## Tesi etd-06132016-102601 |

Thesis type

Tesi di dottorato di ricerca

Author

SERRA, DANIELE

URN

etd-06132016-102601

Title

Satellite Geodesy of other planets

Settore scientifico disciplinare

MAT/07

Corso di studi

MATEMATICA

Supervisors

**tutor**Prof. Milani Comparetti, Andrea

**commissario**Prof. Tortora, Paolo

**commissario**Dott. Locatelli, Ugo

Parole chiave

- jupiter
- juno
- planetary science
- radio science
- orbit determination

Data inizio appello

09/07/2016;

Consultabilità

Parziale

Data di rilascio

09/07/2019

Riassunto analitico

This thesis is divided in two parts. In the first part we focus on the numerical simulations of the Radio Science Experiment of the mission Juno in jovicentric orbit. The second part deals with the analysis of real data of the cruise-stage of the mission Juno and the assessment of the numerical error introduced by the orbit determination software developed for the analysis of such data.

Chapter 1 contains a brief summary of the previous space missions to Jupiter as well as a detailed description of the Juno mission, its objectives, and a specific focus on the Gravity Science experiment and the design of the orbit of Juno when at Jupiter.

Chapter 2 deals with the mathematical formulation of Orbit Determination and describes the algorithms necessary to process the data obtained during a RSE. Moreover, it contains a presentation of the ORBIT14 Orbit Determination software developed at the Department of Mathematics of the University of Pisa, which has been used to perform the simulations presented in this work.

The results of the simulations regarding the gravity field of Jupiter are described in Chapter 3. Here, we start introducing a semi-analytical method to predict the uncertainties of the spherical harmonics coefficients of the gravity field of a planet, valid in general for any spacecraft orbiting a celestial body. Then, we cope with the results of the simulations for the spherical harmonics coefficients of Jupiter. Finally, since the observations of the planet will be confined to a latitude band in the north hemisphere of the planet, we introduce a local model for the gravity field of Jupiter, based on ring shaped mascons. This chapter also deals with the determination of Jupiter's Love numbers, measuring the tidal response of the planet to the attraction of its natural satellites and the Sun.

In Chapter 4 we tackle the determination of Jupiter's pole of rotation and the magnitude of its angular momentum, the latter particularly important because it is strictly connected to Jupiter's normalized polar moment of inertia, fundamental for the determination of the interior structure of the planet. The joint discussion is due to the fact that we found high correlation between the parameters related to these physical quantities, mirroring the fact that their effects on the motion of the spacecraft are indistinguishable. We propose a possible solution and hint at an alternative method for determining Jupiter's moment of inertia.

The second part deals with the analysis of real data from the Juno spacecraft. Although the scientific content of these data is rather poor because they have been obtained during the cruise phase, when the relative position of the Earth-Sun-spacecraft would not allow a Solar Conjunction Experiment, the reasons for such an analysis are at least two. Firstly, it was a chance to assess the performance of the telecommunication system onboard and test the quality of the data. The second motive is more relevant for the scope of this thesis and is the validation of the ORBIT14 software and the assessment of the numerical noise introduced therein.

We will show that the software is in good condition and well-performing, the numerical error being negligible.

Chapter 1 contains a brief summary of the previous space missions to Jupiter as well as a detailed description of the Juno mission, its objectives, and a specific focus on the Gravity Science experiment and the design of the orbit of Juno when at Jupiter.

Chapter 2 deals with the mathematical formulation of Orbit Determination and describes the algorithms necessary to process the data obtained during a RSE. Moreover, it contains a presentation of the ORBIT14 Orbit Determination software developed at the Department of Mathematics of the University of Pisa, which has been used to perform the simulations presented in this work.

The results of the simulations regarding the gravity field of Jupiter are described in Chapter 3. Here, we start introducing a semi-analytical method to predict the uncertainties of the spherical harmonics coefficients of the gravity field of a planet, valid in general for any spacecraft orbiting a celestial body. Then, we cope with the results of the simulations for the spherical harmonics coefficients of Jupiter. Finally, since the observations of the planet will be confined to a latitude band in the north hemisphere of the planet, we introduce a local model for the gravity field of Jupiter, based on ring shaped mascons. This chapter also deals with the determination of Jupiter's Love numbers, measuring the tidal response of the planet to the attraction of its natural satellites and the Sun.

In Chapter 4 we tackle the determination of Jupiter's pole of rotation and the magnitude of its angular momentum, the latter particularly important because it is strictly connected to Jupiter's normalized polar moment of inertia, fundamental for the determination of the interior structure of the planet. The joint discussion is due to the fact that we found high correlation between the parameters related to these physical quantities, mirroring the fact that their effects on the motion of the spacecraft are indistinguishable. We propose a possible solution and hint at an alternative method for determining Jupiter's moment of inertia.

The second part deals with the analysis of real data from the Juno spacecraft. Although the scientific content of these data is rather poor because they have been obtained during the cruise phase, when the relative position of the Earth-Sun-spacecraft would not allow a Solar Conjunction Experiment, the reasons for such an analysis are at least two. Firstly, it was a chance to assess the performance of the telecommunication system onboard and test the quality of the data. The second motive is more relevant for the scope of this thesis and is the validation of the ORBIT14 software and the assessment of the numerical noise introduced therein.

We will show that the software is in good condition and well-performing, the numerical error being negligible.

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