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D. Dirkx

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Master thesis (2026) - R.J. Mc Intyre, D. Dirkx
The Yarkovsky effect is a non-gravitational acceleration caused by the anisotropic thermal emission of rotating asteroids. It causes orbital drift and is critical for understanding asteroid evolution and assessing planetary defence risks.

Current research relies on closed-source, proprietary software and research publications often omit precise settings and methodological details, limiting scientific transparency and independent verification of results, and causing researchers to have to repeat the time-consuming process of selecting settings from scratch.

This thesis addresses these limitations by using Tudat — the free, open-source astrodynamics toolbox developed at Delft University of Technology — to transparently document and reproduce Yarkovsky results from literature.

Orbit estimations were performed for 347 asteroids using a weighted least-squares method including estimating the transverse acceleration parameter A2. Successful Yarkovsky detections were achieved for 281 asteroids (81%). The remaining targets yielded low signal-to-noise ratios. The determined A2 values correspond well with values found in literature — they are compatible with values from ESA's NEOCC in 93.2% of cases and JPL's SBDB in 97.7% of cases. ...

Dynamical Parameter Sensitivity, Pole Estimation, and Weighting Strategy Assessment

Master thesis (2026) - A.I. Dzhurkov, D. Dirkx
This study investigates the orbit reconstruction of Triton, Neptune’s largest moon, using exclusively Earth-based astrometric observations spanning 1963 to 2025. The estimation is performed within the Tudat software framework, employing a weighted least-squares procedure to estimate Triton’s initial state and Neptune’s pole orientation parameters. The JPL NEP097 ephemeris kernel serves as the benchmark for assessing solution accuracy.

A sensitivity analysis using simulated observations identifies Neptune’s pole model parameters and gravitational zonal harmonics as the dynamical parameters to which Triton’s orbit is most sensitive. An estimation including Triton’s initial state, Neptune’s pole position, and pole libration parameters achieves sub-kilometre agreement with the NEP097 kernel, demonstrating that the implemented dynamics are sufficient to reproduce the reference ephemeris within the estimation timespan.

When applied to real astrometric data, the inclusion of pole libration parameters as estimated quantities reduces the cross-track difference with NEP097 to below 100 km over the modern observational arc (1990 to 2025), while producing formal errors that closely follow the actual solution discrepancy. The pole libration declination correction of +1.19° is found to be statistically significant at 6.3σ.

Three base and two hybrid observation weighting strategies are derived, implemented, and compared. The conventional per-file weighting scheme, believed to be standard practice in the literature, is found to produce overconfident formal errors. A proposed scaled per-file weighting strategy, which applies per-timeframe deweighting while assigning weights at the file level, produces formal errors that are consistently calibrated with the actual solution accuracy across two independent initialisations.

