Why Do Different Bodies Follow Different Paths?

Why do different bodies follow different paths?
By Raoul Kumrai-Woodruff
Abstract
This essay will look into the world of mechanics that governs the movement of bodies in space. Along the way we will see some of the derivations of famous equations and laws from simple principles. Investigating key concepts such as Newton’s law of universal gravitation, relativity and Kepler’s 3 Laws of planetary motion we can see how Newton’s laws of motion and other key principles of A level mechanics are applied to the Laws of Astrodynamics. This essay is proof that orbital mechanics is not a wildly complex branch of mechanics but in fact it has its grounding in the core principles that shape the world we live in. We will see how not so complex ideas such as angular momentum and the conservation of momentum can be used for a derivation of Kepler's

Orbital mechanics is a fancy term for the motion of bodies in space. It was built on principles and law such as Newton’s second law and demonstrates the interlinking of theory and practical observations. This is best shown by Newton's law of universal gravitation and Kepler's three laws of planetary motion, each of which can be derived from Newton’s law of universal gravitation. The question of the essay itself is a broad question that allows lots of scope for investigation because many different factors influence the flight or motion of a body in space. However, it is still specific enough to give an answer in terms of the effect of changing the laws and rules that control bodies. The derivation of these laws was done by the author unless otherwise stated but they were helped by a few insightful comments of others. Traditional orbital mechanics is Newtonian based yet Einstein and his theories of general and special relativity are needed to correct the Newtonian