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Published in final edited form as: J Geophys Res Planets. 2020 Aug 11;125(8):e2020JE006464. doi: 10.1029/2020je006464

The Evolution of a Spacecraft-Generated Lunar Exosphere

Parvathy Prem 1, Dana M Hurley 1, David B Goldstein 2, Philip L Varghese 2
PMCID: PMC8098081  NIHMSID: NIHMS1660063  PMID: 33959468

Abstract

Understanding how spacecraft alter planetary environments can offer important insights into key physical processes, as well as being critical to planning mission operations and observations. In this context, it is important to recognize that almost any powered lunar landing will be an active volatile release experiment, due to the release of exhaust gases during descent. This presents both an opportunity to study the interaction of volatiles with the lunar surface, and a need to predict how non-indigenous gases are dispersed, and how long they persist in the lunar environment. This work investigates these questions through numerical simulations of the transport of water vapor during a nominal lunar landing and for two lunar days afterwards. Simulation results indicate that the water vapor component of spacecraft exhaust is globally redistributed, with a significant amount reaching permanently shadowed regions (cold traps) near the closest pole, where temperatures are sufficiently low that volatiles may remain stable over geological timescales. Exospheric evolution and surface deposition patterns are highly sensitive to desorption activation energy, providing a means to constrain this critical parameter through landed or orbital measurements during future missions. Contamination of cold traps by exhaust gases is likely to scale with exhaust mass and proximity of the landing site to the poles. Exhaust propagation is perhaps the most widespread and long-lived impact of spacecraft operations on a nominally airless solar system body, and should be a key consideration in mission planning and in interpreting measurements made by landed lunar missions, particularly at near-polar regions.

Plain Language Summary

There has been increasing interest lately in learning more about the origin and distribution of water on the Moon. However, whenever a spacecraft descends to land on the lunar surface, it releases water vapor and other gases into the lunar environment, complicating the situation. In this work, we use computer simulations to understand what happens to the water released by a spacecraft during a typical landing. The simulated landing creates a temporary, very thin atmosphere all around the Moon. The behavior of this atmosphere depends on how strongly water sticks to the lunar surface, such that comparing simulations to measurements of water in the lunar environment during and after future lunar landings could help us figure out the “stickiness” of the lunar surface – something that we don’t yet accurately know, but is important to understanding the past, present and future distribution of water on the Moon. Our simulations also show that some spacecraft-delivered water travels to regions near the poles that are cold enough to trap water for very long periods of time. If the spacecraft is heavier, or lands closer to the poles, its influence on the lunar surface and atmosphere may be more significant.

1. Introduction

Understanding the processes that control the origin, abundance and distribution of water and other volatiles on the surface of the Moon is integral to both understanding the history of the inner solar system and characterizing the in situ resources available for planetary exploration. Motivated in part by these questions, there is widespread interest in returning to the lunar surface over the next decade (ISECG, 2018). However, any soft landing on the lunar surface will almost inevitably involve the release of non-indigenous volatiles (including water) when spacecraft fire their thrusters during descent. Predicting how these exhaust gases are distributed, and how long they persist in the lunar environment, is critical to planning surface operations and interpreting measurements that aim to characterize the extant lunar volatile inventory.

The fact that lunar landings are often active volatile release experiments has been well recognized since the Apollo era. Milford and Pomilla (1967) and Aronowitz et al. (1968) developed the first models to investigate the propagation of Lunar Module exhaust gases, and the contamination of surface samples by exhaust species, respectively. Early in the Apollo program, Chang (1969) discussed the detectability of exhaust gases by surface instrumentation. Vondrak (1992) reviews the Apollo measurements of non-indigenous gases that followed.