The principal limitations of this work are the absence of Voyager 2 data and the inability to reliably estimate the system gravitational parameters. Recommendations for future work include the incorporation of additional observation types and a formal consider parameter analysis. ...
The Planetary Radio Interferometry and Doppler Experiment (PRIDE) is one of the eleven experiments of JUICE, ESA’s mission to explore the icy moons of Jupiter. It repurposes astronomical techniques to estimate the angular coordinates (VLBI) and relative velocity of the spacecraft, characterized through an unusual type of Doppler observable.
Using observations of the 2013 Phobos flyby of Mars Express, this project
presents the first successful application of PRIDE Doppler to scientific orbit estimation, and an original approach to the characterization of uncertainties exploiting the unique characteristics of this experiment. ...
Master thesis (2026) - M.M. Revellino, D. Dirkx, Marco Micheli , Laura Faggioli, K.J. Cowan, B.C. Root
The orbital motion of long-period comets is significantly influenced by non-gravitational accelerations arising from volatile sublimation. These effects are traditionally modelled using the Marsden formulation, introduced in the early 1970s and derived from empirical laws and limited and low-precision astrometric datasets. More recent studies have demonstrated that this model frequently breaks down at large heliocentric distances and poorly represents sublimation of volatiles other than water. This thesis aims to improve the modelling of non-gravitational accelerations in cometary orbits by addressing two closely related aspects: the physical formulation of the non-gravitational acceleration and the quality of the astrometric data used in orbit determination.
We preliminarily determine a tailored approach to cometary astrometric reductions, building on the zero-aperture extrapolation method. We also highlight the importance of high quality astrometric data in the determination of non-gravitational effects, which are easily masked by data inaccuracies.
Using high-precision astrometric datasets, we propose two formulations for the non-gravitational acceleration, respectively representing sublimation of a single volatile and sublimation of multiple volatiles in a subsequent fashion. We demonstrate that the proposed formulations are effective in capturing the effects of the outgassing acceleration, and moreover allow us to retrieve physical characteristics of comets relying exclusively on their dynamical behaviour.
The results of this work highlight the critical importance of high-quality astrometric data and physically informed dynamical models for reliable comet orbit determination, contributing towards high-fidelity trajectory estimation and production of reliable observation forecasts. ...

Radiation pressure and aerodynamic forces models to increase the accuracy of Mars missions scientific results

Master thesis (2025) - N. Maistri, D. Dirkx, R. Alkahal, B.C. Root, D.M. Pool
Precise orbit determination is fundamental for extracting scientific results from planetary missions. While gravitational forces dominate spacecraft motion, non-conservative forces such as solar and planetary radiation pressure, and atmospheric drag introduce accelerations that are many orders of magnitude smaller. This thesis develops and evaluates advanced models to extract these minute signatures, with a particular focus on the Mars Reconnaissance Orbiter (MRO). A panel-based spacecraft macro-model, including self-shadowing (SSH), is implemented to compute radiation pressure and aerodynamic forces and is thoroughly compared to the cannonball model. Different gas–surface interaction models (GSIMs) and atmospheric models are compared, and their influence on orbit determination is assessed through parameter estimation using real mission data. The results show that simplified representations, such as the cannonball model, cannot fully capture the variability of non-conservative forces, whereas detailed panel methods improve consistency and reduce residuals. The study highlights the importance of accurate force modelling for planetary mission analysis and provides recommendations for future studies. ...

Application to an Asteroid Main Belt Exploration Mission

Master thesis (2025) - L. Hinueber, D. Dirkx, M. Pugliatti, W. van der Wal, S. Gehly
Traditional interplanetary orbit determination relies on Earth-based radiometric tracking, for which demand has increased in recent years and is projected to rise further in the future, resulting in oversubscribed ground station networks. Meanwhile, autonomous operations are desirable for faster response times to off-nominal events.

This work investigates the use of celestial navigation from asteroid beacon observations for the cruise phase orbit determination of an exploration mission to the main asteroid belt.
Using covariance analysis, the expected performance of celestial navigation is evaluated during the cruise phase, studied for its sensitivity to the model parameters and compared to traditional radiometric tracking. Under the high dynamical uncertainty associated with solar electric propulsion, beacon navigation yields comparable formal uncertainties to the baseline radiometric tracking setup for trajectory segments within the main asteroid belt. Beacon-augmented orbit determination could therefore potentially reduce the required tracking time, while achieving similar cruise phase performance. ...
The ESA Voyage 2050 program has identified Saturn's moon Enceladus as a primary target for
future outer Solar System missions aimed at assessing its potential habitability and internal
structure. To investigate Enceladus' interior, a novel mission concept is proposed, comprising an
orbiter tracked by surface landers. This study quantifies the attainable accuracy in the estimation of
key geophysical parameters by analyzing a range of mission architectures and design
configurations. From the derived uncertainties in selected parameters — including the tidal Love
numbers and libration amplitude — the analysis demonstrates how these observables can constrain
Enceladus' interior, assuming a three-layer structural model. The findings indicate that the proposed
mission architecture enables stringent estimates for Enceladus' geophysical parameters, thereby
yielding refined constraints of its internal properties, including the ice shell thickness, the densities of the core and subsurface ocean, the core radius, and the ice shell shear modulus. ...

