Data from the MErcury Surface, Space ENvironment GEochemistry and Ranging (MESSENGER) spacecraft revealed that Mercury’s surface is volatile-rich and iron depleted. In particular the high sulfur concentration in surface lavas and their low iron content are indicative that Mercury formed under highly reducing conditions. Consequently, its core likely contains a significant amount of silicon along a smaller fraction of sulfur. Additionally, the low surface reflectance and spectral measurements support the presence of substantial amounts of carbon on its surface. Several lines of evidence indicate that Mercury was carbon-saturated early in its evolution and for this reason carbon might be abundant in its core.

Unlike silicon, carbon and sulfur have a strong decreasing effect on the melting temperature of iron and as such, even small amounts of these elements imply a relatively low present-day core liquidus, affecting the inner core radius and magnetic field generation. The partitioning behaviour of light elements between solid inner- and liquid outer impact the density structure of the core and the gravitational coupling strength between the mantle and inner core. As a result, the amplitude of the longitudinal libration of Mercury can be affected by its core composition. Here we study the effect of the core composition on Mercury’s present-day thermal state and assess how its forced and free libration are affected.

How to cite: Rivoldini, A. and Van Hoolst, T.: Implications of Mercury’s core composition on its libration and present-day thermal state, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-1144, https://doi.org/10.5194/epsc2024-1144, 2024.

Due to its eccentric orbit, Mercury experiences varying gravitational pull from the Sun along its orbital course, leading to periodic tidal deformation, i.e, stretching and squeezing of the planet. Prectically speaking, Mercury’s surface will rise “up and down” periodically. The magnitude of these surface height variations, typically quantified by the tidal Love number h₂, depends on properties of the deep interior.  A reliable measurement of the tidal h₂ can thus shed crucial insights into Mercury’s interior structure, especially the size and physical state of its core.  

The estimation of the tidal deformation requires laser or radar altimetric measurements. So far, the tidal h₂ of Mercury has only been measured by Bertone et al. (2021) through minimizing height misfits at the intersection points, cross-overs, of the Mercury Laser Altimeter (MLA) profiles. However, only their lower bound is consistent with the existing modeling results (Steinbrügge et al., 2018; Goossens et al., 2022; Figure 1).

In this study, we look into Mercury's tidal deformation by applying an alternative approach to reprocessed MLA profiles, which is based on the co-registration techniques. Previously, we have successfully applied these techniques to Mars Orbiter Laser Altimeter (MOLA) profiles to obtain the spatio-temporal thickness variations of the seasonal CO₂ snow/ice at Martian polar regions (Xiao et al., 2022a, b). By employing the co-registration procedures to the MLA profiles, the interpolation errors associated with the usage of cross-overs are avoided. During the reprocessing to improve the profiles’ geolocation, we correct for a pointing aberration due to relativity effects (Xiao et al., 2021) and incorporate an updated spacecraft orbit model that has better accounted for the non-gravitational forces (Andolfo et al., 2024). We carry out the study at the very polar region of 77°N to 84°N where footprints are the densest and off-nadir pointing angles are generally the smallest. For verification of the proposed approach and quantification of its uncertainty, we generate realistic synthetic profiles and conduct extensive simulations. We obtain a tidal h₂ of 0.92±0.51 (3-sigma), with a central value 0.63 smaller than that of Bertone et al. (2021, 1.55±0.65), but compatible with existing models (Figure 1). Combined with the most recent gravitational deformation measurements, our measured tidal h₂ favors a small to medium-sized solid inner core (<1000 km, Steinbrügge et al., 2018). Currently, we are investigating in detail other implications of our measurement on Mercury’s interior (Briaud et al., 2024, this meeting).

Further improvement can be expected from global profiles acquired by the upcoming BepiColombo Laser Altimeter (BELA), which will commence data acquisition in the beginning of 2026. As preparation, we plan to apply the verified method to synthetic BELA profiles to assess its capability in obtaining reliable temporal tidal deformation, its tidal phase lag, and in disentangling different components of the dynamic tides, e.g., the ones with 88-day and 44-day periods.

Figure 1: Comparison of our measured tidal h₂ to existing estimates from observation and interior modeling. Error bars mark the 1-sigma and 3-sigma bounds, respectively. Note that modelings from  Steinbrügge et al. (2018) and Goossens et al. (2022) are largely compatible with our measurement at 1-sigma level.

References:

Bertone, S., Mazarico, E., Barker, M. K., Goossens, S., Sabaka, T. J., Neumann, G. A., & Smith, D. E. (2021). Deriving Mercury geodetic parameters with altimetric crossovers from the Mercury Laser Altimeter (MLA). Journal of Geophysical Research: Planets, 126(4), e2020JE006683.

Steinbrügge, G., Padovan, S., Hussmann, H., Steinke, T., Stark, A., & Oberst, J. (2018). Viscoelastic tides of Mercury and the determination of its inner core size. Journal of Geophysical Research: Planets, 123(10), 2760-2772.

Goossens, S., Renaud, J. P., Henning, W. G., Mazarico, E., Bertone, S., & Genova, A. (2022). Evaluation of recent measurements of Mercury’s moments of inertia and tides using a comprehensive Markov chain Monte Carlo method. The Planetary Science Journal, 3(2), 37.

Xiao, H., Stark, A., Steinbrügge, G., Thor, R., Schmidt, F., & Oberst, J. (2022a). Prospects for mapping temporal height variations of the seasonal CO₂ snow/ice caps at the Martian poles by co-registration of MOLA Profiles. Planetary and Space Science, 214, 105446.

Xiao, H., Stark, A., Schmidt, F., Hao, J., Steinbrügge, G., Wagner, N. L., ... & Oberst, J. (2022b). Spatio‐temporal level variations of the Martian seasonal north polar cap from co‐registration of MOLA profiles. Journal of Geophysical Research: Planets, 127(10), e2021JE007158.

Xiao, H., Stark, A., Steinbrügge, G., Hussmann, H., & Oberst, J. (2021). Processing of laser altimeter Time-of-Flight measurements to geodetic coordinates. Journal of Geodesy, 95(2), 22.

Andolfo, S., Genova, A., & Del Vecchio, E. (2024). Precise orbit determination of MESSENGER spacecraft. Journal of Guidance, Control, and Dynamics, 1-13.

Briaud, A., Oberst, J., Stark, A., Hussmann, H., & Xiao, H. (2024). Mercury interior characteristics inferred from geodetic measurements. Europlanet Science Congress, 2024-374. 

How to cite: Xiao, H., Stark, A., Steinbrügge, G., Briaud, A., M. Lara, L., and J. Gutierrez, P.: Mercury's tidal Love number h2 from co-registration of reprocessed MLA profiles, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-139, https://doi.org/10.5194/epsc2024-139, 2024.

