model themotion of the dust coming from each sector is computed as for theisotropic model: the anisotropic coma is the linear combination ofthe six ‘‘sectors coma’’. Bymeans of a trial-and-error procedure, weexplored all the possible weight combinations in order to obtainthe best fit of the observed isophotes, always assuming no nightactivity. The best fit (see Fig. 4) is obtained for the weights:

w(+X) = 5% and w(−X) = 0%

w(+Y ) = 50% and w(−Y ) = 10%w(+Z) = 30% and w(−Z) = 5%.

The very low weight of the night-side sector suggests that al-most no dust comes from the night side. The very low weight ofthe sector containing the subsolar point has no immediate explana-tion:many tests confirmed that the observed coma cannot be fittedassuming a significant dust loss from the subsolar point. As a con-sequence, almost all the dust (95% according to the weights above)seems to come from sectors crossed by the terminator (+/−Y and+/−Z sectors). The model assigns to all dust grains of the samesize bin a constant radial velocity equal to the terminal velocitycomputed in Fulle et al. (2010).

4.3. The RZC near-nucleus coma model

The ab initio dusty comamodel used here is based on the 3D+ tgas-dust comamodel described in Crifo et al. (2004b). Themethodsusedwere described in detail in Rodionov et al. (2002): they consistin solving the three governing Euler flow equations for the gas, andone single-fluid flow equation for each kind of dust grain assumedto be seeded into the gas at the surface, and dragged outwardsby the gas. The grains are assumed to be spherical in shape. Thesingle-fluid method is not a totally rigorous method, but describesthe dust distribution correctly enough for this study (keeping alsoin mind that real grains are not spherical). The input parameters

V. Della Corte et al. / Astronomy and Computing 5 (2014) 57–69 61

Table 2Dust-to-gas ratio scaling factors (C) used to adjust theHalley-like RZC solutions. The size and the densityof the four types of grains used in GIPSI simulations.

Grain type Size (µm) Density (kg/m3) Cpre−landing C3AU

HD500 500 1000 3.5e−02 14e−02HD100 100 1000 0.4e−02 1.8e−02LD500 500 100 0.9e−02 0.36e−02LD100 100 100 0.1e−02 0.4e−02

of the RZC model are the nucleus shape and the distribution ofthe gas and dust fluxes over the surface. They are all a matter ofconjectures and/or coarse approximations and will remain so untilthe first Rosetta observations.

4.3.1. Nucleus modelIn the present study, the RZC model uses the ‘‘starfish’’ shape

described in Crifo et al. (2004b). This shape is an analytical approx-imation to the one derived by Lamy et al. (2003) fromHubble SpaceTelescope 2002 observations. It was found unnecessary to recom-pute model dust comas based on the more recent results (Lamyet al., 2007; Lowry et al., 2012), because these shapes lead to simi-lar dust comas in the frame of our GIADA performance simulationwork.We assume the nucleus outer layer to be amixture of porousice and porous mineral dust. We characterize each element of thesurface by its icy area fraction f , ratio of its exposed ice area to itstotal area (Crifo et al., 2004b). The rotation periodwas found (Lamyet al., 2007) to be about 12 h and around the nucleus Z axis. Finally,a spherical gravity field for a nucleus mass of 3.45 × 1012 kg wasassumed. For the present study, the subsolar point latitude was setto 45°, as in our previous studies (e.g. Crifo et al., 2004b). This wasdone to allow the reader to compare the coma structure publishedtherein, in particular the gas outflow structure,with the figures andresults obtained in the present work. This latitude cannot be pre-dicted accurately today. The range of expected values for Rosettanear 3 AU is at least 10°–30°. Our present value should characterizethe large-latitude case about adequately, but additional runs withsmall values are needed for comprehensive studies.

4.3.2. Gas production modelThe two species CO and H2O are assumed to be simultaneously

produced from each element of the surface (see Rodionov et al.(2002) and Crifo et al. (2004b)). The H2O flux, ZH2O, is computedat each point from dusty ice surface sublimation energy budgetequations; thus, it is a function of the heliocentric distance rh, ofthe nucleus orientation angles, and of the subsolar point position.The icy area factor f was assumed to be constant over the surfaceand the value f = 0.05was adopted, in order to obtain a computedperihelion (rotation-modulated) H2O production rate in excellentagreementwith the (rotationally averaged) observed value. At rh =

3AU, this leads to a rotation-modulated total gas production rateof H2O of the order of about 3 × 1026 molecule/s. We postulatearbitrarily the flux of CO, ZCO m−2 s−1, at each point of the surfaceby the following equation:

ZCO = QCO

a0Aext

+(1 − a0)max[cos z⊙, 0]

A⊙(u⃗⊙)

(1)

where z⊙ is the solar zenith angle, QCO is the adopted total CO pro-duction rate, 0 ≤ a0 ≤ 1 is a day-to-night asymmetry parameter,Aext is the external nucleus area, and A⊙ is the nucleus solar lightcapture cross section when the Sun is in the nucleocentric direc-tion with unit vector u⃗⊙. In the present study, we set: (1) QCO atits upper-limit value 1027 already assumed in Crifo et al. (2004b):this value is a realistic upper limit value, as shown by the fact thatthe rate reported by Bauer et al. (2012), 8.2 × 1026 mol/s, is com-patible with their observations, (2) a0 = 0.9 for all RZC solutions

in this paper; (3) Aext = 40 km2 (Lamy et al., 2007); (4) the so-lar zenith angle, z⊙, is the angle between the direction of Sun cen-ter and the direction of the surface point measured with respect tothe nucleus center. This angle assumes a value in general changingwith rotation phase; and (5) A⊙, this parameter in the configura-tion used for the RZC model solution (Sun placed at 45° from theequator) changes with time, i.e. with the angular position of thenucleus within the rotation period and is of order of 10 km2.