Several developments over the past decade make the problem of exhaust gas propagation worth revisiting. On the one hand, we have a firmer knowledge of some of the important environmental parameters in this problem. Lunar surface temperature, including the location and extent of regions of permanent shadow, has been characterized in unprecedented detail (e.g., Williams et al., 2019, Mazarico et al., 2011). Meanwhile, laboratory experiments (e.g. Poston et al., 2015), in combination with numerical modeling (e.g. Jones et al., 2018, Tucker et al., 2019) and remote sensing data (e.g. Hendrix et al., 2019) provide constraints on the mobility of lunar volatiles, although critical parameters such as the activation energy for desorption of water from lunar regolith remain to be definitively determined. Advances in our understanding of the Moon have also been accompanied by an increasing interest in conducting landed science and exploration at the lunar poles. The temperature-dependence of gas-surface interactions, and the proximity of potential landing sites to cold, permanently shadowed regions (PSRs) also drives the need to revisit how spacecraft-delivered volatiles are dispersed and persist in space and time.

Hurley et al. (2014) recently modeled the propagation of water released by the Chang’e 3 lander during its descent. Meanwhile, Shipley et al. (2014) have developed tools to predict the initial deposition of exhaust gases along a given descent trajectory. In this work, we develop a general method for modeling the global propagation of exhaust gases during and after a powered descent. We apply this method to model the fate of water vapor released by a Chang’e 3 class lander (dry mass ~1200 kg) for a nominal high latitude landing, and investigate the sensitivity of simulation results to the energetics of desorption of water from the lunar regolith.

2. Numerical Method

This section describes key aspects of the numerical method adopted in this work, with more detailed information in Appendix A.

We model the propagation of spacecraft exhaust gases by tracking the transport and eventual loss or deposition of a large number of representative water molecules. The modeled landing trajectory is based on that followed by the Chang’e 3 spacecraft (Liu et al., 2014), but for a landing at 70° S, the approximate latitude of the Chandrayaan 2 hard landing site. We model the final 155 s of descent, beginning when the spacecraft is at an altitude of 1.8 km and 1.82 km north of the landing site – a point after which exhaust gases are directed predominantly towards the lunar surface. The landing is assumed to occur at 7 am lunar local time (i.e., 15° from the dawn terminator), an optimal choice for missions that require sunlight. We arbitrarily chose a far side landing site, with the plane of descent aligned with 180° E, but the choice of longitude has relatively little influence on simulation results, since we do not model topography in detail; more important is the choice of time of day, which determines surface temperature near the landing site.

The release of water vapor along the descent trajectory is modeled by initializing simulated molecules within a spherical source region (40 m in radius) centered at the nozzle exit. Spacecraft position, velocity and orientation as a function of time are provided as input. During each time-step, the source region is populated with molecules, with initial positions, velocities and internal energies based on density, velocity and temperature fields computed based on an analytical expression for density as a function of distance from the exit (Roberts, 1966) and the isentropic flow relations.

Since water vapor is a volatile of particular interest, we currently model only the H2O component of the exhaust (~30% of the total exhaust mass per Lee, 2017). Once molecules exit the source region, collisional gas dynamics in the near-field are modeled using a DSMC code (Stewart, 2010). DSMC (Bird, 1994) is a stochastic method that simulates gas behavior by modeling the motion of a large number of representative molecules, and the transfer of momentum and energy between molecules through collisions. When a gas is sufficiently rarefied, DSMC transitions gracefully to the collisionless limit; i.e., molecules continue to move and to interact with the lunar surface and the space environment, but no longer interact with each other. While DSMC has previously been used to model plume impingement on the lunar surface for a series of hovering altitudes (Morris, 2012), this is the first such implementation to include a continuously moving source.

Exospheric loss processes included in the simulation are escape, photodestruction and cold trap capture. Molecules that cross the boundary of the computational domain (10,300 km above the lunar surface) are assumed to escape lunar gravity. The rate constant for photodestruction is 1.21×10–5 s–1 (Huebner and Mukherjee, 2015) and for the purposes of this work, dissociation and ionization products are not modeled. We also assume that molecules adsorbed to the lunar surface are not subject to photodestruction. The simulated lunar environment includes the 20 largest PSRs (7 in the north and 13 in the south), modeled as circular patches with locations and sizes from Cisneros et al. (2018). The remaining PSR area poleward of 60° N/S is accounted for stochastically; i.e., the probability of cold trapping is equal to the fractional areal coverage of PSRs, derived from Mazarico et al. (2011) and McGovern et al., (2013). Although not all PSRs may operate as cold traps over geological time scales, most have temperatures sufficiently low to trap migrating water at least temporarily.