Context

The first estimation of Venus’ moment of inertia (Margot et al. 2021) paves the way for addressing geophysical questions such as the estimation of size of its core. In parallel, three exploration missions have been selected to study Venus for the next decade. Notably, one of EnVision mission objectives is a geophysical investigation of Venus (ESA 2023).

Examining the rotational dynamics of an object can offer clues about the nature and properties of its interior. The motion of the spin axis of a planet can be described with respect to the fixed celestial sphere (precession and nutation) or with respect to the planetary surface itself (polar motion), both motions bringing complementary clues about the planet’s interior. The precession motion of the spin axis of Venus has been recently measured for the first time, albeit with an uncertainty too large to help constrain interior models (Margot et al. 2021), while its polar motion has yet to be measured.

Aim

We develop a model of polar motion for Venus, and we study the influence of geophysical parameters such as the moment of inertia and the size of the core, in anticipation of its future exploration by the EnVision mission.

Model

A polar motion solution of a triaxial planet is obtained through the Euler-Liouville equation accounting for the solar torque, the rotational and tidal deformations of a viscoelastic mantle, and the varying inertia and angular momentum of the atmosphere. We compute the frequency of the free motion (Chandler wobble) and its characteristic damping time, as well as the frequencies and amplitudes of the forced motion.

The solar torque may affect the Chandler Wobble of Venus because of its slow rotation. On the other hand, whereas deformations due to the centrifugal potential (pole tide) significantly decreases the Chandler frequency of the Earth, they are negligible in the case of Venus due to its largely non-hydrostatic shape.

Figure 1 - Motions in the ICRF of the spin axis of Venus (in green) and the figure axis (polar moment of inertia axis, in orange) for a 30000 years period centered on J2000. The spin axis moves clockwise, and the figure axis circles anti-clockwise around the spin axis with a period of 243 days. Colored dots indicate axes orientations at epoch J2000. RA is right ascension, DEC is declination.

Figure 2 - Polar motion of the spin axis of Venus, in the figure frame (principal moments of inertia axes) for a 15000 years period beginning at epoch J2000. mx and my are the equatorial components of the unit spin vector, R is the mean radius of Venus. The 30 different solutions (in green) are the results of sampling from the uncertainty distributions for Venus’ gravity field and moment of inertia. The nominal solution is plotted in black.

Future measurements

The EnVision orbiter will use its radar to image the surface of Venus with a resolution of tens of meters over a few years. The polar offset derived from its gravity field (Konopliv et al. 1999) would suggest that the polar motion of Venus would be measurable by EnVision, on top of the precession motion.

By tracking the position of surface control points in inertial space, one can constrain the rotation model of a planet. For Venus, it has been achieved with Magellan radar imaging for a uniform rotation model (Davies et al. 1992), and has been studied for a precession model (Cascioli et al. 2021). In this work we will analyze the potential recovery of the combined precession and polar motion of Venus ; the measurement of these rotational dynamics will contribute to refining models of the planet's internal structure.

References

Margot, JL., Campbell, D.B., Giorgini, J.D. et al. (2021) Spin state and moment of inertia of Venus. Nat Astron 5, 676–683. https://doi.org/10.1038/s41550-021-01339-7

ESA (2023), “EnVision, Understanding why Earth’s closest neighbour is so different”, Definition Study Report (Red Book), ESA document reference.
https://www.cosmos.esa.int/documents/10892653/0/EnVision+Red+Book_ESA-SCI-DIR-RP-003.pdf

Konopliv, A. S., Banerdt, W. B., & Sjogren, W. L. (1999). Venus gravity: 180th degree and order model. Icarus, 139(1), 3-18. https://doi.org/10.1006/icar.1999.6086

Davies, M. E., Colvin, T. R., Rogers, P. G., Chodas, P. W., Sjogren, W. L., Akim, E. L., ... & Zakharov, A. I. (1992). The rotation period, direction of the north pole, and geodetic control network of Venus. Journal of Geophysical Research: Planets, 97(E8), 13141-13151. https://doi.org/10.1029/92JE01166

Cascioli, G., Hensley, S., De Marchi, F., Breuer, D., Durante, D., Racioppa, P., ... & Smrekar, S. E. (2021). The determination of the rotational state and interior structure of Venus with VERITAS. The Planetary Science Journal, 2(6), 220. https://doi.org/10.3847/PSJ/ac26c0

How to cite: Phan, P.-L. and Rambaux, N.: Polar motion of Venus and Envision measurements, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-551, https://doi.org/10.5194/epsc2024-551, 2024.

Results

Figure 1 shows the difference in surface heat flux, which is the radially integrated tidal dissipation, after one iteration compared to the initial pattern. The pattern shows a slight shift to the east of the anti-subjovian point, located at zero degrees longitude. Additionally, the local increase in melt-fraction induces higher peak-to-peak variations of tidal heating.

After 89 iterations, a steady solution is found and we retrieve a difference in surface heat flux as shown in Fig. 2. The eastward shift has grown to roughly 35 degrees at the equator, and the peak-to-peak variations have also grown. Tests with different values for c and other coupling methods, not shown here, also show this eastward shift but the resulting pattern can be different. In general, a stronger coupling between dissipation and melt-fraction, represented by a higher c, causes a larger shift and bigger peak-to-peak values which is consistent with previous results that used finite element modelling [4].

Given that we started with a spherically symmetric interior it might be surprising that an asymmetry arises. We suspect the cause for the eastward shift is an inherent asymmetry in the forcing since the tidal potential can be represented as having an eastward and westward propagating component, of which the eastward component has a larger amplitude [9]. To confirm this, we set the amplitude of the westward and eastward components to the same value and no longer observe a shift.

Overall, our results show that the feedback between tidal heating and rheology can induce an eastward lateral shift in tidal heating and hence melt-fraction. This demonstrates that solid-body tides can account for the observed eastward shift in the volcanic heat flow pattern which is especially relevant in anticipation of Juno’s measurement of Io’s k2 Love number, which could confirm or rule out the presence of a magma ocean. Our results are not particular to Io, hence suggesting that the same mechanism might lead to 3D structure in tidally heated exoplanets and exomoons.

Figure 2:  Surface heat flux pattern at convergence after 89 iterations minus the initial pattern.

