Univ. Cote d’Azur (Nice)
Prof. A. Fienga,
Prof. A. Mémin

Space mission 2: The Radio Science Experiment: from BEPI-COLOMBO to JUICE
(S3, elective, 6 ECTS) – offered from A.Y. 2024/2025
Learning Outcomes:Radio science experiments are very common in solar system exploration. They are involved into major discoveries like the existence of oceans under the crust of icy satellites and effective tests of fundamental physics. In this lecture, we will consider the case of two major European missions for which radio science experiments have an important role: the MORE experiment on board the Bepi-Colombo mission and the 3GM experiment for the JUICE mission. Bepi-Colombo is an ESA large mission of exploration of Mercury. Its main goal is the characterization of its internal structure together with the tests of general relativity (GRT). The Juice mission is also an ESA large mission of exploration of the main satellites of Jupiter. Its main goal is the characterization of the ocean under the surface of Ganymede, the largest Jupiter satellite. In this lecture, we will firstly see how radio science experiment can be a very efficient tool for testing general relativity at the close vicinity of the Sun but also for exploring the internal structures of the Jovian satellites, the formation of this tiny solar system and its evolution.
Knowledge and Understanding:
The students will perform numerical simulations based on simplified versions of numerical codes used for computing probe and planetary orbits in GRT as well as tidal deformations of planetary bodies. The students test the impact on radio-science measurements induced by different theories of gravity or different internal structures of the bodies. After getting familiar with the code in C/python/fortran language, the students will implement different theories of gravity (such as MOND) or internal structure (such as with or without subcrustal ocean, with water or with ammoniac). In a second step, by comparisons with the mission specifications, they will see what models could be rules out by the radio science experiments and which one would not be.
Applying Knowledge and Understanding:The course aims at introducing methods and concepts related to the modern challenges of fundamental physics and planetology in the solar system with the help of radio experiments.
PrerequisitesYou must be familiar with basic mechanics and of course previous knowledge about space dynamics will be of some help.
ProgramThe theoretical lecture will introduce concepts related to i) the navigation of probe in the solar system ii) GRT framework iii) tidal deformations and rheology. The lecture will constitute one third of the module. The second third of the module will be constituted by supervised implementation of the probe orbit computation and radio-science data simulation in the context of GRT and tidal deformations. Finally, on the last part of the module, two different applications of the lecture can be proposed in the context of a small project to be done during the module. It will be the choice of the student to select which one he/she wants to do. i) The first option is to work on GRT and alternative theory simulations with Bepi-Colombo. After first bibliographic research, the student will choose an alternative theory to implement using numerical codes such as REBOUND (in C or python). An integration of the orbits of the probe and of the light path will be considered. An evaluation of the impact of the theory on the probe motion and consequently on the radio science experiment will be done with a covariance analysis of the results. ii) the second option is to work on the internal structure of bodies with the context of the JUICE. After first bibliographic research, the student will identify possible scenario for the internal structure of Ganymede. The student will estimate the influence of the Jupiter tides on the Ganymede gravity field in using the software ALMA for several possible internal structures. He/she will implement the modified Ganymede gravity field in the REBOUND software to estimate the impact on the JUICE orbit as seen from Earth. With the radio science experiment published accuracy, it will then be possible to assess the potential detectability of some internal structure hypothesis by considering covariance analysis on the Love numbers.

Description of how the course is conductedThe course will be shared in three parts. The first weeks the basics of orbital dynamics including GRT framework and tidal deformations will be introduced. Then, in a second step, the student will code probe orbit computation in GRT framework and for tidal deformation under supervision. In a third part, they choose a project: either Bepi-Colombo with fundamental physics tests and the implementation of alternative theories or JUICE with modelization of tidal deformations based on different Ganymede interiors. Both projects involve studying the impact of GRT or tidal deformations on the s/c orbit as seen from the Earth through radio science experiments.
Description of the didactic methodsPowerPoints, published papers and code development
Description of the evaluation methodsThe evaluation will be done firstly by the results obtained by the simulations and an oral presentation where he/she will introduce a publication of his/her choice stressing the interest for the topic and its innovative aspects.
Adopted TextbooksThe lecture will make an intensive use of the living reviews in relativity (https://www.springer.com/journal/41114) Bertotti et al. Physics of the solar system (https://link.springer.com/book/10.1007/978-94-010-0233-2) Tapley et al.: Statistical orbit determination Dermott and Murray: Solar system dynamics
Recommended readingsBepi-Colombo mission overview: http://www.esa.int/Our_Activities/Space_Science/BepiColombo_overview2 Testing GR with the Bepi-Colombo mission : http://inspirehep.net/record/601561/citations?ln=en Juice mission overview : http://sci.esa.int/juice/49837-juice-assessment-study-report-yellow-book/ http://es.ucsc.edu/~fnimmo/website/Tobie_Titan.pdf