When a molecule encounters the lunar surface, it is modeled as having a mean surface residence time given by tres = (1/ν0)·exp(Ea/kBTsurf), where ν0 = 1.0×1013 s–1 (Kolasinski, 2002), Ea is the desorption activation energy, kB is Boltzmann’s constant, and Tsurf is the local surface temperature. Molecular velocities upon desorption are sampled from a Maxwell-Boltzmann distribution at the local surface temperature. In order to examine the sensitivity of the exospheric response to the energetics of desorption, we consider two different values of desorption activation energy, Ea = 0.5 eV and 0.7 eV (~50 and 70 kJ/mol). For simplicity in exploring parameter space, we do not consider a distribution of desorption activation energies (e.g. Farrell et al., 2016) or potential differences between mare and highlands regolith (Poston et al., 2015). Surface temperature outside PSRs is modeled using an analytical expression derived by Hurley et al. (2015). During descent, the local surface temperature at the landing site is ~200 K, corresponding to tres = ~0.4 s and ~12 h for Ea = 0.5 and 0.7 eV, respectively.

The simulations end when the spacecraft is at an altitude of 46 m and 1.8 m north of the landing site. Beyond this point, it becomes increasingly important to consider the transfer of heat and momentum between impinging exhaust gases and the lunar regolith (e.g. Morris et al., 2015). During Apollo Lunar Module landings, dust mobilization became noticeable at altitudes of ~30 m (Metzger et al., 2011). The thrust modeled here is ~18 times less than that of the Lunar Module descent engine, and as such, regolith scouring is likely to begin at lower altitudes. Since this work focuses on examining the dispersion and persistence of exhaust gases, we do not model surface alterations, which likely occur only shortly before landing and involve a relatively small amount of the total exhaust mass.

3. Results and Discussion

Figure 1 illustrates the initial creation of a spacecraft-generated exosphere and its short-term evolution, governed by the interaction of water with the lunar surface. The initial asymmetry in the shape of the expanding vapor cloud is due to the orientation of the spacecraft – thrusters are initially pointed downrange, and then normal to the surface as the spacecraft approaches the landing site. The difference in desorption activation energy affects the balance between adsorbed and migrating water vapor in the two cases. For perspective regarding exospheric density and scale, the typical density of the lunar exosphere is ~104 #/cm3 (primarily noble gases; e.g. Benna et al., 2015) and the widely studied south polar crater Shackleton is 21 km in diameter.

Figure 1.

Figure 1.

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Cross-sectional views (in the plane of descent) showing H2O gas density at 10, 25 and 155 s after thruster firing commences, for Ea = 0.7 eV (a,c,e) and 0.5 eV (b,d,f). The distance already traversed by the spacecraft along the descent trajectory is marked in black, and the distance remaining to be traversed is marked in white.

Spacecraft operations may temporarily increase exospheric density by several orders of magnitude, but the lunar exosphere remains exceedingly rarefied. Figure 2 shows the mean free path between molecular collisions (computed from gas density), and indicates the boundary of the collisional region, which extends ~1–2 km from the spacecraft. The overall extent of the collisional region is larger when desorption activation energy is lower, due to the fact that in this case, molecules that hit the surface are rapidly re-released and interact with impinging vapor, spreading the plume footprint.

Figure 2.

Figure 2.

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Cross-sectional views (in the plane of descent) showing mean free path (computed from gas density) at 25 s after thruster firing commences, for Ea = 0.7 eV (a) and 0.5 eV (b). Black dots mark the distance along the descent trajectory already traversed by the spacecraft, and white dots mark the distance remaining to be traversed. The collisional region is outlined in magenta. The apparent absence of molecules near the centerline in both plots is due to the decreasing size of grid cells close to the axis of the spherical computational domain.

