Mathematics behind the elliptical orbits of planets

Mathematics behind the elliptical orbits of planets

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.

Why planets move in elliptical orbits

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What you will 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

Rating: 4.5

Level: All Levels

Duration: 3.5 hours

Instructor: Emanuele Pesaresi