The present work seeks to expose an introductory study regarding the description of the
movement of a particle attracted to a fixed point, developed in Celestial Mechanics. Looking
for the best progress of the work, initially concepts of Calculus and Analytic Geometry
are fixed, followed by the formulation of the problema, as a Newton Ordinary Differential
Equation. Moreover, starting from the Newton’s Gravitation Law, there are established the
three Kepler’s Laws, resulting also in the constants generated by conservation of energy,
conservation of momentum, and excentricity. Furthermore, with the development of the
work, relations between the constants will be verified, exposing how its values determine
the orbit of a particle. Finally, techniques are introduced for determining the position
on the orbit of the particle in a given instant of time, based on the initial values of its
position and velocity vectors.
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