 

Bibliography

[1] Davies, A. G., Perry, J. E., Williams, D. A., & Nelson, D. M. 2024, Nature Astronomy, 8, 94; [2] Steinke, T., Hu, H., H ̈oning, D., van der Wal, W., & Vermeersen, B. 2020a, Icarus, 335, 113299; [3] Tyler, R. H., Henning, W. G., & Hamilton, C. W. 2015, The Astrophysical Journal Supplement Series, 218, 22; [4] Steinke, T. 2021, PhD thesis, Delft University of Technology; [5] Beuthe, M. 2013, Icarus, 223, 308; [6] Rovira-Navarro, M., Matsuyama, I., & Berne, A. 2024, Planetary Science Journal, 5; [7] Lainey, V., Arlot, J.-E., Karatekin, ̈O., & van Hoolst, T. 2009, Nature, 459, 957; [8] Spencer, D. C., Katz, R. F., & Hewitt, I. J. 2020, Journal of Geophysical Research (Planets), 125, e06443; [9] Chen, E. M. A., Nimmo, F., & Glatzmaier, G. A. 2014, Icarus, 229, 11 

How to cite: Veenstra, A., Steinke, T., Rovira-Navarro, M., and van der Wal, W.: Effect of tidal-heating on the rheology of Io, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-1131, https://doi.org/10.5194/epsc2024-1131, 2024.

Introduction

Io, one of the Galilean moons, is the most active volcanic body in our Solar System. The volcanic activity is driven by tidal heating due to its orbital resonance with Europa and Ganymede. The tidal response of a planetary body depends on its size, internal structure, and the orbital parameters. Dissipation can occur both in the solid and liquid parts of the body. In the solid layers, dissipation depends on the shear modulus and anelastic behavior of the rock which strongly depends on the melt fraction, while in the liquid layers, the dissipation depends on the viscosity and can be strongly affected by the Coriolis force. The existence of a liquid magma ocean on Io is a subject of debate. Earlier studies of tidal heating of Io assume that most of the tidal heat is generated in a partially molten layer beneath the lithosphere or in deeper mantle (1–4). Recently, Miyazaki and Stevenson (5) suggested the possibility of a magma ocean on the top of a partially molten layer. In this study, we compute the tidal dissipation and the gravitational response of Io with a magma ocean. Assessing Io’s tidal response and its implications for the internal structure can help to understand the processes in the tidally heated exoplanets.

Method

Most of the previous models of the tidal response of a planetary body with a subsurface liquid ocean were obtained by solving two-dimensional Laplace tidal equations (LTE). LTE models assume that the radial flow in the ocean is negligible compared to the lateral flow and the ocean thickness is small compared to the radius of the body (e.g., 6–8). In this study, we model the tidal response of Io by solving the three-dimensional Navier-Stokes equations. Unlike previous 3D models (9, 10), our model self-consistently links the flow in the liquid ocean with the viscoelastic deformation of the solid layers (11).

The thickness of the magma ocean is varied from 100 m to 10 km. The viscosity of the magma ranges from 100 Pa s (hot mafic magma) to 10⁷ Pa s (low-temperature magma with solid crystals (10)). The lithosphere above and the mantle below the ocean are assumed to behave as a Maxwell viscoelastic solid, and the magma ocean is treated as a Newtonian viscous liquid. The density structure of Io is set to satisfy the constraints of the total mass and moment of inertia factor, and the upper lithosphere is chosen to be 30 km thick.

Tidal dissipation and the Love numbers

We show that the tidal flow produced by our model gives a wide range of tidal heating patterns (Figure 1). In all the models, the tidal heating is concentrated in the equatorial regions. Some models show a distinct pattern that is independent of longitude. The purely zonal character of the dissipation pattern is unusual in the context of eccentricity tides. This heat distribution has a noteworthy correspondence with the geological map of Io (see Figure 2 in (13)).

The question of whether there exists a magma ocean on Io can be answered by analyzing time variations of the gravity signal of Io (1). In the previous models, the tidal Love number is computed with a hydrostatic magma ocean (e.g., 2). In here we present that tidal response of Io can be strongly affected by dynamic flow in the magma ocean. Unlike the case with solid body tides, in the presence of a magma ocean, degree-2 Love numbers can depend on the harmonic order due to strong Coriolis effect. In Figure 2, we present the Love numbers as a function of ocean thickness and viscosity (for detailed definitions of the Love numbers see (13)). The Love number for harmonic order 0 is increasing with the ocean thickness, reaching a maximum of 0.85, while the Love numbers for harmonic order 2 are strongly affected by the Coriolis term and reach a maximum that is 10 times larger.

 Conclusions

Tidal heating given by our model confirm the results of previous studies (e.g., 7) but our model gives a broader set of heat flux patterns. The heat distribution depends on the viscosity and thickness of the magma ocean and is concentrated in the equatorial regions. This is consistent with new observations by Juno spacecraft which suggest that hot spots at lower latitudes emit more energy than the hot spots in the polar regions (14).

The tidal Love numbers can be strongly affected by the dynamics of the ocean. If the tidal heating occurs in the present-day magma ocean (100 TW, red lines in Figure 2), then the degree-2 Love numbers are either less than 0.1 or greater than 0.7 depending on the ocean thickness and viscosity.  The Love numbers are insensitive to the presence of a thin ocean which should be considered in the future analysis of Io’s gravitational response.

 Acknowledgements

B.A. acknowledges the support form the Charles University project SVV 260709.

References

1. C. J. Bierson, F. Nimmo, J. Geophys. Res.: Planets. 121, (2016), doi:10.1002/2016JE005005.

2. M. Kervazo et al., Astron. Astrophys. 650 (2021), doi:10.1051/0004-6361/202039433.

3. T. Steinke et al., Icarus. 335 (2020), doi:10.1016/j.icarus.2019.05.001.

4. M. N. Ross, G. Schubert, Icarus. 64, (1985), doi:10.1016/0019-1035(85)90063-6.

5. Y. Miyazaki, D. J. Stevenson, Planet. Sci. J. 11, (2022), doi:10.3847/PSJ/ac9cd1.

6. M. Beuthe, Icarus. 280, (2016), doi:10.1016/j.icarus.2016.08.009.

7. R. H. Tyler et al., Astrophy. J. Supp. S. 218, (2015), doi:10.1088/0067-0049/218/2/22.

8. I. Matsuyama et al.,, Icarus. 312, (2018), doi:10.1016/j.icarus.2018.04.013.

9. M. Rovira-Navarro et al., Icarus. 321, (2019), doi:10.1016/j.icarus.2018.11.010.

10. J. Rekier et al., J. Geophys Res Planets. 124, (2019), doi:10.1029/2019JE005988.

11. B. Aygün, O. Čadek, J. Geophys. Res.: Planets. 128 (2023), doi:10.1029/2023JE007907.

12. A. R. Philpotts, J. J. Ague, Principles of Igneous and Metamorphic Petrology Cambridge University Press, Cambridge, UK, 2nd edition., 2009.

13. B. Aygün, O. Čadek, Geophys. Res. Lett. 51 (2024), doi:10.1029/2023GL107869.

14. A. G. Davies et al., Nat. Astron. 8, (2024), doi:10.1038/s41550-023-02123-5.

How to cite: Aygün, B.: Impact of the subsurface magma ocean on tidal dissipation and the Love numbers, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-825, https://doi.org/10.5194/epsc2024-825, 2024.

