Orbital Mechanics: The Mathematics of Elliptical Orbits

This course provides a thorough mathematical derivation of Kepler's laws, offering a clear and structured approach to proving these fundamental principles of planetary motion. The mathematical equations are carefully derived and solved step-by-step, ensuring a deep understanding of the physical concepts behind them. Initially, the two-body problem is formulated using Newton's laws of motion and the universal law of gravitation.

The equations are then systematically solved while preserving their physical intuition, making the approach both rigorous and accessible. Additionally, key conservation principles-such as angular momentum and energy-are introduced and motivated, demonstrating their significance in orbital mechanics. Important orbital parameters, including perihelion, aphelion, and orbital period, are explicitly expressed in terms of essential quantities like energy, angular momentum, and planetary mass.

This allows for a direct understanding of how changes in these physical quantities influence the characteristics of planetary orbits. The course is designed for those who want not only to learn Kepler's laws but also to grasp the deeper mathematical relationships governing celestial motion. Whether you're a student of physics, engineering, or astronomy, this course provides valuable insights into orbital mechanics, equipping learners with strong problem-solving skills and a solid theoretical foundation in classical mechanics, astrophysics, and applied mathematics.

Physical and mathematical intuition are favoured throughout the course, instead of carrying out the nitty-gritty mathematics in a blind manner.