Expected improvements in planetary ephemerides and asteroid mass estimations

Master thesis (2025) - L.R. Busquets, D. Dirkx, Steve Nerem
Our current knowledge of Solar System dynamics is limited by a combination of unknowns, including the masses of most asteroids and the mass loss rate and oblateness of the Sun. Highly precise Interplanetary Laser Ranging (ILR) measurements have been suggested to enable the reconstruction of subtle dynamical effects, allowing the determination of several of such unknowns. Following the mission proposal by the name of Trilogy, we simulate a triple ILR setup obtaining frequent range measurements between space-based transceivers orbiting the Earth, Mars and Venus. Simultaneous spacecraft orbit determination allows for the generation of highly accurate planet-to-planet ranges by adding constant range biases as parameters to estimate at every orbit determination arc. We find that such resulting ranges can reach millimetric precision and accuracy, assuming state-of-the-art ILR hardware, accurate spacecraft dynamical modeling and favorable geometry between the ILR links and the spacecraft orbital planes. The usage of such measurements alone in a planetary batch estimation after a five-year mission is found capable of estimating the radial positions of the three planets with millimetric true errors, whereas only a few tens among the 350 main perturbing asteroids are found to get their true and formal errors reduced by a significant amount (i.e., one order of magnitude). We make a series of recommendations for future studies, including the testing of alternative mission architectures (e.g., placing one vertex around a Main Belt asteroid instead of Venus to reach more sensitivity to the asteroid perturbations) or more complex orbit estimation methods (e.g., coupled, constrained multi-arc) to get the most information out of the inter-spacecraft laser range measurements. ...

