The effect of internal inhomogeneity on the activity of comet nuclei - Application to Comet 67P/Churyumov-Gerasimenko

We present thermal evolution calculations of inhomogeneous asymmetric initial configurations of a spherical model of Comet 67P/Churyumov-Gerasimenko, using a fully 3-dimensional numerical code. The initial composition is amorphous H₂O ice and dust, in a “layered-pile” configuration, where layers differing in ice/dust ratio and thermal properties extend over a fraction of the surface area and about 10 m in depth and may overlap. We analyze the effect of one such layer, as well as the combined effect of many layers, randomly distributed. We find that internal inhomogeneities affect both the surface temperature and the activity pattern of the comet. In particular, they may lead to outbursts at large heliocentric distances and also to activity on the night-side of the nucleus. The rates of ablation and depths of dust mantle and crystalline ice outer layer as functions of longitude and latitude are shown to be affected as well.     

The nuclei of Jupiter family comets: A critical review of our present knowledge

Of the currently over 300 identified Jupiter family comets (JFCs), we have estimated nucleus sizes and shapes for fewer than 70 and have detailed nucleus observations arising from spacecraft fly-bys for just 3: 19P/Borrelly (Deep Space 1), 81P/Wild 2 (Stardust), and 9P/Tempel 1 (Deep Impact). These observations reveal similarities but also significant diversity. In this review, we make a critical assessment of our knowledge of JFC nuclei and suggest a priority list for observations of the nucleus of the JFC, 67P/Churyumov-Gerasimenko, the Rosetta target comet.     

Evolution of depressions on Comet 67P/Churyumov-Gerasimenko: Role of ice metamorphism

This work is intended to investigate the influence of temperature-dependent metamorphism of ice on the shape of small depressions in the surface of cometary nuclei. We are mainly interested in the role of initial cohesivity of a nucleus. For this purpose we simulate sublimation of ice from the facets of initially cylindrical depressions in ice of different initial structure. The simulations account for the diurnal and orbital changes of insolation and its dependence on the current shape of the depressions. Our model includes heat transport in the cometary material and metamorphism of ice. We present the results obtained for the nucleus of the Comet 67P/Churyumov-Gerasimenko, target of the ESA cornerstone mission Rosetta.     

Nucleus properties of Comet 67P/Churyumov-Gerasimenko estimated from non-gravitational force modeling

By considering model comet nuclei with a wide range of sizes, prolate ellipsoidal shapes, spin axis orientations, and surface activity patterns, constraints have been placed on the nucleus properties of the primary Rosetta target, Comet 67P/Churyumov-Gerasimenko. This is done by requiring that the model bodies simultaneously reproduce the empirical nucleus rotational lightcurve, the water production rate as function of time, and non-gravitational changes (per apparition) of the orbital period (ΔP), longitude of perihelion (Δ?), and longitude of the ascending node (ΔΩ). Two different thermophysical models are used in order to calculate the water production rate and non-gravitational force vector due to nucleus outgassing of the model objects. By requiring that the nominal water production rate measurements are reproduced as well as possible, we find that the semi-major axis of the nucleus is close to 2.5 km, the nucleus axis ratio is approximately 1.4, while the spin axis argument is either 60°±15° or 240°±15°. The spin axis obliquity can only be preliminarily constrained, indicating retrograde rotation for the first argument value, and prograde rotation for the second suggested spin axis argument. A nucleus bulk density in the range 100-370 kg m⁻³ is found for the nominal ΔP, while an upper limit of 500 kg m⁻³ can be placed if the uncertainty in ΔP is considered. Both considered thermophysical models yield the same spin axis, size, shape, and density estimates. Alternatively, if calculated water production rates within an envelope around the measured data are considered, it is no longer possible to constrain the size, shape, and spin axis orientation of the nucleus, but an upper limit on the nucleus bulk density of 600 kg m⁻³ is suggested.     

