Mathematics behind the elliptical orbits of planets

Why planets move in elliptical orbits

What you'll learn

The mathematical reason why planets move in elliptical orbits
How to prove the three Kepler's laws
The physical quantities which influence the perihelion, aphelion, eccentricity of the orbit
How to calculate the period of the orbit

Requirements

Calculus (especially: derivatives, integrals)
Not necessary, but knowledge of Lagrangian mechanics might help (it is used in just one video of the course)
Newton's laws of motion and universal law of gravitation

Description

This course shows how to mathematically prove the well-known Kepler's laws. The mathematical equations are derived and solved step-by-step. First, the two-body problem is formulated by using Newton's laws of motion and the universal law of gravitation. Then, the equations are solved, still preserving the physical intuition behind them. Besides, the conservation of the angular momentum, energy of the planet will be motivated and important parameters of the orbit such as: perihelion, aphelion, period, are explicitly written in terms of the energy, angular momentum, mass of the planet, etc., in order to show how the former are affected by the latter.

Who this course is for:

Students who want to understand why the orbit of a planet is an ellipse
Students who want to formulate and solve the problem of planetary motion through the language of mathematics