The Galilean moons' dynamics in the JUICE-Europa Clipper era

Since Galileo Galilei’s first discovery of natural satellites orbiting around other planets, observing and reconstructing their dynamics has been at the core of our efforts to understand and characterise these distant worlds. Far from following perfect, frozen in time Keplerian orbits, the dynamics of these satellites keep evolving, with tides as driving mechanism. The dissipation of energy in natural bodies due to their visco-elastic response to tidal forcing both heats up the moons’ interiors and causes their orbits to expand or shrink, as well as to become more circular or elliptical. Refining the moons’ ephemerides (i.e., tabulated solutions of their motion as a function of time) is thus key to studying not only their present-day dynamics, but also the long-termthermal-orbital evolution of planetary systems.... ...
Master thesis (2024) - F. Dahmani, D. Dirkx
The primary motivation for this work was the lack of open-source or clearly motivated studies describing the orbit estimation of natural satellites. The capability to accurately model the trajectory of the moons of Jupiter is crucial for properly understanding the evolution of the Jovian system and, by extension, the solar system. Considering the small Jovian moons remain relatively unknown, they will be the focus of this study. The goal of this project was to develop a framework for the full estimation process, based on the Tudat software library, starting from raw astrometric observations, to be made available publicly. The first step was designing a new data processing algorithm, capable of uniformising the observational data. These measurements are reported in a wide variety of formats, with differences in time format, time scale, orientation, and observation type, amongst others. The developed software was able to produce Tudat-compatible observations with limited user interaction. These processed measurements were then analyzed and validated, first by examining the mean residuals with respect to existing ephemerides to detect remaining biases in the data, before comparing the standard deviation of these residuals to those reported in their original publication, whenever available. Secondly, the estimation framework was set up. Based on the processed astrometric observations, the orbits of three minor Jovian satellites, Himalia, Elara, and Amalthea were estimated as case studies. Each of these posed its own set of challenges, but together they yield a good representation of the full range of outer moons. The SPICE kernel ephemerides were used to evaluate the quality of these orbital solutions. Estimating Himalia’s orbit proved the easiest, as it is the minor moon that is observed the most, in combination with its relatively slow dynamics. One problem was the fact that there was a remaining unmodeled bias in the oldest, i.e. pre-1960, observations due to errors in converting from old to new frames. Removing these observations and replacing them with simulated measurements with realistic residuals both proved to reduce the difference with respect to the SPICE benchmark to within the uncertainty level of this very benchmark. This proves that the framework allows to accurately estimate the ephemerides of Himalia, although no conclusions could be drawn on the exact contribution of the old observations. Elara’s orbit is in many ways similar to that of Himalia, as they are part of the same orbital group. However, a close approach with this more massive Himalia in 1949 had a significant impact on Elara’s trajectory. Therefore, estimating Elara’s orbit is not limited to its initial state. Instead, Himalia’s gravitational parameter is determined concurrently to optimize the solution. However, even when determining this gravitational parameter, it became apparent that the current dynamical model could not perfectly capture the dynamics at the close approach, due to the limited amount of data before the event, leading to an error of several hundred km. This is still well below the residual of the observations, however. Finally, Amalthea proved to be the most difficult body to get an accurate orbital solution for. Since Amalthea is an inner moon, as opposed to the outer moons Himalia and Elara, its angular velocity is over 500 times higher. This logically makes both timing and position errors significantly more impactful. Additionally, the very limited amount of data, which is constrained to just a few campaigns of several nights, further hamper accurate orbit determination. By limiting the step size of the update in the estimated initial state between iterations to a standard deviation of 100 km by defining the a-priori covariance, a stable solution, accurate to several 100 km could be found. A preliminary investigation of the contribution of simulated spacecraft data indicated that the few available spacecraft observations of Amalthea have a large impact, which warrants further studies. Thus, through determining and analyzing the orbit of these three case studies, the quality of the developed framework is ascertained. The solutions proved to lie within the uncertainty region of the ephemerides published in SPICE. Inaccuracies in the estimated orbit could always be linked to deficiencies in the input data, thus not taking away from the quality of the framework. ...
Master thesis (2024) - J. Slimmens, D. Dirkx, A. Cervone, K.J. Cowan
With the development of space research into novel areas, new complex problems arise. The interest in solving space routing problems considering large numbers of targets has recently grown. This paper proposes a novel method to solve the optimal trajectory in such combinatorial space routing problems. This paper focuses on a global optimisation algorithm implemented to solve the problem posed in the 4th Global Trajectory Optimisation Com- petition (GTOC4). The solution is a trajectory of multiple legs, where each leg links two targets and has a specific flight time. To enable the use of the powerful mixed-integer linear problem solver software, Solving Constraint Integer Programs (SCIP), the routing problem concerned with visiting as many target bodies with a predetermined fuel and time budget is split into linear sub-problems. The Fixed Budget sub-problem selects a subset of the given set of targets. The Full Tour sub-problem orders the targets in the subset, and the Fixed Tour sub-problem optimises the flight time for every leg of the given trajectory to find the solution with the lowest total fuel consumption. Each of these sub-problems is formulated in a linear form and is solved using SCIP. The global optimisation algorithm evolves a population where every individual exists of a set of initial guesses for the time of flight values. Analysis shows that initialising this population with a mix of randomly generated individuals and individuals containing a constant value for all entries leads to the fastest convergence towards the optimal solution. In a population of 20, seeding ten individuals is found to be optimal. It is also found that the algorithm performance can be further increased by evolving individuals with infeasible solutions instead of iterating them until a feasible solution is found and eliminating the Full Tour sub-problem. These simplifications allow for an increase in the cost budget multiplier, which leads to finding better objective values without further increasing computational time. The best-performing setup, which uses a cost budget multiplier of 10, can find the optimal solution to the test problem in 100% of the runs, on average in 9 iterations, with a computation time of 5.82 seconds per evaluation. The results show that the global optimisation algorithm produces results that closely match known results for GTOC4 consistently and accurately. ...