Cometary dust trail associated with Rosetta mission target: 67P/Churyumov-Gerasimenko

A thin, bright dust cloud, which is associated with the Rosetta mission target object (67P/Churyumov-Gerasimenko), was observed after the 2002 perihelion passage. The neckline structure or dust trail nature of this cloud is controversial. In this paper, we definitively identify the dust trail and the neckline structure using a wide-field CCD camera attached to the Kiso 1.05-m Schmidt telescope. The dust trail of 67P/Churyumov-Gerasimenko was evident as scattered sunlight in all images taken between September 9, 2002 and February 1, 2003, whereas the neckline structure became obvious only after late 2002. We compared our images with a semi-analytical dynamic model of dust grains emitted from the nucleus. A fading of the surface brightness of the dust trail near the nucleus enabled us to determine the typical maximum size of the grains. Assuming spherical compact particles with a mass density of 10³ kg m⁻³ and an albedo of 0.04, we deduced that the maximum diameter of the dust particles was approximately 1 cm. We found that the mass-loss rate of the comet at the perihelion was on or before the 1996 apparition, while the mass-loss rate averaged over the orbit reached . The result is consistent with the studies of the dust cloud emitted in the 2002/2003 return. Therefore, we can infer that the activity of 67P/Churyumov-Gerasimenko has showed no major change over the past dozen years or so, and the largest grains are cyclically injected into the dust tube lying along the cometary orbit.     

A fully 3-dimensional thermal model of a comet nucleus

A 3-D numerical model of comet nuclei is presented. An implicit numerical scheme was developed for the thermal evolution of a spherical nucleus composed of a mixture of ice and dust. The model was tested against analytical solutions, simplified numerical solutions, and 1-D thermal evolution codes. The 3-D code was applied to comet 67P/Churyumov-Gerasimenko; surface temperature maps and the internal thermal structure was obtained as function of depth, longitude and hour angle. The effect of the spin axis tilt on the surface temperature distribution was studied in detail. It was found that for small tilt angles, relatively low temperatures may prevail on near-pole areas, despite lateral heat conduction. A high-resolution run for a comet model of 67P/Churyumov-Gerasimenko with low tilt angle, allowing for crystallization of amorphous ice, showed that the amorphous/crystalline ice boundary varies significantly with depth as a function of cometary latitude.     

Fully 3-dimensional calculations of dust mantle formation for a model of Comet 67P/Churyumov-Gerasimenko

A fully 3-dimensional implicit numerical model for comet nucleus evolution is presented, emphasizing dust mantle formation. A spherical configuration is considered with an initial composition of amorphous H₂O ice and dust, taking into account a discrete dust-grain size distribution. The model is applied to Comet 67P/Churyumov-Gerasimenko, adopting its orbital elements, rotation period and rotation axis inclination. We find that the dust mantle thickness varies over the surface from 1 cm to about 10 cm (thus lower and higher than the diurnal skin-depth, respectively). The size distribution of ejected grains varies along the orbit and is steeper than the initial one adopted for the nucleus. The crystallization front advances inward in spurts, and its depth varies between 1 and several meters. We test the effect of the thermal conductivity on the surface temperature distribution and depths of the dust mantle and crystallization front.     

短周期彗星表面水冰升华分布研究

彗星是太阳系遗留的原始星子,研究彗星彗核的演化对理解太阳系其他天体的形成和演化历史具有重要意义.在太阳的辐射作用下,彗星携带的挥发性成分会发生升华,并带动尘埃运动,造成彗核物质的损失.因此,彗核的升华活动对其表面形貌甚至整体形状演化都会产生影响.从IAU (International Astronomical Union) MPC (Minor Planet Center)获取轨道数据,并考虑了彗核的自转以及进动,利用MONET (Mass lossdriven shape evolution model)形状演化模型对短周期彗星做数值模拟,计算得到了短周期彗星1P/Halley、9P/Tempel 1、 19P/Borrelly、 67P/C-G (Churyumov-Gerasimenko)、 81P/Wild 2和103P/Hartley 2在一个轨道周期内的太阳辐射能量以及表面侵蚀深度的分布,结合其动力学参数讨论了自转、进动和公转等特性对其表面水冰升华分布的影响以及造成南北侵蚀差异的可能性.     

