MATEMÁTICA 01. Sejam r, s, t e v números inteiros positivos tais que v t s r <. Considere as seguintes relações : () () v v t s s r. I + < + () v t t s r r. II + < + () () v s t r s r. III + + < () () v t r s t r. IV + < + O número total de relações que estão corretas é: a) 0 b) 1 c) 2 d) 3 e) 4 ⇔ + < + v t r s t r v(r + t) < s(r + t) ⇔ v < s, porém não sabemos se isso é verdade. Contra-exemplo: Faça r =1, s = 3, t = 5, v = 4

This document aims to support students in the “Adaptation” class of the Space Mechanics and Control – Space Engineering and Technology post-graduate course at INPE. It has been updated and revised in recent years, so this is the second and most recent version. It introduces the orbit mechanics concepts by applying the Newton’s laws to the two-body problem and to the study of trajectories in a central force field. The Kepler’s laws are presented together with the equations of the elliptical motion. It is shown that the Kepler’s laws are derived from the gravitational force between two bodies, arising the geometrical relations of the orbital ellipse. The orbital elements in space are then studied, which allows to convert the geometric orbit representation, or keplerian elements, to space state representation. It is also presented the main coordinate system used in orbit and astronomic studies, as well as several time and date measuring systems.

Neste artigo, faço uma revisão dos métodos de resolução de problemas dinâmicos usados antes que as equações de Newton fossem descobertas, escritas na forma diferencial e fossem universalmente aceitas. Os argumentos que fundamentam essas soluções tornam inteligíveis equações, que, de outra forma, permaneceriam misteriosas e frutos de um pensamento mágico. Palavras-chave: força, lagrangiana, métodos dinâmicos. In this paper I review the methods used to solve problems in dynamics that were used before the newtonian equations were found, put in differential form, and universally accepted. The arguments on which the laws of dynamics were founded are rationale that make intelligible equations that otherwise would remain misterious and magic.