How is the trajectory of a space probe designed? What are the invisible laws that govern the flight of satellites and their encounters with distant worlds? In this treatise, The author guides the reader through a logical and mathematical journey that reveals the secrets of space navigation. Starting from Newton's fundamental principles and Kepler's laws, the work explores with clarity and rigor the pillars of orbital dynamics: u2022 The basics of motion: From circular orbits to the energy analysis of bound systems. u2022 Flight technology: The operation of rocket engines, the Tsiolkovsky equation, and propellant management. u2022 Interplanetary maneuvers: The Hohmann transfer, the study of spheres of influence, and the complex geometry of Lagrange points. u2022 The Mars mission: A detailed, step-by-step analysis for planning a trip to the Red Planet. u2022 The slingshot effect: How to use the gravity of planets (Gravity Assist) to navigate the Solar System without consuming propellant. Richly illustrated and accompanied by a precise mathematical framework, Orbital Motions is an essential work for physics students, space enthusiasts, and anyone who wishes to understand orbital mechanics.