4.3.3. Dust production modelThe RZC code assumes that the surface dustmass flux is, at each

point, and for each grain size, proportional to the total net gasmassflux at this point, and that all grains are spherical and of a commonspecific mass density. Then the constant of proportionality χ(md)between the two fluxes depends only upon the grain mass md.In Crifo et al. (2004b), Halley χ(md) values (Crifo and Rodionov,1997) were adopted, for want of information on 67P/C–G values.Since then, Fulle et al. (2010) have derived 67P/C–G dust loss rates.Hence, here the Halley values were replaced by new χ(md) valuescomputed such that the dust loss rates obtained are in agreementwith Fulle et al. (2010):

F Fulle(md) =

smdρd(χ67P)(v⃗d · u⃗)dS (2)

where ρd is the dust grain number density, χ67P is the 67P/C–Gdust-to-gas ratio, v⃗d is the dust velocity vector, u⃗ is the unit vectorin the radial direction, and S is the surface of a sphere with radiusequal to the distance between the S/C and the nucleus center. Inearlier studies on the prediction of the dust amount that was tobe measured during the flyby of the Stardust mission to comet81P/Wild 2, Landgraf et al. (1999) also provided an adjustmentof the dust activity to the observed data through the scaling ofthe dust-to-gas ratio. It is to be noted that Fulle et al. (2010)have derived quite different dust rates for pre-landing conditions(3.2 AU) and post-landing conditions (3 AU), viz. 23 and 112 kg/s,respectively. Yet we here assume the same gas production in bothcases (about 56 kg/s). Table 2 shows the derived values of C(md) =

χ67P/χHalley.

5. GIPSI: GIADA simulator

The GIPSI tool is a Java client software able to simulate GIADAperformances (Fig. 6).More specifically, GIPSI forecasts howGIADAreacts to dust environment along specific orbits for defined timeintervals. Inputs to GIPSI are the outputs coming from 3D + tdust models (e.g., grain number density, dust size distribution,and velocity). As inputs to GIPSI, in addition to the 3D + t modeloutputs, we use the S/C and comet orbits (S/C attitude, S/Cposition, and speed along the orbit for each time step) and GIADA’sparameters (i.e. Field of View, sensitive surface area, subsystemssensitivities). Any dust model output can be used as input for GIPSIcomputations. The efficiency of each GIADA sensor can be adjustedduring the mission, for ad hoc simulations.

For each time step and position along the S/C orbit, GIPSItransforms the vector parameters of the dust model outputs intoGIADA instrument reference frame considering the rotation of the

62 V. Della Corte et al. / Astronomy and Computing 5 (2014) 57–69

nucleus and the velocity of the S/C . The simulation outputs are:(1) the number of dust grains detected separately by the GDS andIS subsystems and by the coupled GDS + IS system; (2) the dustmass accumulated on each QCM of the MBS system; (3) the dustparameters along the specific orbit (dust velocity and flux); and(4) the S/C orientation and attitude to the comet.

6. Results

The RZC model was used to calculate the dust rates and ve-locity of four grain types: two different sizes, 500 and 100 µm,and two different densities, high density (HD) and low density(LD), 1000 and 100 kg/m3, respectively (see Table 2). These dustgrain sizes have been selected in order to cover the experimentallytested sensitivity range of the GDS + IS subsystem. In fact, dur-ing the GIADA calibration activity, the smallest cometary analoggrains dropped into the GIADA instrument were about 100 µm inradius. It is to be noted that the lower limit of the sensitivity rangereported in Table 1 is obtained by an extrapolation of the exper-imental data. For the extrapolated lower limit, we estimated thatthe dust rates based on the 67P/C–G dustmass loss rate (Fulle et al.,2010) remains below the maximum number of events per seconddetectable by GIADA. In addition, we do not expect that the dustgrains entering GIADA accumulate on the IS surface. The impingingparticles bounce back with a high probability of falling apart the ISsensitive surface. Thus, high dust fluxes hardly arrest the GDS+ ISmeasurements.

