Leonardo Saud Maia Leite: Choreography of Celestial Bodies

Abstract

People have observed and studied celestial bodies since antiquity. Babylonians, Greeks and Egyptians used these observations for making calendars to help with agricultural planning. Great names in ancient astronomy, such as Ptolemy and Hipparchus, and of modern astronomy, such as Copernicus, Tycho Brahe, Kepler and Galileo, obtained several measurements referring to the movements of the Moon and several planets with good accuracy. It is widely accepted today that the birth of Celestial Mechanics as a science takes place with the launch from the work "Principia", in 1686, by Sir Isaac Newton. In this talk, we will study the famous N-body problem. This is a problem that studies the motion of N bodies given their initial velocities and positions. We will see that only the solutions for N \leq 2 are completely known. We will learn why it is so difficult and we will study some particular cases, such as homothetic, homographic and choreographic solutions and the Lissajous curves. In particular, we will pay special attention to homographic solutions, also known as central configurations, a topic that is widely studied today and that we can find examples of this class of solutions in our own Solar System.