Figure 3 shows the column density of exospheric (i.e. non-adsorbed) water and the surface density of adsorbed water after 155 s of powered descent. Due to the increased mobility of water molecules in the lower desorption activation energy (Ea = 0.5 eV) case, water is more widely dispersed, and exospheric column density is higher. In the Ea = 0.7 eV simulation, a region ~2.3 km by 1.8 km around the landing site is saturated with more than a monolayer of water (assuming a perfectly smooth surface; in reality, more than 1015 #/cm2 is likely to be required to form a monolayer coating over the lunar regolith). For perspective, the LRO LAMP instrument may be sensitive to migrating lunar H2O at surface coverage levels < 1013 #/cm2 (Hendrix et al., 2019). Notably, the area affected by exhaust gases is considerably larger than the blast zone (~100 m in extent) identified by Clegg-Watkins et al. (2016) through photometric analysis of Chang’e 3 landing site images.

Figure 3.

Figure 3.

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Exospheric column density (a,b) and surface coverage (c,d) of water around the landing site after 155 s of powered descent, for Ea = 0.7 eV (a,c) and 0.5 eV (b,d). The simulated descent trajectory (viewed from above) appears as a horizontal black line. In (c), the area covered by more than a monolayer of adsorbed water (assuming monolayer coverage = 1015 #/cm2) is outlined in white.

Figure 4 tracks the fate of the exhaust water vapor over the course of two lunar days. At the end of this period, ~60–70% of the water released has been photodestroyed, and ~13% is cold-trapped in the modeled polar PSRs. Since we assume that molecules adsorbed to the lunar surface do not undergo photolysis, the amount of water photodestroyed is higher in the Ea = 0.5 eV case, where more molecules are aloft at any given time. There is a negligible amount of escape in the Ea = 0.7 eV case, since our simulations begin at a point when thrusters are largely directed towards the lunar surface, which in this case adsorbs impinging water vapor. However, in the Ea = 0.5 eV case, 7% of the water released escapes the computational domain. This is due to the fact the mean exhaust velocity of 2.7 km/s is slightly greater than lunar escape velocity (2.38 km/s), and in the Ea = 0.5 eV case, molecules are not immobilized by the cold surface. In fact, we find that intermolecular collisions in the region shown in Figure 2 tend to accelerate water vapor outward from the landing site.

Figure 4.

Figure 4.

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The amount of water (as a percentage of the total mass released during spacecraft descent), that is temporarily adsorbed (primarily to the night side surface) or aloft at any given time, and the cumulative amount that has been photodestroyed, captured at north and south polar cold traps, and has escaped the computational domain, over the course of two lunar days. Solid lines indicate values for Ea = 0.7 eV and dash-dotted lines indicate values for Ea = 0.5 eV.

Most of the migrating (i.e., not cold-trapped) water vapor in the lunar environment at any given time is temporarily adsorbed to the lunar night side and is released as the surface warms after sunrise. However, modeled surface temperatures near the poles (Hurley et al., 2015) are sufficiently low that in the Ea = 0.7 eV case, some water may remain adsorbed to non-PSR surfaces for long periods of time. The local peak in exospheric mass at ~0.5 lunar days after landing (see Figure 4) is due to the release of water that was deposited near the dusk terminator at the time of landing. The shape and location of this peak differ in the two cases simulated – when desorption activation energy is lower, molecules desorb more readily as the surface rapidly warms at sunrise. It should be noted that even two lunar days after the simulated landing, ~10– 30% of the exhaust water vapor released is found to persist in the lunar environment. The results shown in Figure 4 are consistent with previous work (Prem et al., 2018), which indicates that it takes one or two lunar days after an episodic release before the lunar exosphere reaches a quasi-steady state (characterized by exponentially decaying loss and deposition rates) and that a “stickier” surface tends to prolong exospheric longevity.