Polar wander is the reorientation of a body following a perturbation in the moment of inertia due to a mass anomaly. It has occurred on Mars as a result of the formation of the Tharsis region (e.g. Matsuyama and Manga 2010), on Pluto due to volatile ice deposition (Keane et al. 2016) and has also been proposed for icy moons such as Europa (Schenk et al. 2020). Pluto and icy moons have a tidal bulge in addition to being flattened due to rotation. In that case the polar wander path is more complicated and involves both a reorientation around the tidal axis (pointing to the central body) and one around the rotational axis. The path and speed of the anomaly depend on the size and location of the load and the mantle viscosity, with the end location determined by the strength of the outer shell with very high viscosity. Thus, if there are observational clues about polar wander, different scenarios in terms of size and timing of load, and internal structure can be tested. Most studies assume approximate solutions or focus on the end points of polar wander. Sometimes small angle polar wander is assumed, such as for polar wander due to Pleistonene deglaciation for Earth. In that case the linearized form of the Liouville equation is used where it is assumed that the rotational axis is the z-axis and the equatorial bulge is perpendicular to that. Here we present sensitivity studies of the complete  path for large angle polar wander to changes in loading.

We use a semi-analytical solution for reorientation of a rotating tidally deformed body with a high-viscosity visco-elastic shell (Hu et al. 2019) valid for large polar wander (>10 degrees). The method does not assume that the body is fully relaxed at any moment of the reorientation (the so-called fluid limit solution). Therefore, it works for faster loads (e.g. due to impacts) and can provide the complete reorientation path. Results of this method have recently been reproduced by Patočka and Kihoulou (2023) using a simpler approach.

We use Triton as case study. Polar wander on Triton can occur because of volatile migration (Rubincam 2003). Here we assume a point load. For Triton we use a 5-layer model as given in Hu et al. (2019) with a mantle viscosity of 10¹⁹ Pa s, overlain by ice shells with a viscosity of 10²¹ Pa s.

Figure 1: The movement of a mass anomaly emplaced on the Triton model. The rotational axis is at the origin pointing out of plane, the tidal axis pointing to the central body is at 0° longitude, pointing to the right. The starting position of the mass anomaly is at 15 ° colatitude and 15 ° longitude. Circles: Heaviside load for a point mass of 1.5×10¹⁷ kg, open squares: Heaviside load for a point mass of 3×10¹⁷ kg which roughly corresponds to a 100m thick disc of ice of 100 km radius. Crosses: load increasing linearly in time over 15 Ma to a magnitude of 3×10¹⁷ kg.

We apply a point mass with a magnitude of 3×10¹⁷ kg which roughly corresponds to a 100 m thick disc of ice of 100 km radius. The load is applied as instantaneous (Heaviside) forcing or linearly increasing (ramp). The path of a mass anomaly in the so-called bulge-fixed reference frame is shown in figure 1. For a larger mass the anomaly ends up closer to the tidal axis, as is expected. The ramp load leads to a path that is not very different from that of the Heaviside load. However, if the time over which the load increases is increased, the path is closer to that of the smaller Heaviside load (not shown). Thus, the path of the mass anomaly is an important constraint on the magnitude and timing of the load.

In future work we aim to study Pluto. The Sputnik Planitia region is the remnant of an impact. This by itself would cause a negative mass anomaly which would induce polar wander such that it moves towards the north pole. However, if the impact basin that was compensated by uplift in the subsurface ocean (Keane et al. 2016) possible compounded with the buried remnant of the impactor (Ballantyne et al 2024) it would shift towards the sub-Charon point. We will investigate various initial positions and thickness of a nitrogen ice layer and study possible end locations.

References

Ballantyne, H.A., Asphaug, E., Denton, C.A., Emsenhuber, A. and Jutzi, M., 2024. Sputnik Planitia as an impactor remnant indicative of an ancient rocky mascon in an oceanless Pluto. Nature Astronomy, pp.1-8.

Hu, H.X.S., van der Wal, W. and Vermeersen, L.L.A., 2019. Rotational dynamics of tidally deformed planetary bodies and validity of fluid limit and quasi-fluid approximation. Icarus, 321, pp.583-592.

Keane, J.T., Matsuyama, I., Kamata, S. and Steckloff, J.K., 2016. Reorientation and faulting of Pluto due to volatile loading within Sputnik Planitia. Nature, 540(7631), pp.90-93.

Matsuyama, I. and Manga, M., 2010. Mars without the equilibrium rotational figure, Tharsis, and the remnant rotational figure. Journal of Geophysical Research: Planets, 115(E12).

Patočka, V. and Kihoulou, M., 2023. Dynamic reorientation of tidally locked bodies: Application to Pluto. Earth and Planetary Science Letters, 617, p.118270.

Rubincam, D.P., 2003. Polar wander on Triton and Pluto due to volatile migration. Icarus, 163(2), pp.469-478.

Schenk, P., Matsuyama, I. and Nimmo, F., 2020. A very young age for true polar wander on Europa from related fracturing. Geophysical Research Letters, 47(17), p.e2020GL088

How to cite: van der Wal, W., Hu, H., and Vermeersen, B.: Polar wander on tidally deformed rotating bodies – sensitivity study for various load cases, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-746, https://doi.org/10.5194/epsc2024-746, 2024.

1. Binary asteroid modeling in GRAINS

Tidal theory for binary asteroid systems is in a low state of development in comparison to the theory for planetary systems. However, massive N-body simulations present an opportunity to directly simulate and observe relevant physics for binary asteroid systems. The software GRAINS is unique in its N-body formulation, with non-spherical mass elements subject to friction and contact dynamics modeled via the Chrono physics engine [1]. We focus on the spin dynamics of the secondary, modeling a super-synchronously rotating 3000 particle rubble pile secondary orbiting around a point mass primary. The system considered is the Didymos-Dimorphos system, but with Dimorphos spun up to an initial rotation of twice the orbital mean motion, with the axis of rotation perpendicular to the initial orbit plane. This yields a mainly planar problem, simplifying an already complex analysis. This scenario could be loosely representative of a primordial Didymos-Dimorphos before the tidal locking of the secondary, but it also has relevance because of the possibility that the DART impact significantly changed Dimorphos’ initially tidally locked spin state [2]. A depiction of the initial configuration is given in Figure 1 – note that all lengths shown are in non-dimensional units inherent to GRAINS.

Figure 1. Spherical Didymos and rubble pile Dimorphos modeled in GRAINS (non-dimensional units L).