Comet 67P/Churyumov-Gerasimenko: Modeling of orientation and structure

The comet 67P/Churyumov-Gerasimenko is the current target of the mission Rosetta, initially planned to investigate comet 46P/Wirtanen. These two comets have similar orbits, except the distance to the Sun at perihelion, but different orbital histories and different masses. Thus, structures of the nuclei can be significantly different. The evolution of comet Wirtanen was simulated by several authors, while comet Churyumov-Gerasimenko became an object of high interest only recently and is not well investigated. In the present work we simulate the evolution of the nucleus, down to tens of meters below the surface, using an extended version of the model previously applied for comet Wirtanen [Kossacki et al., 1999. Comet 46P/Wirtanen: evolution of the subsurface layer. Icarus 142, 202-218.]. The model includes strengthening of the nucleus due to sintering of the ice grains. Simulations are performed for different latitudes, accounting for the evolution of the orbit and for changes of the nucleus orientation, as well as diurnal and seasonal changes of insolation. The calculated loss of water vapor from the comet is integrated over the nucleus surface and is compared with the observational data. We have found, that the sublimation through the dust mantle can be large enough to reproduce the profile of the total water production as a function of time from perihelion. The required dependence of thickness of the dust layer on latitude qualitatively matches present distribution of the absorbed solar flux. The non-gravitational acceleration in the comet motion together with the simulated sublimation flux are used in order to estimate the mass and the bulk density of the nucleus.     

Comet 9P/Tempel 1: Sublimation beneath the dust cover

In the current work we analyze properties of the dust mantle, its thickness and thermal conductivity, necessary to reproduce observed rate of water production of Comet 9P/Tempel 1. For this purpose we considered simplified shape of the comet nucleus approximated by the symmetric prolate ellipsoid with smooth surface. We have performed simulations, using models with dust mantle of the thickness either constant, but nonuniform (Model A), or evolving (Model B). The simulated profiles of water production versus time were compared with observations. In addition, we compared the calculated surface temperature with the real temperatures derived from IR observations (the Deep Impact mission). This new double-stage verification procedure, shows that our model A is a good representation for the nucleus of Comet Tempel 1. This indicates, that the dust mantle thickness should be nonuniform, but does not change significantly with time. We show, that reproducing observed high temperatures of the nucleus requires dust mantle, that is almost everywhere thick and has extremely low thermal inertia. The latter should be close to zero as already predicted by others. The agreement between the simulated and measured water production can be obtained when the dust is regionally thin and has the thermal inertia higher than average, according to our simulations about 100 W s^1/2 K⁻¹ m⁻². Such regions should be located in the south hemisphere of the nucleus.     

Gas kinetics and dust dynamics in low-density comet comae

Extensive regions of low-density cometary comae are characterized by important deviations from the Maxwell-Boltzmann velocity distribution, i.e. breakdown of thermodynamic equilibrium. The consequences of this on the shapes of emission and absorption lines, and for the acceleration of solid bodies due to gas drag, have rarely been investigated.These problems are studied here to aid in the development of future coma models, and in preparation for observations of Comet 67P/Churyumov-Gerasimenko from the ESA Rosetta spacecraft. Two topics in particular, related to Rosetta, are preparation for in situ observations of water, carbon monoxide, ammonia, and methanol emission lines by the mm/sub-mm spectrometer MIRO, as well as gas drag forces on dust grains and on the Rosetta spacecraft itself.Direct Simulation Monte Carlo (DSMC) modeling of H₂O/CO mixtures in spherically symmetric geometries at various heliocentric distances are used to study the evolution of the (generally non-Maxwellian) velocity distribution function throughout the coma. Such distribution functions are then used to calculate Doppler broadening profiles and drag forces.It is found that deviation from thermodynamic equilibrium indeed is commonplace, and already at 2.5 AU from the Sun the entire comet coma displays manifestations of such breakdown, e.g., non-equal partitioning of energy between kinetic and rotational modes, causing substantial differences between translational and rotational temperatures. We exemplify how deviations from thermodynamic equilibrium affect the properties of Doppler broadened line profiles. Upper limits on the size of liftable dust grains as well as terminal grain velocities are presented. Furthermore, it is demonstrated that the drag-to-gravity force ratio is likely to decrease with decreasing cometocentric distance, which may be of relevance both for Rosetta and for the lander probe Philae.     

Challenging a Paradigm: Do We Need Active and Inactive Areas to Account for Near-Nuclear Jet Activity?

We briefly describe an advanced 3D gas dynamical model developed for the simulation of theenvironment of active cometary nuclei. The model canhandle realistic nucleus shapes and alternative physical models for the gas and dust production mechanism.The inner gas coma structure is computed by solving self-consistently(a) near to the surface the Boltzman Equation(b) outside of it, Euler or Navier-Stokes equations.The dust distribution is computed from multifluid ``zero-temperature' Euler equations,extrapolated with the help of a Keplerian fountain model.The evolution of the coma during the nucleus orbital and spin motion,is computed as a succession of quasi-steady solutions. Earlier versions of the model using simple,``paedagogic' nuclei have demonstrated that the surface orographyand the surface inhomogeneity contribute similarly to structuring the near-nucleusgas and dust coma,casting a shadow on the automatic attribution of such structures to ``active areas'.The model was recently applied to comet P/Halley, for whichthe nucleus shape is available. In the companion paper of this volume,we show that most near-nucleus dust structuresobserved during the 1986 Halley flybys are reproduced, assuming that the nucleus is strictly homogeneous. Here, we investigate the effect of shape perturbations and homogeneityperturbations. We show that the near nucleus gas coma structure is robust vis-a-vissuch effects. In particular, a random distribution of active and inactive areaswould not affect considerably this structure, suggesting that such areas,even if present, could not be easily identified on images of the coma.     