Longer term simulations (Prem et al., 2018) further indicate that ~67% of cold-trapping after an episodic release occurs within the first two lunar days. Applying this scaling factor, we infer that ~20% of the total exhaust mass may ultimately be cold-trapped. In absolute terms, the amount of water cold-trapped in this particular scenario is relatively small, since only ~43 kg H2O was released over the 155 s of powered descent. It can be seen from Figure 4 that due to the location of the landing site at 70° S, most cold-trapped water is delivered to south polar cold traps. However, a small amount of water also reaches north polar cold traps. In the Ea = 0.5 eV case, where water molecules are more mobile, more than twice as much water reaches north polar cold traps compared to the Ea = 0.7 eV case. The distribution of water between PSRs at each pole is controlled by the proximity of individual PSRs to the descent trajectory, as well as local time (migration to cold traps occurs predominantly during the day). Over time, as the dawn terminator sweeps around the pole and the exosphere becomes more symmetric, we anticipate that water would become more evenly distributed between PSRs, although some asymmetry may remain.

Figure 5 shows global views of the Moon at 1, 4, and 24 hours after the simulated landing. (Although this is only a fraction of a lunar day, the most significant changes in exospheric structure occur over this short duration.) There are broad similarities between the results shown in Figure 5 and simulations by Goldstein et al. (2001) of exospheric evolution following an impulsive release of vapor. At night-side temperatures (< 130 K), residence times are longer than a lunar day, such that any vapor that falls back to the night side remains immobile until dawn. This implies that the differences seen in the distribution of water over the night side in the two modeled cases are not due to nocturnal migration of water vapor, but rather due to the differences in gas behavior near the landing site. We emphasize that Figure 5 shows only exhaust water vapor, and does not account for other exospheric species that may be present.

Figure 5.

Figure 5.

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Exospheric density (up to an altitude of 500 km in the plane of descent) and surface coverage of water at 1, 4 and 24 hours after landing, for Ea = 0.7 eV (a,c,e) and 0.5 eV (b,d,f). The line of sight is normal to the plane of descent, such that most of the night-side hemisphere is visible. The dawn terminator is to the right. The apparent “gap” in exospheric density along the spherical grid axis (indicated by the solid black line) is a visualization artefact.

Several other notable features in Figure 5 include the following: (i) Molecules traveling on long trajectories may re-converge antipodal to the landing site. This is most clearly visible in Figure 5(a). (ii) Even 24 hours after the landing, there is still some north-south asymmetry in exospheric structure. This will likely persist for at least half a lunar day, until material adsorbed to the night side has been mobilized. (iii) The scale of the spacecraft-generated vapor cloud is generally larger than the scale of typical lunar topography (+/− 7 km), but small-scale temperature variations and topographical shadowing may still play a role in determining the detailed distribution of exhaust volatiles.

4. Summary and Conclusions

Every powered lunar landing is, almost inevitably, an active volatile release experiment. In this work, we model the final stages of a nominal descent trajectory (based on that of the Chang’e 3 spacecraft) in order to explore the fate of the water vapor component of spacecraft exhaust, and the sensitivity of results to the energetics of desorption of water from lunar regolith – a parameter that remains to be definitively determined.

We find that for a simulated landing at 70° S, ~600 km from the South Pole, ~13% of the water released reaches polar PSRs (primarily PSRs near the closest pole, but also PSRs near the opposite pole) within two lunar days after landing. Projections based on previous work indicate that ~20% may be ultimately cold-trapped, after several more lunar days. If 15% of the water initially released is assumed to be evenly distributed over the ~17,000 sq. km of permanent shadow in the south, the resulting surface coverage is ~1012 #/cm2. (One monolayer is often assumed to be ~1015 #/cm2.) Since larger landers typically release more exhaust, surface coverage should increase with lander mass, as well as with proximity of the landing site to the pole. It should be noted that these simulations only include water vapor, about a third of the total exhaust mass for the assumed propellant properties. One of the implications of this is that the effect of intermolecular collisions is underestimated. The sensitivity of simulation results to surface interaction parameters provides a means to constrain those parameters if orbital and/or surface-based measurements are taken during or after a lunar landing.