2. Estimating Q/k₂

The fraction Q/k₂ gives the ratio of the quality factor Q to tidal love number k₂, where smaller ratios indicate a more dissipative nature. We opt for a direct measurement of Q/k₂ via rearrangement of the classical MacDonald tidal torque expression [3], and then averaging over full rotations of the super-synchronously rotating Dimorphos:

where L_z gives just the z component of the torque of Didymos on Dimorphos, and this analysis should only be performed for planar super-synchronous rotation. Using this equation and the numerically estimated tidal torques, we obtain estimates for Q/k₂ ranging from 79.4 to 10.7 depending on the averaging window and time in the simulation, and we note that this result is significantly more dissipative than expected [4]. Moreover, we observe significant slow-down of Dimorphos’ spin of ~13% in the ~72 hours simulated. Note that BYORP effects are not included, but the timescale is short, and we are more interested in the spin dynamics than the orbital evolution.

3. Rock movement and tidal motion

Because the location of every rock in the rubble pile is tracked, we can perform complex studies of rock movement. We observe a tendency for a few rocks close to the surface to migrate longitudinally from their original positions with respect to their neighbors. We also observe that in the body frame which diagonalizes the inertia tensor of our rubble pile Dimorphos, there is still some small residual longitudinal oscillation of the topography. Indeed we would only expect the topography to appear static in such a principal axis frame if the body is perfectly rigid. To better isolate relative rock movement patterns, we also define an alternate body frame – a “topographic” frame. This is done via basis vectors computed from the barycenter-relative positions of a few select rocks deep in the interior, wherein we hypothesize that rock movement is mitigated by overburden pressure in comparison to at the surface. At t=0, the first and third basis vectors of this topographic frame are collinear with those of a Hill frame parameterized by the radial direction from Didymos and the direction of the orbital angular momentum vector.

Figure 2. Equatorial cross-section showing rock movement in a body-fixed topographic frame (length units L).

While this study is conducted for rubble piles, which are governed by granular (discretized) physics in lieu of rheological (continuum) physics, we identify global patterns in rock displacement that defy expectations from the unimodal MacDonald model, which predicts a static lag offset between the ground track of the perturber and the raised tide. Figure 2 depicts the relative displacement of rocks at three distinct times in an equatorial (i.e. z-axis) cross-section of Dimorphos. The axis collinear with the peak of a longitudinally traveling tidal “wave” is clearly visible, traveling clockwise, catching up with and overtaking the ground track of Didymos (black arrow), which also travels clockwise in the topographic/body frames. This behavior is somewhat reminiscent of the non-stationary tidal lag predicted from classical Darwin-Kaula theory and other recent related works [5].

4. Conclusions

This work directly explores binary asteroid tidal physics using the GRAINS N-body model. We compute lower-than-expected Q/k₂ for Dimorphos, ostensibly due to the new consideration of high-fidelity contact and friction effects. If accurate, a real-world implication of this could be the revelation of a surprisingly settled rotational state of post-DART impact Dimorphos upon the arrival of the Hera mission. With this model we can also directly observe rock movements and tidal distortion, presenting GRAINS as a useful tool for new developments in rubble pile tidal physics.

5. Disclaimer

Funded by the European Union. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.

6. Acknowledgements

This work was performed as part of an MSCA postdoctoral fellowship, grant agreement ID: 101063274.

References

[1] Ferrari, F., Tasora, A., Masarati, P. et al. (2017). N-body gravitational and contact dynamics for asteroid aggregation. Multibody Syst Dyn, 39, 3-20.

[2] Agrusa, H. F., Gkolias, I., Tsiganis, K. et al. (2021). The excited spin state of Dimorphos resulting from the DART impact. Icarus, 370, 114624.

[3] Murray, C. D., Dermott, S. F. (1999). Solar System Dynamics. Cambridge University Press.

[4] Pou, L., Nimmo, F. (2024). Tidal dissipation of binaries in asteroid pairs. Icarus, 411, 115919.

[5] Efroimsky, Michael. (2012). Bodily tides near spin-orbit resonances. Celestial Mechanics and Dynamical Astronomy, 112, 283-330.

How to cite: Burnett, E. R., Fodde, I., and Ferrari, F.: Enhanced tidal dissipation in rubble pile binary secondaries revealed via numerical studies , Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-1174, https://doi.org/10.5194/epsc2024-1174, 2024.

We have completed a study which aims to guide future searches for near-Earth asteroid (NEA) families. The discovery of NEA families would help understand the formation, composition, and dynamical properties of NEAs [1][2], and with 100,000 potential new NEAs from Vera Ruben Observatory’s LSST [3], an efficient search will need to be completed. We have run n-body simulations of model NEA families with a wide range of orbital parameters and properties, to find those which cause the dispersion of families to be slowest, and our results are as follows:

The standard deviation of the orbital elements are significantly affected by the oscillations caused by the Kozai-Lidov effect [4], as changes in the family’s eccentricity, and thus the radius from the Sun at the ascending and descending nodes, will bring their orbits closer to those of the nearest planet. How quickly this occurs is affected by the inclination and the proximity to the nearest planet. Families with smaller inclinations will have faster Kozai-Lidov oscillations, and the closer a family is to a planet, the more quickly the oscillations will bring them together. A comparison of how this affected our models can be seen in Fig. 1.

We have also studied the effects of mean-motion resonances on the orbital dispersion of NEA families. Due to the previous work on a pair found in the 5:3 Venus MMR [5][6], we placed our models within, and near, this resonance. We found that dispersion is slower when breakup occurs within the resonance, if all family members remain within immediately after breakup. This is again due to the Kozai-Lidov oscillations, which appear to slow within the MMR. However, though the close approaches are delayed, once they do happen, we observe a larger dispersion increase than for the models placed outside of the resonance.

The D-criterion [7][8] has been used frequently to search for NEA families, and gives a value which represents the closeness of two objects’ orbits. We have analysed its performance within the 5:3 Venus MMR, and found that the Drummond D-criterion value for a pair is smaller for around 40,000 years longer than for a pair placed outside of the MMR.

We conclude that future searches should focus on NEA families at high inclination and far from the nearest planet, and within strong MMRs. 

Figure 1 Top: the time evolution of the radius at the descending node of the simulated cluster r_D, where the coloured lines show three models with different initial inclination i_c, and P_diff, the difference between initial planet and particle perihelion, indicated by the legend. The radius of the nearest planet’s orbit at the same angle as the parent body r_D is indicated by a black dashed line. Bottom: the standard deviation of the difference between the semi-major axis of each particle and the parent body, for the three models.