Student report (2023) - Dominik Stiller, Dominic Dirkx
Precision orbit determination for geodetic applications requires force models even for small perturbations. Radiation from the Sun and Moon is a significant source of perturbation in lunar orbits and inadequate modeling of radiation pressure (RP) can lead to large position errors. This paper describes the short-term effect of RP on the Lunar Reconnaissance Orbiter (LRO), which has a position knowledge requirement of 50 m to 100 m in total and below 1 m radially. We compared models of varying complexity to determine the benefits and computational cost of high-accuracy RP modeling. We found that (1) the accelerations differ greatly depending on the Sun position, (2) only a paneled spacecraft model can account properly for changing orientation and geometry of LRO, and (3) a constant-albedo model is sufficient for lunar radiation, which is dominated by the thermal component. A spherical harmonics model for lunar albedo increases computational cost with little gain in the attained accuracy. If RP is neglected, the along-track position errors can be as large as 1100 m and the radial error varies periodically with an amplitude of up to 24 m, highlighting the importance of adequate force modeling to meet LRO's orbit determination requirements. ...
Master thesis (2023) - M.J.M. van Nistelrooij, D. Dirkx, Jinglang Feng
Small solar system bodies have received increasing scientific attention over the past decades. Studying their primitive origins can reveal important insights on the formation of planets, as well as the general evolution of the Solar System. Also their potential threat to life on Earth upon collision and their potential to act as stepping stones for deep space exploration make these bodies interesting to explore. Especially CubeSats, being small and lightweight, are promising candidates for such missions.
To facilitate the design of small body missions, this research investigates the non-linear effects of uncertainties in an asteroid’s environment on the orbital motion of a CubeSat. Uncertainties in the asteroid’s mass, irregular gravity field and solar radiation pressure have been studied prior. Rotational state uncertainties have not been researched, but do affect the CubeSat’s motion indirectly through the orientation of the irregular gravity field. These are therefore selected as the subject of this work. This aids in identifying orbits that are robust against these uncertainties, thereby minimizing the required fuel for trajectory corrections and maximizing the mass for science instruments or increasing the mission duration.
The study of the non-linear effects of rotational state uncertainties requires the application of non-linear uncertainty propagation methods. Non-Intrusive Polynomial Chaos was selected for its ease of implementation, promising computational efficiency and ability to provide statistical information directly. In this method, a set of samples from the uncertain domain are propagated to a desired time according to the black-box dynamics that govern the orbital motion. Subsequently, a polynomial approximation, a so-called Polynomial Chaos Expansion, is constructed for these final states as a function of the uncertain variables. This then allows for finding the final states for all possible characterisations of these uncertain variables, in a Monte Carlo like fashion, without further numerical integrations. Above that, the Polynomial Chaos Expansion terms can be used to compute statistics, such as the mean and covariance, analytically. In this work, different initial conditions are propagated and the states at various times are approximated by Polynomial
Chaos Expansions. All Polynomial Chaos Expansions were verified by comparison with Monte Carlo simulations.
A study on the settings of Non-Intrusive Polynomial Chaos was conducted. It showed that the required settings, such as polynomial order, number of samples and method of solving for the coefficients can vary significantly, depending on the studied case. In addition, limitations in the application of this method to
Kepler elements were encountered for orbits that approach the singularities in this element set. In general, the results show an increase in the trajectory dispersions and non-linearities encountered with an increase in propagation times and with a decrease in orbital altitude. However, exceptions to this
trend were encountered. In the case of a retrograde equatorial orbit, the inclination was found to reach its maximum dispersion already within 5 days and stagnates thereafter. This is a result of the accelerations exerted by the asteroid’s gravitational bulges in its equatorial plane, which varies in space along with changes in the rotation pole under these uncertainties.
A comparison to uncertainties in the asteroid’s mass revealed that the effects of rotational state uncertainties are relatively small, especially considering the small uncertainty in mass that was used. However, again an exception was encountered. The right ascension of the ascending node of a polar orbit at 5 km was found more sensitive to changes in the asteroid’s rotation pole than in its mass. Thus, depending on the objective of an analysis, mission designers could be required to include rotational state uncertainties in their analyses.
Finally, a broader study of different initial orbital geometries revealed that retrograde orbits are more stable against rotational state uncertainties. However, depending on the exact initial orbital geometry, in terms of inclination and right ascension of the ascending node, prograde orbits can be just as stable. Also
here it was found, though, that the inclination is more stable for polar orbits than for inclined and equatorial orbits.
In conclusion, the finding that retrograde orbits are more stable against rotational state uncertainties helps mission designers to select promising orbits for actual missions. As these orbits are also beneficial for geodetic parameter estimation, they both minimise the required fuel for trajectory corrections and maximise the scientific return. Nonetheless, a wide variety of non-linear effects due to rotational state uncertainties can be encountered in the asteroid’s environment. Therefore, their influence should always be checked in mission design studies, even though in general their effects are relatively small. ...
Master thesis (2023) - K.G. Zenk, D. Dirkx, M.S. Fayolle-Chambe
Owing to the assumed presence of sub-surface oceans, the Galilean satellites - Io, Europa, Ganymede, and Callisto - are among the most promising candidates for potential extraterrestrial habitats within our Solar System. To this end, the moons are going to be extensively studied by the upcoming JUICE and Europa Clipper missions. Ultimately, understanding the dynamics of the Jovian system is a means to shed light on the general existence and stability of these presumed habitable worlds as well as the formation and evolution of the entire Solar System. Yet, while the dynamics of Ganymede (in particular via the orbital phase of JUICE) and Europa (mainly via the various flybys of Europa Clipper) are going to be observed to an unprecedented level of accuracy, the absence of flybys of Io due to its harsh radiation-environment results in a significantly imbalanced data set. To stabilise the numerical data inversion, spaced-based imaging by the camera subsystem of JUICE is crucial to constrain the dynamics of Io.

