CBL - Campus del Baix Llobregat

Projecte llegit

Títol: Benchmarking celestial mechanics models for practical applications

Estudiants que han llegit aquest projecte:

Director/a: MASDEMONT SOLER, JOSEP JOAQUIM

Departament: MAT

Títol: Benchmarking celestial mechanics models for practical applications

Data inici oferta: 28-01-2025     Data finalització oferta: 28-09-2025


Estudis d'assignació del projecte:
    MU AEROSPACE S&T 21
Tipus: Individual
 
Lloc de realització: EETAC
 
Paraules clau:
RTBP, Restricted Three Body Problem, ERTBP, Hill Three Body Problem, Hill Four Body Problem, Bicircular Four Body Problem, Quasi-Bicircular Four Body Problem, comparison of the three body problem models
 
Descripció del contingut i pla d'activitats:
The objective of this project is to identify and evaluate astrodynamics and celestial mechanics models to determine which are best suited for specific scenarios and applications.

The main tasks to be carried out are summarized as follows:
1) Conduct an exhaustive bibliographic review, exploring models available in the literature.
2) Understand the development and fundamental principles of the models.
3) Implement and compare different models across a range of applications, presenting the results and conclusions.
 
Overview (resum en anglès):
The Three Body Problem is one of the fundamental challenges in celestial mechanics. Understanding the interactions of three gravitationally bound bodies is not only of theoretical interest but also highly relevant to spacecraft trajectory planning. There are numerous space missions planned for which the analysis of trajectory using three body problem models is crucial. Despite numerous approaches, a systematic comparison of commonly used Three Body Problem models remains scarce.

This thesis aims to analyse and compare nine dynamical models of the Three Body Problem with real life ephemeris model to assess which model provides the most accurate description of the dynamics around L1 and L2 libration points. The dynamical models implemented are: Restricted Three Body Problem, Elliptical Three Body Problem, Hill's Three Body Problem, Elliptical Hill's Three Body Problem, two versions of Bi-Circular Four Body Problem, two versions of Quasi Bi-Circular Body Problem and Hill's Four Body Problem. The real ephemeris model was implemented using MICE SPICE Toolkit. In order to compare the models, conversion of coordinate system functions were built and integrated with the models. The work is complemented by a software package that offers ready-to-use implementations of the models along with functions for their analysis.

The dynamical models were evaluated around the areas of interest by comparing their acceleration for 10000 sampled initial states for different starting dates with acceleration calculated using ephemeris model. These differences in acceleration were then presented using statistical methods. For areas around L1 and L2 the largest deviations were shown by the BC4BP model in Sun-Earth frame. The area around L1 was most accurately modeled by the QBCP in Earth-Moon frame, while RTBP gave the smallest errors for the area around L2.

Overall, the comparative study presents the differences of the models and their accuracy in regards of areas around libration points L1 and L2. These findings provide insights into selecting the most suitable model for given application and serves as a basis for further research in the field of model comparison.

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