In our simulations, we considered two different phases of theRosetta mission: the ‘‘pre-landing phase’’ and the ‘‘post-landingphase at 3 AU’’. The ‘‘pre-landing phase’’ starts in the middleof September 2014 and lasts till the end of the lander nominalmission, that is, the middle of November 2014, and it is dividedinto the Global Mapping Phase (GMP) and the Close ObservationPhase (COP). The GMP is focused on studying the comet physicaland dynamical parameters and the nucleus surface, whereas theCOP is designed for an in-depth analysis of the candidate landingsites. In this work on the pre-landing, we will focus on the COP.The ‘‘post-landing phase at 3 AU’’ begins at the end of the landernominal mission; its duration will depend on the actual cometaryactivity that constraints the feasibility of the bound orbits. For thesimulations, we considered the following specific orbits providedby the ESA/Rosetta Scientific Ground Segment (ESA/SGS) (Fig. 7):

– Quasi-circular orbit with a 5 km peri-center radius and a 10 kmapo-center radius (pre-landing COP). The time range is from2014-10-13T11:00:00 to 2014-10-15T23:00:00.

– Bound polar circular orbit at 10 km radius with 20° tilt from theterminator (post-landing 10 km orbit). The time range is from2014-11-15T00:00:40 to 2014-11-17T10:00:40.

– Bound dawn to dusk circular orbit at 30 km radius (post-landing30 km orbit). The time range is from 2014-11-15T00:00:40 to2014-11-27T10:00:40.

In Fig. 5, the density distribution (left plates) and the dustvelocity (right plates) for the four types of grains along the threeorbit scenarios are given. The distributions represent the dustenvironment in the 10 km post-landing orbit plane. In the plots aresigned five positions of the S/C along the orbits where a specificRZC solution is valid.

All the simulations are performed imposing an inclination forthe comet rotation axis to have the subsolar point at 45° latitudein the comet fixed reference frame.

6.1. Pre-landing COP orbit

In this section, we report the GIPSI estimations of the dust ratesdetected by GIADA along the pre-landing COP orbit. A time interval

Table 3Cumulative dust collected byGIADA along the different orbit scenarios as calculatedwith GIPSI using RZC and Fulle coma dust model solutions.

Orbit HD100 LD100 HD500 LD500

Collected dust grains using RZC model output

Pre-landing 438 392 16 213 AU 10 km 1203 1202 37 593 AU 30 km 551 540 0 27

Collected dust grains using Fulle model output

Pre-landing 256 316 10 133 AU 10 km 271 326 11 133 AU 30 km 313 360 13 14

of 60 h, that is, longer than the S/C orbital periodwas used; thus, anoverlap in the S/C trajectory takes place. The dust rate varies withhigh frequency along the whole orbit (Fig. 8). The dust rate profileshows a wide enhancement between the 27th and 37th hour.

Fig. 9 shows the velocity profiles for the four types of grains.Velocity profiles remain similar, but we obtain higher velocities forLD particles, LD100 and LD500. In addition, the enhancement in thevelocity profiles between equal-density grains is maintained alongthe entire simulated orbit and it is comparable for both classes ofdensity types (HD and LD).We report a study on the dust velocitiescomputed with the RZC model in comparison with the measuredvalues by GIADA along the three orbit scenarios in Section 7.

As expected, the smaller the particle sizes, the higher thecollection rate of particles (Fig. 8). For LD100 and HD100 grains,we estimate a number of collected particles about 20 times thenumber for LD500 and HD500, respectively. The LD particles (i.e.,LD100 and LD500) are more abundant in comparison with theiranalogs, in size, of higher density.

Since the S/C orbit period (about 43 h) is not a multiple of thenucleus rotational period (about 12 h), GIADA is able to see thecoma dust environment evolved from two different nucleus areasat the same local time (Fig. 8). Quite a high number of particles(Table 3) along the pre-landing COP orbit is collected in a relativelyshort time. The low dust load prevised at 3.2 AU is compensatedby the vicinity of the S/C to the nucleus along the pre-landing COPtrajectory.

6.2. Post-landing 10 km bound orbit

The capability of GIADA to describe the variation in the dustycoma on a short time scale is proved by the GIPSI simulations(Fig. 10). The lack of dust detection HD500 in the time intervalfrom the 26th to the 32th hour (see Fig. 10 and Table 4) is dueto the relative velocity between the S/C and the dust grainswhich causes deviation of the particle motion from the instrumentboresight direction and it leaves the grains outside the GIADAsubsystems FOV (Fig. 10). The velocities measured by GIADA alongthe 10-km-bound orbit using the RZC solutions are reported inFig. 11. In comparison with the pre-landing case, we note thatthe velocity profiles are smoother. Nevertheless, single dust grainschange significantly the velocity direction deviating from the radialone for the same time interval for which we obtained a lack ofdetection. The velocity values of the low density particles havehigher velocities than the denser ones, as expected.

The results obtained with the post-landing 10-km-bound orbitscenario show that GIADA is able to collect a statistically meaning-ful number of particles (see Section 7) in a short observational time(about 2.5 days) for all type of grains, even if there is no detectionof HD500. This allows the detection of the 67P/C–G dust mass lossrate variation on a short time scale even for high anisotropy in thecoma.