However, while the analysis of orbital dynamics is usually performed with respect to the centre-of-mass (COM) of natural satellites, optical space-based astrometry provides measurements of the position of a body's centre-of-figure (COF), introducing a discrepancy between the dynamical and observational model. Explicitly accounting for the offset between the observed centre-of-figure and the propagated centre-of-mass during ephemeris estimation, however, ensures the consistency of the dynamical and observational model. In turn, this allows us to assess the extent to which optical space-based astrometric observations might either validate the merely indirectly obtained radio science data or contribute to the overall orbital solution of Io. Finally, obtaining a measure of the offset between the centre-of-figure and centre-of-mass yields an entirely new constraint on the interior structure and composition of Io.

In order to quantify the COF-COM-offset, we have simulated optical astrometric observations by JUICE and subsequently determined the formal uncertainties of the estimated offset using covariance analyses. Using suitably computed \textit{a prioir} covariance matrices, we have constrained our analyses to the averaged propagated formal errors of Io that would arise from the radiometric tracking set-up of JUICE and Europa Clipper. We have found that the contribution of optical space-based astrometry to the COF-COM-offset of Io and its estimated state highly depends on the observations' quantity, quality, and geometry. Thus, an algorithm for the selection epochs at which images are to be simulated based on the main drivers - the absolute uncertainties and relative geometries of a series of observations - of the formal errors COF-COM-offset has been developed. However, owing to the largely equatorial alignment of JUICE with respect to Io - observations of the in-plane contribution have been found to be obstructed by the brightness of Jupiter. To maximise the scientific return of optical space-based astrometry, in particular, astrometry during the high-inclination phase has proven beneficial.

