Mathematical models of the planetary system

• Grant number: 24/10717-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2024
• End date: September 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: José Antonio Salvador
• Grantee: Giovanna Lopes da Silva
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In this scientific initiation project, our focus will be on Applied Mathematics in the context of teaching and research, with an emphasis on astronomical concepts. Initially, we will explore the apparent movement of the Sun and shadows, using mathematics for the construction of a sundial, both in equatorial and horizontal assembly.Additionally, we will conduct an introductory research in General Astronomy, focusing on the movements of celestial bodies, especially planetary motion. We will address the main mathematical models of the planetary system, including the geocentric model, represented by circles and hypocycloids, and the heliocentric model of Copernicus and Kepler, represented by circles and conics.We will investigate Kepler's laws, Newton's laws, and their mathematical relationships in the study of planetary motion, with an introduction to the theory of universal gravitation. We will establish mathematical connections to enhance and universalize the fellow's knowledge in this area.These insights are fundamental as they provide the necessary foundation for further studies in Ordinary Differential Equations (ODEs) applied to Celestial Mechanics, the theme of the second part of our project focused on Applied Mathematics research, one of the main objectives of this research.This process aims to cultivate advanced research skills and the ability to generate comprehensive understanding, preparing the fellow for further studies at the postgraduate level.