Determination of the Gravity Field of Titan

Determination of the Gravity Field of Titan: Simulated Measurements and Estimation Prospects with Cassini Tracking Data

Mateo Aguaron, Alfonso (TU Delft Aerospace Engineering)

van der Wal, W. (mentor)

Delft University of Technology

Aerospace Engineering

2022-10-03

During its thirteen-year long mission in the Saturnian system, the Cassini spacecraft routinely used Titan, Saturn’s largest moon, for performing its gravity assists. The problem of determining the gravity field of Titan by performing a precise fit of Cassini’s orbit to the available Doppler tracking data was reviewed in this study. The knowledge of the gravity field of Titan can be used to constrain the moon’s internal structure and composition, providing clues about its formation process and the properties of an internal ocean (Grasset et al., 2000). Previous solutions obtained by Durante et al. (2019) and van Noort (2021) were respectively found to have inconsistencies regarding the reported small uncertainties given the noise level of the Doppler measurements and the estimation of an unfeasible negative value for the second-degree Love number k₂. It was demonstrated in the present work that this last parameter should be estimable. Here, the data from the ten Titan flybys considered in those studies was analysed and emulated by using a relativistic model for Doppler measurements in search of ways of improving the accuracy of the gravity field solution. Both the GEODYN (McCarthy et al., 2015) software from NASA GSFC and Tudat libraries (see appendices in Dirkx et al., 2019) developed by the Astrodynamics and Space Missions department at TU Delft were used to investigate the nature of this gravity determination problem and compare the results against the previous solutions. A model mismatch in Doppler in the order of 10² mHz was found between the estimation setups with GEODYN and Tudat. In the search for the source of the mismodelling, it was tested that the empirical accelerations, measurement biases, measurement timing and the spherical harmonics of Saturn have a great influence on the solution and residuals. Thus, they should be reviewed with care for future estimation efforts. It was proven that the flyby geometry is not favourable for resolving the dipole field spherical harmonics coefficients, especially J₂, C₂₂ and k₂, which reveal information about the tidal interactions from Saturn on Titan. They were found to be highly correlated and, when simulating equivalent noises to those found in the previous research, presented similar uncertainties to those obtained by van Noort (2021), but large in relation to the ones determined in Durante et al. (2019). Nevertheless, there are some prospects of estimating the dipole coefficients without the need of adding constraints on the solution, although the search for well grounded constraints is recommended and necessary when pursuing a more accurate solution. The power of fully simulated gravity field estimations as a means for addressing the quality of the available real data and verifying models and constrains, has been manifested throughout this study.

Gravity
Orbit Determination
Outer moons
Titan
Saturn
Cassini
Doppler tracking

http://resolver.tudelft.nl/uuid:3ed48ebc-6a86-4542-8daa-7061ef5a706c

Student theses

master thesis

© 2022 Alfonso Mateo Aguaron