Overall, significant constraints of the discrepancy between the centre-of-figure and centre-of-mass and the orbital solution of Io have been obtained. For an expectable number of about 1300~images being taken of Io, realistically attainable formal uncertainties in the estimated COF-COM-offset of no more than 300~metres have been obtained. Furthermore, since notable contributions to the orbital solution already occur for reasonable radio science true-to-formal-error ratios between two and five, we have concluded a high likelihood of space-based astrometry contributing to the orbital solution. This potential of space-based imaging to balance and contribute to the orbital solution of Io thus motivates future research concerning the offset between the centre-of-figure and centre-of-mass. ...

Reconciling the ephemeris and rotation models

Master thesis (2023) - J. Martínez Castillo, D. Dirkx
This thesis studies the dynamics of Phobos, Mars’ bigger moon, as part of the preparation for coming Phobos-bound missions. Existing observations have not been able to properly constrain the interior of the two Martian moons in general and Phobos in particular, being therefore inconclusive about their origin and formation. Thus, on-site measurements with the aid of Phobos landers is planned for the near future. In particular, this thesis focuses on the couplings between Phobos’ translational and rotational dynamics. Their effect in state propagation is quantitatively described and their impact on parameter estimation is assessed. For this, the trajectory of Phobos has been computed by propagating a given initial state in two ways. A first manner integrates Phobos’ translational and rotational equations of motion simultaneously; a second manner integrates Phobos’ translational equations of motion alone, and assumes that Phobos is in a fully-locked configuration with a once-per-orbit longitudinal libration. A first part of the results is an analysis of the differences between these two solutions, in terms of position and orientation. A second part of the solution is the analysis of least-squares estimations, by which the uncoupled model is fit to observations taken from the coupled trajectory. In doing so, the best way in which the uncoupled model can imitate the coupled model by changing some dynamical parameters is found.
The results are analyzed in terms of estimation post-fit residuals - the final differences between the coupled and uncoupled solutions - and differences between the parameter estimates and the true parameters. These parameters comprise mostly the once-per-orbit libration amplitude and the quadrupole gravity field, all of which provide information of Phobos’ interior. The outcome of this thesis is a detailed and quantitative study of the extent to which an uncoupled model can imitate a coupled model and how the differences generated by couplings are absorbed into modifications of estimated parameters to keep the two trajectories as similar as possible. This provides a preliminary approximation of the type of true errors that state-of-the-art estimations contained in their fitted solutions. ...
Master thesis (2022) - C. Fortuny Lombraña, D. Dirkx
The Planetary Radio Interferometry and Doppler Experiment (PRIDE) technique has supported the exploitation of Doppler observations of planetary landers from Earth-based stations in many radio science experiments. The precise retrieval of the estimates of the Mars rotation and Orientation Parameters (MOPs) is an important application of the PRIDE technique and is the subject of this work. The MOPs that are retrieved can be related to four motions: the polar motion, variations of the rotation rate, precession, and nutation. More precisely, the MOPs analyzed consist of a total of 30 parameters that characterizes
all the motion components, including: the core factor, the free core nutation rate, 8 spin variation parameters and 20 polar motion parameters. Properties related to the internal structure of the Red planet can be deduced from these parameters.

The aim of this work is to reduce the MOPs uncertainty and thus help identify the interplay and signatures of the different parameters, which in turn will provide a better understanding of the state and composition of the Martian inner core. In this context, it is required a thorough assessment of the benefits of combining the Doppler observations from the InSight-RISE and ExoMars-LaRa landers using an extended network of Earth-based stations, including 10 extra receive-only radio telescopes. The analysis has been conducted with Tudat astrodynamical toolkit, where a high-accuracy Mars rotation model can be adopted, in order to simulate the formal errors of the MOPs.