In light of the current interest in exploring the lunar poles at close range, it is critical to account for surface and exospheric contamination by non-indigenous species during mission planning and when interpreting measurements. Different landing trajectories may result in different deposition patterns, depending the orientation of thrusters relative to the lunar surface during descent and landing. Choice of landing site also matters; equatorial landings should result in less material reaching cold traps, although at least some almost certainly will (e.g. Schorghofer, 2014). Understanding how spacecraft systems alter their operational environments may become a question of broader significance as we explore other nominally airless solar system bodies at closer range (e.g., Lam et al., 2019).

The global redistribution of exhaust volatiles is perhaps the most widespread (albeit mostly temporary) alteration of the lunar environment caused by a spacecraft. Other mechanisms, such as regolith scouring or modification of the thermal environment by a lander/rover may have a more significant, but also more localized impact. Accounting for migrating and adsorbed exhaust gases is likely to be particularly important when characterizing near-surface volatile content or monitoring the rate of inflow/outflow from polar craters. The lunar landing simulated here was hypothetical, but provides a framework for future, more detailed assessments of specific landing and mission scenarios.

Key Points:

  • Spacecraft exhaust gases can persist in the lunar environment (primarily adsorbed to the surface) for longer than two lunar days.

  • Exospheric density and surface deposition in the initial 24 hours after a landing may be diagnostic of desorption activation energy.

  • In a modeled high-latitude landing scenario, ~20% of exhaust water vapor is delivered to both north and south polar cold traps.

Acknowledgements

This work was funded by NASA through the Solar System Exploration Research Virtual Institute DREAM2 (NNX14AG12A) and LEADER (80NSSC20M0020) teams and the Surface and Exosphere Alteration by Landing (SEAL) instrument (80NSSC19P1196). Simulations were run on the Texas Advanced Computing Center’s Stampede2 supercomputer, accessed through the Extreme Science and Engineering Discovery Environment (XSEDE), Allocation TG-AST190035. XSEDE is supported by National Science Foundation grant number ACI-1548562. PP thanks Mehdi Benna, Ben Greenhagen, Wes Patterson, and many members of the LRO-LAMP team for useful discussions. We also thank two anonymous reviewers for thoughtful and constructive suggestions that improved the quality of the manuscript. This work used the DSMC code described in Stewart (2010), adapted as described in Section 2 and Appendix A. Simulated spacecraft trajectory parameters, and data required to reproduce Figures 1–5 are available at: https://doi.org/10.5281/zenodo.3929761.

Appendix A

This section provides additional information regarding the numerical methods applied in this work, including the simulated spacecraft trajectory, the procedure for the generation of simulated molecules, a description of the permanently shadowed regions (PSRs) included in the model, and DSMC simulation parameters.

A1. Spacecraft Trajectory

The file spacecraft_trajectory.dat (available at https://doi.org/10.5281/zenodo.3929761) contains a descriptive header, and the simulated descent profile in Cartesian coordinates. Spacecraft (x,y,z) coordinates vs. time for the Chang’e 3 descent were obtained from Liu et al. (2014), and spacecraft velocity and acceleration were calculated as first and second derivatives of the position. Gravitational acceleration was subtracted from total spacecraft acceleration to yield the acceleration due to thruster firing. We assumed a constant exhaust velocity (relative to the spacecraft) of 3 km/s in the direction of the thrust vector.

For computational efficiency, spacecraft position, velocity and exhaust pointing direction were transformed into a reference frame centered at the center of the Moon, with the z-axis normal to the lunar surface and the x- and y-axes oriented such that the spacecraft descends approximately in the x-y plane. The landing site is close to (0,0,R) where the radius of the Moon, R = 1738 km. Thruster firing begins at t = 0 as defined in spacecraft_trajectory.dat and ends at t = 719 s. The exhaust centerline velocity initially points away from the lunar surface, but becomes horizontal to the surface at t = 151 s. In this work, our simulations begin at t = 548 s (when the exhaust is first tilted more than 45° below the local horizontal) and end after 155 s at t = 703 s.