V. Della Corte et al. / Astronomy and Computing 5 (2014) 57–69 63

a b

c d

e f

g h

Fig. 5. The dust environment predicted by RZC model for the four types of grains (see Table 2) along the 10 km post-landing orbit. Each RZC solution is valid for severalGIPSI simulation instants, that is, five times for the pre-landing and post-landing 10 km orbits and twenty five times for the post-landing 30 km orbit. In the plots are signedfive positions of the S/C where the same RZC solution has been used. The plots are structured as follows: the left column shows the RZC number density distribution (cm−3)and the right column—the RZC 3D dust velocity distribution in the post-landing 10 km orbit plane; the sequence of plots (from the top to the bottom) are for HD500, HD100,LD500, and LD100 types of grains, respectively.

6.3. Post-landing: 30-km-versus 10-km-bound orbit

Here, we study a post-landing 30-km-bound orbit. The simi-larity of the 10 and 30 km orbit geometries (Fig. 7(a)) allows tocompare the dust rates versus the S/C distance from the nucleus,having in mind that there is a shift in the orbits starting position

of about 40°. In all the comparisons we will present in the follow-ing this orbit shift is taken into account. In fact, since the 30 kmorbit lasts more than five times the 10 km one, the time spent bythe S/C along the 30 km orbit in each coma sector is longer. Theconsequence is that the farther GIADAmeasures from the nucleus,the longer time is needed to get an acceptable number of grains.

64 V. Della Corte et al. / Astronomy and Computing 5 (2014) 57–69

Fig. 6. Block diagram of GIPSI tool.

Table 4Dust velocities predicted by RZC dust model (vmin and vmax) along the orbitscompared to the GIPSI results of GIADA velocity measurements (vms

min, vmsmax) for

the four types of grains. The fifth column shows the mean error of GIADA velocitymeasurements along the three orbits. The velocity values at 3 AU, reported in Fulleet al. (2010) are radial terminal velocities and for four type grains are as follows:vHD100 = 10 m/s; vHD500 = 4.7 m/s; vLD100 = 32 m/s; vLD500 = 15 m/s.

Grain type vmin vmsmin vmax vms

max emean (%)

Pre-landing orbit

LD500 5.03 5.01 11.97 11.94 <1LD100 10.77 10.76 25.45 25.40 2HD500a 1.79 1.63 3.94 3.86 8HD100 3.41 3.41 8.16 8.15 <1

10 km orbit

LD500 5.70 4.75 11.89 11.88 <1LD100 11.80 10.12 25.26 25.25 2HD500a 1.89 1.68 4.05 3.75 11HD100 3.87 3.23 8.11 8.10 <1

30 km orbit

LD500 5.25 5.25 12.52 12.51 <1LD100 10.29 9.90 26.62 26.60 2HD500 1.79 – 7.26 – –HD100 3.56 3.56 8.54 8.53 <1a The mean error for HD500 is high because of the deviation from the boresight

instrument direction.

When the S/C moves farther from the nucleus GIADA samples thesame coma sector for a longer time, hence it is able to describemore accurately the coma sector region. But the disadvantage inthis case is that to resample the same coma region GIADA has towait a longer time (the S/C revolution period). In addition, to ob-tain the same number of particles an about ten times longer acqui-sition interval is necessary. More details on the comparison of thecumulative number of collected grains in each of the orbit scenar-ios are given in Section 7. In the dust rates profiles for the 30 kmorbit (Fig. 12), a hollow-shaped region of about 50 h is evident,

corresponding to the 7 h hollow-shaped region present in the10 kmorbit (Fig. 10). For the 30 kmorbit, the LD100dust rates aver-age in the hollow-shaped region is less than 1 particle/hourwhile itis 10 particles/hour for the 10 km orbit. The ‘‘hollow’’ in the 30 kmdust rates corresponds to the orbit sector around the −Z directionin the reference frame of the RZC model, reproducing the low dustproduction emission foreseen by the RZC model. On the edges ofthe ‘‘hollow’’ there are two wide regions of dust rate high variabil-ity (Fig. 12)which are due to the passage of the S/C in high-activitycoma regions predicted by the RZC solutions (Fig. 5). We note thatin the case of the 30 km post-landing orbit, there is no HD500 col-lection. The reason of no detection of the HD500 particles is thattheir trajectories are out of the instrument FOV.

Velocity profiles of all detected grain types (GIADA completelyloses along this orbit the HD500 particle) along the 30 km orbit(Fig. 13) maintain the same behavior as for the 10 km one (Fig. 11).The velocity profiles obtained along the 30 km orbit, with respectto those obtained at the 10 km one, describe better the velocityvariability owing to the S/C longer residence time in a certain comaregion. As for the 10 km orbit, the bigger the grain, the lower isthe velocity and the smaller the specific density, the higher is thevelocity.

7. Discussion

GIPSI simulations performed with RZC dust environment (Crifoet al., 2004b) for four dust grain types (see Table 2) chosen to coverthe GIADA sensitivity limits allow us to check GIADA performancesat different mission scenarios. In addition, evaluation and rankingof possible trajectories can be done. In the following, discussing theresults obtained we will give an example of how to define a GIADApreferred orbit scenario, it being reminded thatmanymore simula-tions are needed for a robust choice. We will also demonstrate theGIADA capability to detect specific variability or discontinuities inthe dust distribution within the coma and peculiar or specific dy-namical properties of the dust.