The results obtained can be summarized as follows. The considered two-lander geometry configuration allows a more precise retrieval of the MOPs, with a reduction of more than 92 % overall on the MOPs uncertainty compared to a single-lander configuration. The combined exploitation of the RISE and LaRa Doppler observations allows more efficient retrieval of the full set of the MOPs, and particularly, the polar motion parameters. Furthermore, the accuracy of the MOPs is additionally increased in a configuration with the 10 extra receive-only stations. The MOPs accuracy improvements observed in this case are, on average, a 12 % for the core factor, a 10 % for the free core nutation rate, about 25 % for the polar motion parameters at the Chandler frequency, a 5 % for the spin variations, and a 15 % for the other polar motion amplitudes. ...

Application to potential benefits for statistical Delta-V expenditure

Master thesis (2022) - J. Hener, D. Dirkx, M.S. Fayolle-Chambe
This thesis project investigates navigational aspects of the upcoming JUICE (JUpiter ICy moons Explorer) mission, which is expected to deliver valuable data products for the scientific study of the Jovian system, and the three Galilean moons Europa, Ganymede and Callisto in particular. One such data product comes from the 3GM radio science payload, which is expected to contribute towards more accurate ephemerides of the Galilean moons and a refined study of their gravity fields. Accurate and reliable acquisition of these data depends greatly on the successful Guidance, Navigation and Control (GNC) operations, where an efficient GNC performance can unlock excess ∆V capabilities. It is the goal of this work to identify statistical ∆V savings from integration of in-mission radio science ephemeris improvements into the GNC operations. The resulting excess ∆V could be used to effectuate one of the mission enhancement and extension options (e.g. coverage of the Jupiter’s mid-high latitudes or a lower-altitude Ganymede orbit), the enablement of which ultimately motivates this thesis project.
A navigational orbit determination (OD) framework was set up, modelled closely after the OD setup from the JUICE mission analysis team. An interface for simulating moon state knowledge updates from external ephemeris products was implemented. This setup was then extended to support a simplified statistical ∆V analysis. The external ephemeris products were modelled using an adopted high-fidelity OD setup with a coupled filter configuration, which simulates the uncertainty of in-mission ephemeris updates from the 3GM radio science data. These results were then used to simulate external ephemeris updates to the navigation OD and to evaluate their impact on the statistical ∆V expenditure.
It was found that external moon ephemerides in general, and the simulated science data based OD solu- tion in particular, are not suitable for reducing the statistical ΔV cost of post-flyby correction manoeuvres. Within one to two encounters of a given flyby body, the nominal (update-free) navigation OD has improved moon state knowledge to a point where it no longer contributes significantly to size of the correction ma- noeuvres. To generate statistical ΔV savings, the moon state knowledge must be improved for the navigation of the mission’s first encounters. It was thus concluded that moon ephemeris improvements should not be provided from JUICE science data, but from observations that have been collected prior to mission. It was furthermore found that due to its extensive coverage, the navigation tracking data captures system informa- tion that the radio science data is less sensitive to. It could therefore be considered in the post-mission efforts to improve the high-accuracy ephemerides of the Galilean moons. ...
Master thesis (2022) - Bushra Kiyani, D. Dirkx
The Ganymede Circular Orbit Phase (GCO-500) of the JUICE mission will be
the first time a moon beyond Earth’s will be orbited for an extended period of 9 months. This orbit phase, due to its close proximity, opens the window to more accurately determine the spacecraft orbit and thereby unambiguously characterize the interiors of the Galilean moons. Ganymede is believed to harbor an internal ocean and will help understand the habitability of icy worlds in the outer solar system.

In this study results of a sensitivity analysis are presented which investigate the settings of a model developed for the GCO-500 phase. The model aims to realistically emulate the JUICE mission concept, by specifically focusing on the radio science experiment 3GM, responsible for estimating the gravity field. The model also includes non-gravitational accelerations which are accounted
for by the High Accuracy Accelerometer (HAA).
...