Models of P/Wirtanen nucleus: active regions versus non-active regions

From the current understanding we know that comet nuclei have heterogeneous compositions and complex structures. It is believed that cometary activity is the result of a combination of physical processes in the nucleus, like sublimation and recondensation of volatile ices, dust grains release, phase transition of water ice, depletion of the most volatile components in the outer layers and interior differentiation.The evolution of the comet depends on the sublimation of ices and the release of different gases and dust grains: the formation of a dust crust, the surface erosion and the development of the coma are related to the gas fluxes escaping from the nucleus. New observations, laboratory experiments and numerical simulations suggest that the gas and dust emissions are locally generated, in the so-called active regions. This localized activity is probably superimposed to the global nucleus activity. The differences between active and inactive regions can be attributed to differences in texture and refractory material content of the different areas.In this paper we present the results of numerical models of cometary nucleus evolution, developed in order to understand which are the processes leading to the formation of active and non-active regions on the cometary surface. The used numerical code solves the equations of heat transport and gas diffusion within a porous nucleus composed of different ices—such as water (the dominant constituent), CO₂, CO- and of dust grains embedded in the ice matrix.By varying the set of physical parameters describing the initial properties of comet P/Wirtanen, the different behaviour of the icy and dusty areas can be followed.Comet P/Wirtanen is the target of the international ROSETTA mission, the cornerstone ESA mission to a cometary nucleus. The successful design of ROSETTA requires some knowledge of comet status and activity: surface temperatures, amount of active and inactive surface areas, gas production rate and dust flux.     

Crystallization of ice in Comet 17P/Holmes: Probably not responsible for the explosive 2007 megaburst

Our work was inspired by the recent brightening of Comet 17P/Holmes. The recently observed increase in brightness of this comet was correlated with emission of dust, probably larger in mass than the dust mantle of the nucleus. We analyzed the hypothesis that the comet can eject a large mass of dust due to non-uniform crystallization of amorphous water ice. For this purpose, we simulated the evolution of a model nucleus on the orbit of Comet 17P/Holmes. The nucleus is composed of water ice and dust and has the shape of an elongated ellipsoid. The simulations include crystallization of amorphous ice in the nucleus, changes in the dust mantle thickness, and changes in the nucleus orientation in space. Our computations indicate that: (i) ejection of the dust cover triggers crystallization of ice independently on the material properties of the nucleus; (ii) moderate changes in the nucleus orientation (∼50°) may result in an acceleration of the crystallization of ice in the northern hemisphere, while a rather large change in the orientation (∼120°) is needed to cause a significant jump of the crystallization front in the southern hemisphere, where the emission of dust during the recent brightening was strongest. We investigated the possible reason for an explosion and we have found that the crystallization of the water ice itself is probably not sufficient.     

The destruction of the cometary nucleus – The case of 73P/Schwassmann-Wachmann

The paper presents an analysis of the actual brightness change of comet 73P/Schwassmann-Wachmann, which took place in 1995. The consequence of a cometary outburst is the destruction of a fragment of its surface. This causes the emission of comet material from both the surface and from exposed subsurface layers. Therefore, the calculations take into account the scattering cross-sections that come from ice and dust particles. It was assumed that the dust particles are silicates which are characterized by high irregularity of their structure. This assumption is a consequence of the analysis of the results provided by the Rosetta mission to the comet 67P/Churyumov-Gerasimenko. The main factor determining the amplitude of a cometary outburst is the mass ejected as well as the loss of ice that holds the individual nucleus structures together. Consequently, this phenomenon can significantly contribute to the destruction and even decay of the cometary nucleus.     