7.1. Cumulative number of particles detected by GIADA

GIADA performance threshold is reached when it detects astatistically significant number of grains; in order to define it, wehave to assume a dust size distribution. Assuming it is a power lawdust distribution (independently from the slope), the statisticallyacceptable number of grains is defined as at least ten particlesfor each size bin (Clauset et al., 2009). This constraint should betaken into account especially for the less abundant grain type. Weconsider to have good statistics when GIADA collects at least tenHD500 grains.

Table 3 summarizes the total number of particles estimatedto be collected by GIADA along the three orbit scenarios andfor the four grain types. The numbers have been obtained byusing two simulated dust coma scenarios as inputs for the GIPSIsimulations: the RZC and Fulle solutions. The reported numbersshow that independent dust coma representations do not lead toradically conflicting conclusions in terms of GIADA capabilities.In addition, confirm that the global dust parameters (e.g. gasproduction rate) here adopted by RZC are consistent with bestavailable fit of dust-tail data we have, that is, the only onesprovidingdetailed information ondust parameters needed as inputby GIPSI. The results reported in Table 3 for RZC show that short-duration observations (2.5 days) are sufficient to obtain good duststatistics along the pre-landing COP and the post-landing 10-km-bound orbits. In the case of the post-landing 30-km-bound orbitwe have no detection of HD500. In this case, the S/C trajectorydoes not ensure the necessary condition for good statistics, that is,having at least ten HD500 particles, while regarding LD500 grains,

V. Della Corte et al. / Astronomy and Computing 5 (2014) 57–69 65

Fig. 7. Orbits scenarios considered in the GIPSI simulations: (a) the three orbits in J2000 reference frame (the two post-landing orbits have the same geometry and areterminator quasi-polar orbits); the three orbits in the comet-attached RZC model reference frame: (b) the pre-landing COP orbit; (c) post-landing 10 km bound orbit and (d)post-landing 30 km bound orbit.

a 6-day period is sufficient to collect a statistically meaningfulnumber of particles. When GIPSI simulations are performed withFulle solutions with the anisotropic dust distribution describedabove, the number of collected grains seems to be statisticallyacceptable for all types of grains here considered. The differenceamong the cumulative number of grains obtained using the twodifferent dust environments is always less then a factor of four. Thisdifference can be explained recalling the different anisotropy ofthe two simulated dust environments and by the difference in thevelocity direction distribution. In fact, unlike RZC solutions Fulle’sones foresee only strictly radial velocities.

7.2. GIADA dust velocity measurements

The GIPSI simulations of GIADA velocity measurements wasperformed considering the angle between the direction of theGDS + IS system boresight and the dust grain velocity vector. Infact, the GDS + IS subsystem measures the velocity componentalong the boresight (+Z , axis of the S/C). Only in the case of acircular orbit (i.e., the velocity of the S/C is tangent to the orbit andorthogonal to+Z direction) and a perfect nadir pointing of the S/C ,GIADA velocity measurements are not affected by the movementof the S/C .

In Table 4 are reported the dust velocities predicted by theRZC model and those that GIPSI simulations foresee as GIADAvelocitymeasurements for the four types of grains. Themean errorof the simulated measured velocity with respect to the velocitycomputed by the model along the orbit emean, reported in Table 4,

gives the difference between the dust grain velocities predicted bythe RZC model and GIADA velocity measurements simulated byGIPSI. Themaximum error in the velocitymeasurements can reach30% for particles having trajectories with slight deviation from theradial direction, for example, LD100 dust grains at 96th, 147th and267th hour in the 30 km bound orbit (Fig. 13) or at 35th hour inthe pre-landing case (Fig. 9). This can be explained by the fact thatsmaller and low density dust grains are better coupledwith the gasflux and thus follow the gas flow trajectory. The majority of thegrains show small errors in the velocity measurements (Table 4)suggesting they move in radial direction.

Here, we will discuss the differences in the measured velocitiesobtained by GIPSI simulations for the three orbit scenarios. Weplotted the distribution of the dust velocity magnitudes for everytype of grains along the three test orbits (Figs. 14–17). Themaximum measured velocities for all the grains type, obtainedwith RZC solutions, are about 20% less than the correspondingvalues given by Fulle et al. (2010). Ifwe compare themean values ofthe velocities predicted by the RZC model along the 10 and 30 kmorbits, we obtain that at 10 km the dust grains have achieved about90% of the velocity they would reach at 30 km. Hence, we couldassume that at the distance of 10 km the grains already move withtheir terminal velocity. Moreover, the mean velocities for each ofthe four grains types of RZC model solutions are about of the halfof the corresponding values given by Fulle et al. (2010).

In the case of the post-landing 10 km orbit the velocities’ ra-tios (Fulle vs. RZC) are greater because the grains are still in theacceleration region for the RZC solutions while Fulle uses terminalvelocities. This observation is also confirmed by the distribution

66 V. Della Corte et al. / Astronomy and Computing 5 (2014) 57–69

Fig. 8. GIPSI estimated dust rates as detected by GIADA along the pre-landing COPorbit with RZC model output. The profiles for different sizes and densities of thegrains are similar. Since the orbital period is longer than the comet rotational periodwe see dust rates obtained by two different nucleus areas at the same local time.

