Introduction to dynamical astronomy

• Grant number: 09/15022-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2010
• End date: December 31, 2010
• Field of knowledge: Physical Sciences and Mathematics - Astronomy - Positional Astronomy and Celestial Mechanics
• Principal Investigator: Masayoshi Tsuchida
• Grantee: André Amarante Luiz
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

Abstract

The first studies to search in Dynamical Astronomy are the two-body problem and its generalization, the N-body problem. This scientific initialization project is based on these problems. The two-body problem will be studied in the whole, initially introducing the central force problem and showing the conservation of angular momentum and total energy. In sequence the gravitational force is considered to study the different types of orbits and the position of the body on these orbits. The motion relatively to the center of mass and the relative motion also will be studied. During the study of two-body problem the mathematical proof of Kepler's laws will be presented. The formulation of the N-body problem will be obtained in the Cartesian coordinates, and the first integrals and perturbation function analyzed. A very important particular case is N = 3, that is, the three-body problem. The studies of conservation of energy and angular momentum, as well as the relative motion and stationary solutions will be developed for this problem. Finally some numerical simulations will be performed to have a good insight about the theoretical concepts.