A practical tool for simulating the presence of gas comae in thermophysical modeling of cometary nuclei

A longstanding problem in thermophysical modeling of cometary nuclei has been to accurately formulate the boundary conditions at the nucleus/coma interface. A correct treatment of the problem, where the Knudsen layer gas just above the cometary surface (which is not in thermodynamic equilibrium) is modeled in parallel with the nucleus, is extremely time-consuming and has so far been avoided. Instead, simplifying assumptions regarding the coma properties are used, e.g., the surface gas density is assumed equal to zero or set to the local saturation value, and the coma backflux is neglected or given some realistic but approximate value. The resulting inaccuracy regarding the exchange of mass, energy, and momentum between the nucleus and the coma, may introduce significant errors in the calculated nucleus temperature profiles, gas production rates, and momentum transfer efficiencies. In this paper, we present a practical, accurate, and time-efficient tool which makes it possible to consider the nucleus and the innermost coma of a comet (the former assumed to consist of a porous mixture of crystalline water ice and dust) as a coupled, physically consistent system. The tool consists of interpolation tables for the surface gas density and pressure, the recondensing coma backflux, and the cooling energy flux due to diffusely scattered coma molecules. The tables cover a wide range of surface temperatures and sub-surface temperature profiles, and can be used to improve the boundary conditions used in thermophysical models. The interpolation tables have been obtained by calculating the transmission distribution functions of gas emerging from sublimating porous ice/dust mixtures with various temperature profiles, which then are used as source functions in a Direct Simulation Monte Carlo model of inelastic intermolecular collisions in the Knudsen layer.     

The dust trail of Comet 67P/Churyumov-Gerasimenko between 2004 and 2006

We report on observations of the dust trail of Comet 67P/Churyumov-Gerasimenko (CG) in visible light with the Wide Field Imager at the ESO/MPG 2.2 m telescope at 4.7 AU before aphelion, and at with the MIPS instrument on board the Spitzer Space Telescope at 5.7 AU both before and after aphelion. The comet did not appear to be active during our observations. Our images probe large dust grains emitted from the comet that have a radiation pressure parameter β<0.01. We compare our observations with simulated images generated with a dynamical model of the cometary dust environment and constrain the emission speeds, size distribution, production rate and geometric albedo of the dust. We achieve the best fit to our data with a differential size distribution exponent of −4.1, and emission speeds for a β=0.01 particle of 25 m/s at perihelion and 2 m/s at 3 AU. The dust production rate in our model is on the order of 1000 kg/s at perihelion and 1 kg/s at 3 AU, and we require a dust geometric albedo between 0.022 and 0.044. The production rates of large (>) particles required to reproduce the brightness of the trail are sufficient to also account for the coma brightness observed while the comet was inside 3 AU, and we infer that the cross-section in the coma of CG may be dominated by grains of the order of .     

Rosetta—one comet rendezvous and two asteroid fly-bys

One of the two planetary cornerstone missions of the European Space Agency is the Rosetta mission to comet 67P/Churyumov-Gerasimenko. Rosetta is a rendezvous mission with a comet nucleus, which combines an Orbiter with a Lander. It will monitor the evolution of the comet nucleus and the coma as a function of increasing and decreasing solar flux input along the comet’s pre- and post-perihelion orbit. Different instrumentations will be used in parallel, from multi-wavelength spectrometry to in-situ measurements of coma and nucleus composition and physical properties. Rosetta will go in orbit around the nucleus of its target comet 67P/Churyumov-Gerasimenko, when it is still far from the Sun and accompany the comet along its way to perihelion and beyond. In addition the Rosetta Lander Philae will land on the nucleus surface, before the comet is too active to permit such a landing (i.e. at around r = 3 AU) and examine the surface and subsurface composition of the comet nucleus as well as its physical properties.     

Compositional and physical results for Rosetta's new target Comet 67P/Churyumov-Gerasimenko from narrowband photometry and imaging