Fig. 9. The dust velocity profiles obtained for four types of grains using GIPSI alongthe pre-landing COP orbit having in input the dust environment reproduced by theRZC model.

velocities plots. Indeed, by moving farther from the nucleus, thatis, from the post-landing 10 km orbit to the post-landing 30 km or-bit, the peak of the velocity distribution in the histograms shifts tohigher values, due to the acceleration of the ejected grains. For ex-ample, the peak of the velocity for LD100 and LD500 changes from14 to 16 m/s and 7 to 8 m/s (Figs. 17 and 16). In the cases of the LDparticles (LD100 and LD500), the distribution ismore disperse thanHDgrains (Figs. 15 and 14). Comparing the velocity distribution be-tween the pre-landing (COP) orbit with the post-landing 10 km or-bit, the peak in the velocity distribution shifts from higher to lowervalues. This is because of the different geometries of the trajecto-ries, that is, the quasi-equatorial pre-landing orbit pass closer tothe subsolar point, where the RZC model show higher total dustvelocity (Crifo et al., 2004b).

We checked the instrument capabilities by analyzing simulatedGIADA velocity measurements. In particular, based on the velocitydata for grains with the same optical cross section, we couldassociate the velocity distribution to dust grains having a specificmass density (Figs. 9, 11, and 13). For instance, LD100 and HD100

Fig. 10. GIPSI estimated dust rates as detected by GIADA along the post-landing10 km bound orbit with RZC model output. Smoother dust rates profiles incomparison with the pre-landing (COP) orbit case.

Fig. 11. The dust velocitymeasured by GIADA along the post-landing 10 km boundorbit with RZCmodel output. The velocity profiles are smoother in comparisonwiththose in the pre-landing case.

grains have the same optical cross section but different velocityprofiles and mean values for RZC model. Nevertheless, grainswith same sizes and different specific mass density have distinctvelocities. The velocity distribution predicted by dust modelscan be verified by GIADA, and vice versa dust models can becalibrated with GIADA in situ measurements. GIADA can measurethe velocity, momentum, and the optical cross section of dustgrains. Even if we have partial information on these measuredquantities, a calibratedmodel will allow to complement the GIADAscientific data. Therefeore, by measuring optical cross sections andvelocity we can infer, by means of a calibrated model, informationon the specific mass of the particles.

8. Conclusions

Once the orbit and the attitude of the S/C are defined, operationplanning could be well constrained for the remote-sensinginstruments objectives. These actions turn out to bemore laboriousfor the in situ instruments, especially when measurements of

V. Della Corte et al. / Astronomy and Computing 5 (2014) 57–69 67

Fig. 12. Dust rates as detected by GIADA along the post-landing 30 km bound orbitestimated by GISPI using RZC dust model solutions. The ‘‘hollow’’ describes a lowactivity coma portion foreseen in the anisotropy of the RZC dust model. The HD500particles are not detected at all in this scenario.

Fig. 13. GIPSI simulations of GIADA grain velocity measurements along the 30 kmbound orbit obtained using the RZC dust model solutions.

Fig. 14. Measured RZC dust velocity magnitude distribution for HD500 grains. Thedistribution is normalized with respect to the maximum frequency and is given forthree studied orbits. The two histograms show the evolution of the velocities vs. thedistance from the nucleus.

Fig. 15. Measured RZC dust velocity magnitude distribution for HD100 grains. Thedistribution is normalized with respect to the maximum frequency and is given forthree studied orbits. The three histograms show the evolution of the velocities vs.the distance from the nucleus.

Fig. 16. Measured RZC dust velocity magnitude distribution for LD500 grains. Thedistribution is normalized with respect to the maximum frequency and is given forthree studied orbits. The three histograms show the evolution of the velocities vs.the distance from the nucleus.

highly variable physical quantities have to be performed. In orderto achieve the scientific goals of an in situ instrument like GIADA itis needed to have simulated cometary dust environment togetherwith the S/C orbits and the payload performance.

We checked GIADA capability in reproducing 3D + t dust en-vironment along different S/C trajectories by using the followingcomponents: the predictions from a coma dust model, the differ-ent possible mission orbit scenarios, and the GIPSI software that

68 V. Della Corte et al. / Astronomy and Computing 5 (2014) 57–69

Fig. 17. Measured RZC dust velocity magnitude distribution for LD100 grains. Thedistribution is normalized with respect to the maximum frequency and is given forthree studied orbits. The three histograms shows the evolution of the velocities vs.the distance from the nucleus.

simulates theGIADA instrumentmeasurements. In order to be pre-pared when Rosetta S/C will encounter 67P/C–G, it is essential todetermine the most adequate mission scenario well in advance tomaximize the collection of GIADA valuable scientific data on pur-suing the Rosetta missions goals.

GIPSI allows a quick evaluation of GIADA measurements alongdifferent S/C orbits. This evaluation is critical to constrain theinstrument response with respect to different mission scenarios.