A2. Molecule Creation

As discussed in Section 2, simulated molecules are initialized within a spherical source region (40 m in radius) centered at the nozzle exit. Roberts (1966) provides an analytical expression for gas density as a function of distance from the center of the nozzle exit:

ρρe=γ(γ−1)Me22(reh)2(cosθ)γ(γ−1)Me2 (1)

where 𝜌 is the gas density at a distance ℎ from the center of the nozzle exit and azimuthal angle 𝜃 from the nozzle centerline. 𝜌𝑒 and 𝑀𝑒 are the density and Mach number at the nozzle exit, 𝑟𝑒 is the exit radius, and 𝛾 is the ratio of specific heats for the exhaust gas mixture.

In order to set up the problem, we assume the stagnation temperature (𝑇0) and exhaust gas composition provided by Lee (2017) for the combustion of MMH-NTO fuel, and specify 𝑟𝑒 = 0.3 m, 𝑀𝑒 = 5.0, and a constant thrust 𝐹 = 2500 N (nominal values for a Chang’e-3-class lander). These input parameters are listed in Table A1. We compute temperature and velocity in the source region using the isentropic relations:

T0T=(ρ0ρ)γ−1=(1+γ−12M2) (2)

Here, Mach number M≡u/γRT, where 𝑢 is bulk velocity, 𝑅 is the specific gas constant and 𝑇 is temperature. Density 𝜌 is calculated using Eq. (1), and stagnation density 𝜌0 can be found by substituting 𝜌𝑒 and 𝑀𝑒 in Eq. (2). Exit density 𝜌𝑒 can be determined from the expression for thrust, F=ρeue2Ae, where 𝐴𝑒 is the nozzle exit area. In using the isentropic relations, we neglect any viscous separation that may occur within the nozzle, as well as any thermodynamic non-equilibrium close to the nozzle exit.

During each time-step, initialized molecules are allowed to cross the boundaries of the source region and move into the computational domain. A conservative time-step size of 0.005 s was chosen in order to avoid physically unrealistic ‘emptying’ of the source region during any time-step. Any molecules remaining in the source region at the end of the time-step are deleted. This approach assumes that conditions within the source region are not affected by the evolving water vapor exosphere outside the source region, a reasonable assumption since (i) gas flow out of the source region is supersonic, and (ii) the mass swept up by the source region as it descends through the spacecraft-generated exosphere is relatively small over the duration simulated. The evacuation of the source region at the end of each time-step creates a small sink for any molecules that happen to fall into the source region during the time-step. Though this is not physically realistic, accounting in more detail for how water vapor may interact with the spacecraft inside the source region is beyond the scope of this work.

Figure A2 presents a schematic view of the molecule creation process and the other physical processes included in our model.

A3. Permanently Shadowed Regions

Table A2 lists the 20 largest lunar PSRs from the LROC PSR Atlas (Cisneros et al., 2017), which were modeled as circular patches in this work. Together, these large PSRs account for 6,151 km2 poleward of 80° S and 2,066 km2 poleward of 80° N. Mazarico et al. (2011) estimated the total PSR area poleward of 80° S and N to be 16,055 km2 and 12,866 km2, respectively. This implies that smaller PSRs cover 3.51% and 3.77% of the remaining area poleward of 80° S and N, respectively. Similarly, McGovern et al. (2013) estimated 898 km2 and 1,271 km2 of permanent shadow between 60–80° S and N, accounting for 0.04% and 0.06% of the total area in the 60– 80° S and N latitude rings, respectively.