Bibliography 

[1] Schunová E., Granvik M., Jedicke R., Gronchi G., Wainscoat R., Abe S., 2012, Icarus, 220, 1050–1063

[2] Fu H., Jedicke R., Durda D. D., Fevig R., Scotti J. V., 2005, Icarus, 178, 434–449

[3] Jones R. L., et al., 2018, Icarus, 303, 181–202

[4] Naoz S., 2016, Annual Review of Astronomy and Astrophysics, 54, 441

[5] de la Fuente Marcos C., de la Fuente Marcos R., 2018, Monthly Notices of the Royal Astronomical Society: Letters, 483, L37–L41

[6] Moskovitz N. A., et al., 2019, Icarus, 333, 165

[7] Southworth R. B., Hawkins G. S., 1963, Smithsonian  Contributions to Astrophysics, 7, 261

[8] Drummond J. D., 1981, Icarus, 45, 545–553

How to cite: Humpage, A. and Christou, A.: A Numerical Study of Near-Earth Asteroid Family Orbital Dispersion, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-910, https://doi.org/10.5194/epsc2024-910, 2024.

Abstract

Several space missions like Mars Global Surveyor, Mars Express and Phobos 2 have already visited the Martian moon Phobos and performed measurements regarding its geophysical properties. Those have shown that it has a low average density (1861±11)kgm^-3 [1], indicating a high proportion of porosity. Comparison with other objects is a challenging task, as it is not entirely clear whether Phobos is a C-type or D-type asteroid. Phobos has a highly irregular shape, resembling a heavily cratered asteroid. The limited information about its inner mass distribution makes it an interesting object for future research. By determining the gravity field through precise orbit determination around the body, it is possible to draw assumptions on the body’s mass distribution. Information on the interior properties can then be used to make conclusions about Phobos formation and evolution. However, to investigate Phobos inner structure, some challenges must be overcome. First, a precise conversion to discrete elements of the body’s shape is mandatory due to its contribution on the gravitational field. Secondly, a suitable simulation environment is necessary, which can compute the geophysical properties efficiently with high precision.

This study compares two shape models of Phobos, Ernst et. al [1] and Willner et. al [2] using a voxel-based mass-concentration method [3], to discretize each shape model for different cube resolution and reconstruction algorithms. We investigate the influence of the shape model, the cube edge length and the choice of the reconstruction algorithm for the following geophysical quantities, assuming a homogeneous mass distribution:

• Gravity Coefficients C_nm, S_nm
• Near-Surface Acceleration
• Principle Moments of Inertia I_xx, I_yy, I_zz
• Libration Amplitude Θ

We are able to compute the Gravity Coefficients up to an arbitrary order, but focus our analysis on C₂₀ and C₂₂, since current measurements are only available for values up to order two.

Preliminary results for the volume reconstruction are shown in the following. Figure 1 shows a discretization of Ernst’s shape model using voxels with an edge length of 400m and a pointcloud algorithm for reconstruction. It can be observed that the shape and various characteristics, such as larger craters and especially the Stickney crater, are well represented. 

Figure 1: Voxel reconstruction of Phobos using the Ernst model.

Figure 2 illustrates the reconstructed volume of Phobos for the Ernst model using different voxel edge lengths and reconstruction algorithms. The green lines denote upper and lower boundaries of Phobos volume, while red and blue dots correspond to the used reconstruction algorithm. The voxel representations demonstrate consistency with the measurement data, accounting for uncertainties and numerical errors. Results regarding the other parameters will be discussed in this study.

Figure 2: Volume of the voxel approximation of Phobos using the Ernst model.

References

[1] ERNST, Carolyn M., et al. High-resolution shape models of Phobos and Deimos from stereophotoclinometry. Earth, Planets and Space, 2023, 75. Jg., Nr. 1, S. 103

[2] WILLNER, Konrad; SHI, Xian; OBERST, Juergen. Phobos' shape and topography models. Planetary and Space Science, 2014, 102. Jg., S. 51-59.

[3] HASER, B., et al. Voxel-based Density Models for accurate gravitational Field Computation, EGU24

How to cite: Haser, B. and Andert, T.: Comparison of Phobos Geophysical Properties for different Shape Models using Voxel Mascons, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-507, https://doi.org/10.5194/epsc2024-507, 2024.

Hera is a planetary defense space mission led by the European Space Agency (ESA), with a targeted launch in October 2024. Its primary goals encompass a thorough exploration of the Didymos binary asteroid system, marking the assessment of its internal characteristics. Additionally, Hera will meticulously analyze the results of NASA's DART mission's kinetic impactor experiment. The data gathered by Hera promises to be invaluable for any future asteroid deflection endeavors and scientific research, deepening our insights into asteroid geophysics and the evolutionary dynamics of the solar system's formation.

In this context, the precise orbit determination of Hera, along with its companion CubeSats Juventas and Milani, will enable the accurate estimation of critical physical parameters. These parameters are essential to determine the momentum enhancement resulting from the DART impact, as well as for analyzing their dynamical state, internal structure, and evolution. Key parameters include mass, mass distribution, gravity, rotational states, relative orbits, and dynamics of Didymos and Dimorphos asteroids.

The conventional approach to planetary radio science analysis, which typically treats rotational states as independent variables described by time-dependent polynomials, might not be adequate for interpreting the data collected by the Hera mission. This limitation arises primarily from the anticipated challenge posed by the spin-orbit coupling of the asteroids. Given the irregular shapes and close proximity of Dimorphos to Didymos, a more sophisticated dynamical modeling approach, like the Full Two-Body Problem (F2BP), might be necessary to accurately capture the complex dynamics of the binary system.

In this study, we present the Hera orbit determination covariance analysis employing the F2BP model within JPL's Mission Analysis, Operations, and Navigation Toolkit Environment (MONTE) orbit determination software. We show the expected sensitivity to the key scientific parameters, including the gravity field of Didymos, the relative orbit of Dimorphos, the moments of inertia of the bodies, and their rotational states. As the dynamical state of Dimorphos post-DART impact is uncertain, we explore both non-chaotic and chaotic scenarios to evaluate the results' sensitivity to varying conditions. Additionally, we conduct a comparative analysis between the F2BP outcomes and those obtained using standard radio science models.

How to cite: Gramigna, E., Lasagni Manghi, R., Zannoni, M., Tortora, P., Gaitanas, M., Tsiganis, K., Gkolias, I., and Park, R. S.: Covariance Analysis of the Hera Mission at the Didymos System with the Full Two-Body Problem Dynamical Model, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-895, https://doi.org/10.5194/epsc2024-895, 2024.

Quantum Technologies have been rising in the past years. With commercial interest on the rise and finished products being made available, quantum-based gravitational field measurements are the first real-life application.

To realize a quantum gravimeter or a quantum gradiometer, here, atom interferometers are discussed. Atom interferometers function by subjecting a cloud of atoms to three successive laser beams. Due to the mass of the atoms, they are subject to outside accelerations. The effect of the acceleration is then seen in the phaseshift of the interferometeric signal in the readout ports. The achievable precission of the measurement is determined by the stability of the laser gratings and the temperature of the underlying atom ensemble. Consequently, the atom cloud is typically cooled to improve the measurement and the obtained signal.

Following that line of reasoning, atom interferometers allow for very precise and drift free measurements. This gives a strong advantage over classical systems, which always include residual friction and thereby drift in the measurement.