The GIADA main scientific objectives are to characterize dy-namical and physical properties of the coma dust grains, especiallythe size andmass distribution. These goals should be achieved dur-ing anymission phase, in order to characterize the evolution of thecometary dust environment with respect to the heliocentric dis-tance.

We explored three different orbit scenarios, evaluating theirimpact on the GIADA scientific objectives during the phasemissionjust before and after the lander delivery: pre-landing COP orbitand post-landing 10-km- and 30-km-bound circular orbits. Resultsobtained simulating GIADA performances in the above scenariosallow us to rank the three orbit scenarios, taking into accountthe following criteria: (1) the capability of describing size andnumerical distribution of dust grains connected to the collectablenumber of cumulated particles in a given time interval, (2) thepossibility of characterizing the dynamical properties of the dust,and (3) the ability to identify the evolved dust environment as aconsequence of the nucleus activity.

We can conclude that the pre-landing COP case is the optimalchoice from a scientific point of view. Although the comet is stillfar from the perihelion during the pre-landing COP orbit scenario,GIPSI simulations show that the comet activity is high enough toallow GIADA to detect a statistical meaningful number of grains toachieve its science objectives, that is, contributing to the missionscientific goals. In particular:

– It is the closest orbit scenario to the nucleus, that is, it will allowto describe the acceleration region of the dust grains;

– Thanks to the elliptical trajectory, it will allow a 3D + tdescription of the circumnuclear dust coma; and

– It is the orbit scenario during which an ‘‘image’’ of the comaevolution will be captured in the shortest time.

Short distances, as for the pre-landing COP and post-landing10 km orbit, ensure high fluxes and statistically meaningful num-ber of dust grains in a short time. In addition, the collected dustgrains have a shortmotionhistory; thus, themeasureddust param-eters can be connected straightforward to the nucleus activity ar-eas. On the contrary, along the post-landing 30-km-boundorbit theparticles have traveled longer at larger distance and have under-gone to all changes caused by external space environment (frag-mentation, solar illumination, etc.). Furthermore, it is true that thecoma spatial evolution can be better described (lower S/C orbitalvelocity and longer residence time in the same coma region), butwith the important drawback of the lack of an accurate determina-tion of the nucleus areas fromwhere the grains have been ejected.

The GIPSI tool, together with a realistic ab initio cometary dustmodel (Crifo et al., 2004b) scaled to 67P/C–G dust abundancesobtained by astronomical observations (Fulle et al., 2010), has beencrucial to conclude that the pre-landing COP orbit is best suitedfor the GIADA instrument. We verified the GIADA capability todescribe the 67P/C–Gdust environment, detecting its peculiarities:the large-scale anisotropy and/or the high-frequency small-scalevariations in the dust parameters. We plan to follow up thepresent work evaluating GIADA capability to reconstruct thedust environment along any orbit scenarios provided by theESA/Rosetta Scientific Ground Segment (ESA/SGS) having as inputto GIPSI any 3D + t simulated dust environment.

Acknowledgment

This research has been supported by the Italian Space Agency(ASI) (Ref: n. I/032/05/0).

References

Bauer, J.M., Kramer, E., Mainzer, A.K., Stevenson, R., Grav, T., Masiero, J.R.,Walker, R.G., Fernández, Y.R., Meech, K.J., Lisse, C.M., Weissman, P.R., Cutri,R.M., Dailey, J.W., Masci, F.J., Tholen, D.J., Pearman, G., Wright, E.L., TheWISE Team, 2012. WISE/NEOWISE preliminary analysis and highlights of the67p/Churyumov–Gerasimenko near nucleus environs. Astrophys. J. 758, 18.http://dx.doi.org/10.1088/0004-637X/758/1/18.

Clauset, A., Shalizi, C.R., Newman, M.E., 2009. Power-law distributions in empiricaldata. SIAM Rev. 51, 661–703.

Colangeli, L., Lopez-Moreno, J.J., Palumbo, P., Rodriguez, J., Cosi, M., Della Corte,V., Esposito, F., Fulle, M., Herranz, M., Jeronimo, J.M., Lopez-Jimenez, A.,Epifani, E.M., Morales, R., Moreno, F., Palomba, E., Rotundi, A., 2007. The grainimpact analyser and dust accumulator (GIADA) experiment for the Rosettamission: design, performances and first results. Space Sci. Rev. 128, 803–821.http://dx.doi.org/10.1007/s11214-006-9038-5.

Crifo, J.F., Fulle, M., Kömle, N.I., Szego, K., 2004a. Nucleus-coma structuralrelationships: lessons from physical models. pp. 471–503.

Crifo, J.F., Lukyanov, G.A., Zakharov, V.V., Rodionov, A.V., 2004b. Physical model ofthe coma of Comet 67P/Churyumov–Gerasimenko. In: Colangeli, L., MazzottaEpifani, E., Palumbo, P. (Eds.), The New Rosetta Targets. Observations,Simulations and Instrument Performances. p. 119.

