As seções cônicas, as primeiras leis de Kepler e o paraboloide de revolução

Abstract

Neste trabalho, n´os usamos uma constru¸c˜ao menos conhecida, atrav´es de paraboloides de revolu¸c˜ao inscritos em um cone de revolu¸c˜ao, para demonstrar que as se¸c˜oes cˆonicas, nesse contexto, s˜ao as elipses e as hip´erboles. E ent˜ao, como uma aplica¸c˜ao `a Mecˆanica Celeste, descrevemos as ´orbitas keplerianas el´ıpticas e hiperb´olicas. Abstract In this work, we use a less known construction, through of paraboloids of revolution inscribed into the cone of revolution, to demonstrate that the conic sections are ellipses and hyperbolas. And then, as an application to Celestial Mechanics, we completely describe the elliptical and hyperbolic Keplerian orbits.