Problema de dois corpos na mecânica celeste - Antunes, Lucas Vinicius (Universidade Federal de São Carlos, 2021)
The objective of this work is to study celestial mechanics by retracing the mathematical foundations of Kepler's three laws, in connection with Newton's law of gravity, as to describe the planetary orbits as conic sections, ellipses, parabolas, hyperbolas. After describing the orbits in the plane. we address the two-body problem in the three dimensional space using as starting point the differential equations that describe such motion. In order to do this, we consider a suitable change of coordinates in which one of the bodies is at the origin.
The two-body problem in celestial mechanics
Keywords: leis de Kepler; lei da gravitação universal; equações diferenciais; Kepler's laws; Law of gravitation; Differential equations; CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA::FISICA MATEMATICA