Crifo, J.F., Rodionov, A.V., 1997. The dependence of the circumnuclear comastructure on the properties of the nucleus. Icarus 127, 319–353.http://dx.doi.org/10.1006/icar.1997.5690.

Epifani, E.M., Bussoletti, E., Colangeli, L., Palumbo, P., Rotundi, A., Vergara, S., Perrin,J.M., Lopez Moreno, J.J., Olivares, I., 2002. The grain detection system for theGIADA instrument: design and expected performances. Adv. Space Res. 29,1165–1169. http://dx.doi.org/10.1016/S0273-1177(02)00133-3.

Esposito, F., Colangeli, L., della Corte, V., Palumbo, P., 2002. Physical aspect of an‘‘impact sensor’’ for the detection of cometary dust momentum onboard the‘‘Rosetta’’ space mission. Adv. Space Res. 29, 1159–1163.http://dx.doi.org/10.1016/S0273-1177(02)00132-1.

Festou, M.C., Keller, H.U.,Weaver, H.A., 2004. A brief conceptual history of cometaryscience. pp. 3–16.

Fulle, M., 1987. A new approach to the Finson–Probstein method of interpretingcometary dust tails. Astron. Astrophys. 171, 327–335.

V. Della Corte et al. / Astronomy and Computing 5 (2014) 57–69 69

Fulle, M., 1989. Evaluation of cometary dust parameters from numericalsimulations—comparison with an analytical approach and the role ofanisotropic emissions. Astron. Astrophys. 217, 283–297.

Fulle,M., 1992. A dust-tailmodel based onMaxwellian velocity distribution. Astron.Astrophys. 265, 817–824.

Fulle, M., Barbieri, C., Cremonese, G., Rauer, H., Weiler, M., Milani, G., Ligustri, R.,2004. The dust environment of Comet 67P/Churyumov–Gerasimenko. Astron.Astrophys. 422, 357–368. http://dx.doi.org/10.1051/0004-6361:20035806.

Fulle, M., Colangeli, L., Agarwal, J., Aronica, A., Della Corte, V., Esposito, F., Grün,E., Ishiguro, M., Ligustri, R., Lopez Moreno, J.J., Mazzotta Epifani, E., Milani,G., Moreno, F., Palumbo, P., Rodríguez Gómez, J., Rotundi, A., 2010. Comet67P/Churyumov–Gerasimenko: the GIADA dust environment model of theRosetta mission target. Astron. Astrophys. 522, A63.http://dx.doi.org/10.1051/0004-6361/201014928.

Glassmeier, K.H., Boehnhardt, H., Koschny, D., Kührt, E., Richter, I., 2007. The Rosettamission: flying towards the origin of the solar system. Space Sci. Rev. 128, 1–21.http://dx.doi.org/10.1007/s11214-006-9140-8.

Lamy, P.L., Toth, I., Davidsson, B.J.R., Groussin, O., Gutiérrez, P., Jorda, L.,Kaasalainen, M., Lowry, S.C., 2007. A portrait of the nucleus of Comet67P/Churyumov–Gerasimenko. Space Sci. Rev. 128, 23–66.http://dx.doi.org/10.1007/s11214-007-9146-x.

Lamy, P.L., Toth, I., Weaver, H., Jorda, L., Kaasalainen, M., 2003. The nucleus ofComet 67P/Churyumov–Gerasimenko, the new target of the Rosetta mission,in: AAS/Division for Planetary Sciences Meeting Abstracts #35, p. 970.

Landgraf, M., Müller, M., Grün, E., 1999. Prediction of the in-situ dustmeasurementsof the stardust mission to comet 81P/Wild 2. Planet. Space Sci. 47, 1029–1050.http://dx.doi.org/10.1016/S0032-0633(99)00031-8.

Lowry, S., Duddy, S.R., Rozitis, B., Green, S.F., Fitzsimmons, A., Snodgrass, C., Hsieh,H.H., Hainaut, O., 2012. The nucleus of Comet 67P/Churyumov–Gerasimenko.A new shape model and thermophysical analysis. Astron. Astrophys. 548, A12.http://dx.doi.org/10.1051/0004-6361/201220116.

Ootsubo, T., Kawakita, H., Hamada, S., Kobayashi, H., Yamaguchi, M., Usui, F.,Nakagawa, T., Ueno, M., Ishiguro, M., Sekiguchi, T., Watanabe, J.i., Sakon, I.,Shimonishi, T., Onaka, T., 2012. AKARI near-infrared spectroscopic surveyfor CO2 in 18 Comets. Astrophys. J. 752, 15. http://dx.doi.org/10.1088/0004-637X/752/1/15.

Palomba, E., Colangeli, E.L., Palumbo, P., Rotundi, A., Perrin, J.M., Bussoletti, E., 2002.Performance of micro-balances for dust flux measurement. Adv. Space Res. 29,1155–1158. http://dx.doi.org/10.1016/S0273-1177(02)00131-X.

Rodionov, A.V., Crifo, J.F., Szegő, K., Lagerros, J., Fulle, M., 2002. An advancedphysical model of cometary activity. Planet. Space Sci. 50, 983–1024.http://dx.doi.org/10.1016/S0032-0633(02)00047-8.