Conic Sections and the Kepler Problem in Classical Physics
Summary
A quick overview of our project, what it entailed and what areas it covered.
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Conic sections has been an area of study that fascinated famous Ancient Greek mathematicians such as Euclid and Archimedes around 250BC. However, the earliest surviving work dedicated to conic sections was written by Apollonius of Perga (262-190BC), also known as the Great Geometer [1]. The eight part work, aptly named ‘Conics’, covered the conic sections (ellipse, parabola and hyperbola) and showed that each conic section could be obtained through the intersection of a plane with a double-napped cone [2]. Each type of conic section comes with its own unique properties and geometric rules, which will be discussed later in the project.
- [1] - https://britannica.com/biography/Apollonius-of-Perga
- [2] - https://www.youtube.com/watch?v=rLpv0ztITpE
- [3] - https://earthobservatory.nasa.gov/features/OrbitsHistory
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Despite Apollonius’ work in the field of astronomy, it was hundreds of years later before progress was made towards the heliocentric model of the solar system, as it was developed and published by Nicolaus Copernicus in 1543 [3]. During a revolution of theories around planetary motion, after the heliocentric model was becoming accepted (despite great reluctance from the religious church and society), Johannes Kepler developed his three Laws of Planetary Motion that laid the groundwork for orbital mechanics as we know it today.
During this project, we will explore what conic sections are, how they link to orbits, and how they can be used to create simulations of orbital mechanics in the context of the Kepler Problem.
Research
Conic Sections
Conic Sections: Introduction
What are the conic sections and how are they relevant in the world of maths?
Maths of Conic Sections
The shapes formed by intersecting a conic section are analogous to the different types of orbits.
Conic Sections and Orbits
How do conic sections link to orbital mechanics, and why are they so important?
Orbital Mechanics and the Kepler Problem
Understanding the Basics of Orbits
Why do orbits occur and what sorts of gravitational interactions happen between objects in space?
The Two Body Problem
The infamous Classical Mechanics problem regarding the prediction of two planets in orbit of each other.
Kepler's Planetary Laws
Discover who Kepler was and why his contributions to orbital mechanics were so fundamental.
Simulations of Orbital Mechanics
Felix
Why do orbits occur and what sorts of gravitational interactions happen between objects in spae?