In this talk, I will give an overview over the state of the art of cold atoms in space and especially the most recent developments in Earth observation. I will then follow this up by discussing the opportunities of atom interferometers in planetary exploration with specific regards to underlying structures, (seasonal) changes, and planetary dynamics.

To illustrate the advantages, I will present the MaQuIs proposal, which is concerned with Mars and its gravitational field. In doing so, I will also cover the advantages and limitations of cold atom systems and hybridization concepts available to improve the signals.

How to cite: Woerner, L.: Quantum Technologies for Planetary Geodesy, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-632, https://doi.org/10.5194/epsc2024-632, 2024.

Improving the data on the gravitational field of Mars enhances our knowledge about Martian planetary dynamics and subsurface water reservoirs. A future dedicated satellite gravimetry mission at Mars following the archetype of GRACE-FO, with two identical spacecraft chasing one-another along a low polar orbit, has been proposed. Measuring changes in their mutual separation could produce valuable data for the derivation of improved static and time variable gravity field solutions of Mars.

Requirement for such a mission are primarily two sensors: an accelerometer located at the center of mass of the spacecrafts and a ranging measurement system. The latter one is used to measure the range variations e.g. via laser interferometry, as the separation between both spacecrafts varies due to gravity anomalies. The accelerometer is needed to distinguish between gravitational accelerations and non-gravitational perturbations acting on the satellite.

Compared to terrestrial missions, the Martian environment implies several challenges. Using doppler tracking instead of a GNSS system reduces positioning accuracy. Insufficiently known data on Mars Orientation Parameters may result in misinterpretations within the gravity field recovery process. Existing models for atmospheric drag fail to describe short term variations in the Martian upper atmosphere. The accelerometer is mitigating this by measuring the non-gravitational accelerations acting on the spacecraft.

Simulating the output of both sensors is valuable to evaluate the sensor requirements needed to ensure the quality of the scientific outcome of the mission. It enables to decide upon technical and mission details such as orbital parameters and to assess the feasibility of such a mission in general. For this purpose, we develop a simulation tool for the precise orbit propagation. It includes the modelling of gravitational and non-gravitational forces for orbit integration. Together with a sensor model for both the accelerometer and a laser ranging interferometer, it can emulate realistic sensor outputs. In this talk, we present the first version of simulated sensor data.

How to cite: Bredlau, M., Bremer, S., Koch, A., Leipner, A., Schilling, M., Weigelt, M., and Wörner, L.: Sensor data simulations for a future dedicated satellite gravimetry mission at Mars, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-820, https://doi.org/10.5194/epsc2024-820, 2024.

Introduction: The laser altimeter data of Mars Global Surveyors (MGS) Mars Orbiter Laser Altimeter (MOLA) [1] instrument provide a global network of laser shots with unprecedented height precision for planet Mars. The determination of planetary radii (i.e. 3D coordinates of points at the surface), requires knowledge of spacecraft trajectory and the instrument’s orientation in space that is often limited, leading to inconsistencies between the nominal ground profiles obtained, as is observed in the original (not adjusted) MOLA mission data record at cross-over points. This occasionally leads to substantially offset outlier profiles. In the final mission data products such discrepancies are reduced by applying adjustment techniques to minimize cross-over residuals [2]. When compared to digital terrain models (DTM) of similar resolution such as HRSC Mars quadrangle DTMs [3], single MOLA tracks still show considerable variability in terms of height differences after co-registration.

We present a method to effectively and accurately co-register MOLA profiles to existing Mars half-quadrangle DTMs which allows to increase the accuracy of the co-registration of the single laser tracks while providing similar internal a-posteriori cross-over accuracies as the archived MOLA data record. The method allows to derive improvements to the extrinsic observation parameters directly and applies Evolution Strategy (ES) techniques for parameter optimization.

The High Resolution Stereo Camera (HRSC) on ESA’s Mars Express (MEX) [4] spacecraft provides a unique data set to derive a global Mars DTM through stereo photogrammetry [3], at improved spatial resolution. As the HRSC DEM is already aligned with the MOLA DTM through a photogrammetric bundle adjustment using MOLA height control data, height differences between the two datasets are already small at the beginning of the ES process and largely related to additional detail represented in the HRSC DTM and the uncertainty of position associated with the MOLA tracks, generally estimated as about 100 m horizontally and one to few meters in height.

Methods: We apply Evolution Strategy (ES) techniques [5,6] that have their strengths in solving large parameter vectors for a given problem. The problem is reduced to implementing the observational equations for each data source, and to formulating a suitable quality function that includes dependencies of all unknown parameters. Here we model a parameter vector comprising the bore-sight vector of MOLA and an orbital shift in along-track, across-track and in height for each laser segment. Segments are defined as continuous sections of the laser data that reach from North Pole to South Pole. Segments are co-registered to DTM half-quadrangles at the equator while laser data points of one segment outside the DTM area will still inherit the parameter optimization.  Potential errors increase with increasing distance to that reference DTM region.

The ES randomly creates a number of parameter vectors and tests the quality of all these child vectors based on the defined quality function. Here we derive the root-mean square of all height differences at the shifted (according to the parameter vector) laser shot locations and the DTM heights. The child vector with the lowest RMS determined is the seed for new random child vectors. We apply an ES-CMA [4] procedure in our implementation as this variant has the capability to self-adjust the search distances applied and thus provides reliable convergence properties.

Results: ES-based adjustment of MOLA tracks was applied using an equatorial HRSC DTM half-quadrangle (MC-13E) and the laser track segments intersecting this quadrangle. The quality of the adjustment was evaluated by visual inspection of gridded DTM data products (Fig. 1) and by analyzing the consistency of the results in terms of height residuals at cross-over points. The corresponding values were also derived for the original MOLA profiles and MEGDR data set. Gridded DTM products mainly show the outlier tracks (see Fig. 1). We note that these quite do occur in the original MOLA, but also still appear in the crossover adjusted version. The ES adjustment, apparently allows for the most reliable integration of outlier tracks, although they cannot be eliminated completely over the full reference DTM.  Height residuals at cross-over points amount to ±3.52 m initially, i.e. before any corrections to the nominal profile solutions while an average residual height difference of only ±0.70 m is achieved with ES-adjusted profiles. Considering outlier-tracks by applying a global 3s-blunder elimination to the height differences, the corresponding values then are to ±2.72 m (nominal case), and ±0.41 m (ES-adjusted).

Figure 1: Color-coded and shaded display of gridded digital terrain model from MOLA profiles of different processing levels (subset of DTM at 463 m/post resolution covering quadrangle MC-13). Left: original MOLA tracks with nominal orientation data. Center: cross-over corrected profiles [2]. Right: MOLA tracks adjusted to HRSC DTM using the Evolution Strategy method. Note different contribution of outlier tracks. For fine-scale differences concerning height accuracy please refer to text.