A4. DSMC Simulation Parameters

In the DSMC simulations presented here, each simulated molecule represents between 1018 and 2×1019 real molecules (i.e. ~2000 – 40,000 molecules enter the computational domain during each 0.005 s time-step). The computational grid is three-dimensional and spherical, with its origin at the center of the planet. In order to maintain sufficient grid resolution in the vicinity of the spacecraft (where exhaust gases are densest), simulations are performed using a series of staged computational domains, shown schematically in Figure A3. The first, second and third domains are approximately cylindrical in shape, with progressively increasing size and cell size. The spacecraft descent trajectory is entirely contained within the first domain. Molecules that cross the boundaries of the first domain during a run are subsequently read in to the second domain, and so on. Once powered descent ends (155 s into the simulation), the long-term evolution of the water vapor exosphere is modeled in the spherical full_planet domain. The buffer cell shown in Figure A3 is a large, collisionless cell that is used to track the (relatively few) molecules that may travel long distances before falling back to the lunar surface.

The time-step of 0.005 s for the first, second and third domains is chosen to avoid emptying the virtual source region during a time-step, as mentioned above. Once powered descent ends, a time-step of 1–10 s is generally sufficient to resolve the ballistic motion of molecules in between collisions. For the full_planet domain, time-step increases from 0.005 s to 10 s as water vapor expands away from the landing site.

Figure A1.

Figure A1.

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The final 171 s (548 – 719 s) of the descent trajectory tabulated in spacecraft_trajectory.dat. Dots indicate spacecraft position at 5 s intervals, and arrows indicate the direction of the exhaust centerline velocity vector, colored by time. The orientation of the (x,y,z) axes is also shown. Note that the origin of the coordinate system is at the center of the Moon.

Figure A2.

Figure A2.

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Schematic view of the key components of the modeling approach adopted in this work.

Figure A3.

Figure A3.

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Schematic depiction (not to scale) and description of DSMC computational domain configuration for the simulations performed in this work.

Table A1.

Values used to compute density, temperature and velocity fields in the source region. M^, 𝑇0 and exhaust gas composition from Lee (2017) are used to derive 𝑅 and 𝛾, while nominal values of 𝑟𝑒, 𝑀𝑒 and 𝐹 for a Chang’e 3 class lander are assumed.

Parameter Value
Nozzle exit radius, 𝑟𝑒 0.3 m
Molar mass, M^ 20.46 g/mol
Specific gas constant, 𝑅 406.35 J/kg·K
Ratio of specific heats, 𝛾 1.4
Stagnation temperature, 𝑇0 3087.4 K
Exit Mach number, 𝑀𝑒 5
Thrust, 𝐹 2500 N
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Table A2.

The 20 largest lunar PSRs, modeled in this work as circular patches with an equivalent area. The remainder of the PSR area poleward of 60° is modeled stochastically, as described above.

Rank PSR Name (Cisneros et al, 2017) Latitude (°N) Longitude (°E) Area (km2)
South
1 Shoemaker crater –88.026 45.279 1075.518
2 Haworth Crater –87.493 357.876 1017.932
3 Faustini Crater –87.146 84.075 663.93
4 Sverdrup Crater –88.249 216.455 548.791
5 Amundsen Crater –83.524 91.015 439.222
7 Cabeus B –81.691 305.381 376.916
8 Wiechert J –85.023 182.607 371.549
10 Idel’son L –83.891 118.47 326.779
12 Cabeus Crater –84.458 313.432 315.029
13 Malapert F Malapert E –82.176 11.104 300.589
17 de Gerlache Crater –88.312 269.143 243.292
18 Haworth Crater Shoemaker Crater –86.744 21.861 237.287
19 Shackleton Crater –89.645 128.203 233.698
North
6 Rozhdestvenskiy U Crater Rozhdestvenskiy Crater 84.558 153.134 397.206
9 Lovelace crater 81.519 250.162 339
11 Sylvester Crater 82.0262 278.3769 317.336
14 Lenard Crater 84.813 251.475 292.028
15 Rozhdestvenskiy K Crater 81.826 213.992 255.946
16 Nansen F Crater 84.319 62.473 253.033
20 Hermite A Crater 87.952 307.678 211.691
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