We present compositional and physical results of Comet 67P/Churyumov-Gerasimenko, the new target of ESA's Rosetta mission. A total of 16 nights of narrowband photometry were obtained at Lowell Observatory during the 1982/83 and 1995/96 apparitions, along with one night of imaging near perihelion in 1996. These data encompass an interval of −61 to +118 days from perihelion, corresponding to a range of heliocentric distances before perihelion from 1.48 to 1.34 AU, and an outbound range from 1.30 to 1.86 AU. Production rates were determined for OH, NH, CN, C₃, and C₂, along with A(θ)fρ, a proxy of the dust production. Water production, based on OH, has a steep () power-law rH-dependence post-perihelion and the minor species are somewhat less steep ( to −4), while the dust is quite shallow (), possibly due to a lingering population of large, slow-moving grains. All species exhibit larger production rates after perihelion, with water having a ∼2×pre/post-perihelion asymmetry, while minor species and dust have larger asymmetries. These asymmetries imply a strong seasonal effect and probable high obliquity of the rotational axis, along with one or more isolated source regions coming into sunlight near perihelion. Peak water production (which occurred about 1 month after perihelion) was and, when combined with a standard water vaporization model, implies an effective active area on the surface of the nucleus of ∼1.5-2.2 km² or an active fraction of only about 3-4%. Abundances of carbon-chain molecules yield a classification of slightly “depleted” in the A'Hearn et al. [A'Hearn, M.F., Millis, R.L., Schleicher, D.G., Osip, D.J., Birch, P.V., 1995. Icarus 118, 223-270] database. The peak dust production (as measured by A(θ)fρ, and uncorrected for phase angle) was ∼450 cm, while the color of the dust is moderately reddened, and the mean radial profile has a power-law slope of −1.3. Large night-to-night variability is also present, presumably due to the source region(s) rotating in and out of sunlight along with effects due to the use of differently sized apertures. A strong sunward radial feature was detected in images obtained near perihelion, along with a significant asymmetry between the two perpendicular directions from the Sun/tail line. These features may be the result of a mid-latitude source region sweeping out a cone with each rotation, which we are viewing from the side and where the sunward radial feature is one edge of the cone seen in projection. When combined with other constraints on the pole orientation, a possible pole solution is found having an obliquity of about 134° at an RA of about 223° and a Dec of −65°, with a source region located near +50° and in overall agreement with the photometric results. In comparison to the original Rosetta target Comet 46P/Wirtanen, Comet Churyumov-Gerasimenko has essentially the same peak water production but a peak dust production about 3 times greater than does Wirtanen based on A(θ)fρ (i.e., if one assumes that the properties of the dust grains are similar) (cf. Farnham and Schleicher [1998. Astron. Astrophys. 335, L50-L55]).     

Non-LTE radiative transfer for sub-millimeter water lines in Comet 67P/Churyumov-Gerasimenko

The European Space Agency (ESA) Rosetta spacecraft (Schulz, R., Alexander, C., Boehnhardt, H., Glassmeier, K.H. (Eds.) [2009]. “ROSETTA - ESA”) will encounter Comet 67P/Churyumov-Gerasimenko in 2014 and spend the next 18 months in the vicinity of the comet, permitting very high spatial and spectral resolution observations of the coma and nucleus. During this time, the heliocentric distance of the comet will change from ∼3.5 AU to ∼1.3 AU, accompanied by an increasing temperature of the nucleus and the development of the coma. The Microwave Instrument for the Rosetta Orbiter (MIRO) will observe the ground-state rotational transition (1₁₀-1₀₁) of H₂¹⁶O at 556.936 GHz, the two isotopologues H₂¹⁷O and H₂¹⁸O and other molecular transitions in the coma during this time (Gulkis, S. et al., [2007]. MIRO: Microwave Instrument for Rosetta Orbiter. Space Sci. Rev. 128, 561-597).The aim of this study is to simulate the water line spectra that could be obtained with the MIRO instrument and to understand how the observed line spectra with various viewing geometries can be used to study the physical conditions of the coma and the water excitation processes throughout the coma. We applied an accelerated Monte Carlo method to compute the excitations of the seven lowest rotational levels (1₀₁, 1₁₀, 2₁₂, 2₂₁, 3₀₃, 3₁₂, and 3₂₁) of ortho-water using a comet model with spherically symmetric water outgassing, density, temperature and expansion velocity at three different heliocentric distances 1.3 AU, 2.5 AU, and 3.5 AU. Mechanisms for the water excitation include water-water collisions, water-electron collisions, and infrared pumping by solar radiation.Synthetic line spectra are calculated at various observational locations and directions using the MIRO instrument parameters. We show that observations at varying viewing distances from the nucleus and directions have the potential to give diagnostic information on the continuum temperature and water outgassing rates at the surface of the nucleus, and the gas density, expansion velocity, and temperature of the coma as a function of distance from the nucleus. The gas expansion velocity and temperature affect the spectral line width and frequency shift of the line from the rest frequency, while the gas density (which is directly related to the outgassing rate) and the line excitation temperature determine the antenna temperature of the absorption and emission signal in the line profile.