From these encouraging results, we conclude that the ES-method performs very well with respect to the reliability and the accuracy of the parameter optimization. As the method establishes a high-quality co-registration between MOLA and the reference DTM, the results are considered very promising with respect to a future revision of the global MOLA data product and joint HRSC/MOLA DTMs.

Acknowledgments: The authors thank the HRSC Experiment team at DLR, Institute of Planetary Research, Berlin as well as the Mars Express Project teams at ESTEC, ESOC, and ESAC for their successful planning and acquisition of data and for making processed data available.

References:
[1] Smith, D. E. et al. JGR 106, 23689-23722 (2001). Doi:10.1029/2000JE001364
[2] Smith, D. E. et al. NASA PDS (2003). MGS-M-MOLA-5-MEGDR-L3-V1.0.
[3] Gwinner, K. et al. PSS 126, 93-138 (2016). Doi: 10.1016/j.pss.2016.02.014
[4] Jaumann, R. et al.  PSS 55, 928-952 (2007). Doi:10.1016/j.pss.2006.12.003
[5] Hansen, N. 75-102 (Springer Berlin Heidelberg, 2006).
[6] Rechenberg, I. Evolutionsstrategie 94. Vol. 1 (Frommann-Holzboog, 1994).

How to cite: Willner, K., Gwinner, K., Stark, A., Elgner, S., and Hussmann, H.: Adjustment of MOLA Laser Altimeter Tracks to HRSC Photogrammetric Stereo DTMs Using Evolution Strategy, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-787, https://doi.org/10.5194/epsc2024-787, 2024.

Transient events are characterized by continuously changing states or those which are governed by rapidly changing states. These events occur in a manner where the observational opportunities are either limited or negligible due to the event being too quick or occurring without any pre-interfaced knowledge of its occurrence. This leaves us humans with general abstract ideas of event occurrence; however no concrete information can be inferred from the event-cognition point of view. Nonetheless, the event does provide an initial understanding of our limitations both philosophical, scientific and technological-readiness, and to be prepared to study it better, in case such events occur again. Transient events in the terrestrial context relate to volcanic eruptions, hydrothermal vents/geysers and in the extraterrestrial context on other planetary surfaces like dust storms on Mars, tidal and lava motions on Jupiter and even solar flares on the sun’s surface.

Fig 01. scene representation for plantary surface activity

However, in order to develop such approaches, it is essential that we are able to develop early cognition towards such events that may or may not catastrophic but can render the possibility of exploring, investigating, testing, validating and verification of various approaches and systems performance. This is also essential in pursuing the co-design of the systems, preferably autonomous systems able to understand the event sequences. To measure the event, it is essential that foundational models of its origin, impact, occurrence, aftermath are developed based on which further scientific progressive models can be generated.
The transient processes are not only representative of actionable events but also are relevant to environment mapping that surrounds the events or target bodies. An example is the possibility to map the erratic gravitational influences of small solar system over well-defined trajectories.
This doctoral thesis identifies the requirements of event cognition as an iterative and procedural process, while sighting the study of singular and multi-agent systems that can be deployed to survey, perform gathering operations, and pursue developmental pipelines to produce holistic and comprehensive scenes. These scenes are expected to closely represent the various phases of the event or the complete event as a whole.
In the terrestrial context, transient events are found in the likes of erupting volcanoes, geysers, and floods. In the extra-terrestrial context, they are characterized by high velocity flybys by interplanetary objects like Oumuamua, jets emancipating from the cometary bodies like 67P and activities on larger planetary bodies like dust storms on Mars and lava flows on Jupiter moons. Respecting the above-mentioned event-cognition philosophy, the thesis addresses the aspects that are essential to be able to capture dynamic events that otherwise, only allow a one-shot observational opportunity and sometimes not even that, for the requirements of producing a high scientific return. The methods are also validated at the Tartu Observatory Space Simulation Facility.
For optimal observations, it is required that scouting agents are positioned at scientifically-viable locations. For that it is essential that the effective observations space is sampled, discrete positions are identified, and trajectories are generated to ensure that our agents are present at the required location within the required time frames. The approach produces educated guesses about the probability that can be used to optimize the spacecraft/agent trajectories. The author’s work with chaotic volumetric sampler reasons the valid spatial distribution, observations from where, mission-specific scientific data from various sensors can be achieved.
A series of simulations are preformed within physics-informed simulators that are developed for the use-case of simulating either full mission or individual mission phases where the consequent spacecraft and target body activities can be represented with near scientific use cases. The simulations provide a comprehensive understanding of the science return that can be envisaged from the missions when launched. These are inclusive of simulating high-velocity flybys, relevant to the case study for the Comet Interceptor Mission or modelling the Venusian atmosphere which can also relate to other (exo)planetary bodies. The event models are inspired from heritage missions like Rosetta, Hayabusa from and active mission like Psyche and upcoming HERA mission. By performing the observations over realistic trajectories, the approach produces results that resemble near-real phases of the missions and expected outcomes from each phase.

To validate the scenarios developed in the simulation environment, the scenes are recreated within the Tartu Observatory Space Mission Simulation Centre. The spacecraft and target body interactions are developed over a series of flybys occurring at different speeds. The target samples are representation of asteroids and comets sampled from the terrestrial domain like volcanic rock islands. Further investigations involving the study of surface morphologies and feature formations like craters and boulders are pursued.
The data collected from the simulations and the analog environments are synthesized to develop scene that represent the evet with fervor and details. The routines generate the environment map with procedural cycles, where the geometry is synthesized in the spatial and the volumetric domains. Alongside reconstructed geometry, we also obtained information about the radiance field interactions with the surface and the light sources in our experiments. Moreover, with efficient scene representation, the possibility also to advance other concept like the gravitational tractor can be expanded by efficient understanding of the various forces that govern the dynamics of potentially hazardous bodies. The author’s relevant work with the autonomous replanning and gravity mapping shows, an iteratively updating gravity model can be developed by in-orbit measurements performed by a spacecraft with efficient on-board motion planning algorithm. The information obtained paves the way to the possibilities of generating more-informed scenarios including transient orbital properties like surface activities like rubble and dust motion and the forces that govern the dynamic states like gravitational perturbations and solar radiation pressure. Work towards endogenous mapping of bodies in space, are validation of the thesis. The aspects of representing a scenario in the space domain are motivated with the idea of enhancing our knowledge about the various events that occur around us and pursue efforts in protecting Earth from catastrophic event. And by all means towards the elevation of human understanding of this vast expanse, that is space.

How to cite: Paul, A. S.: Environment Scene Representation for Dynamic Event Cognition: Towards mapping and characterizing transient events in planetary bodies, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-641, https://doi.org/10.5194/epsc2024-641, 2024.