Kepler’s Laws of Planetary Motion

Kepler’s Laws of Planetary Motion

From mes 3Speak Podcast by Math Easy Solutions

May 30, 2026

About this episode

This episode explores Kepler's laws of planetary motion and their derivation using Newton's laws.

https://3speak.tv/watch?v=mes/c3b94a80 In this video, I go over Johannes Kepler's three laws of planetary motion and derive them using Isaac Newton's second law of motion, F = m a, and his law on universal gravitation. While observing the Danish astronomer Tycho Brahe's astronomical observations, Kepler observed recurring patterns in the data, which he formulated as three laws: A planet revolves around the sun in an elliptical orbit with the sun at one focus. The line joining the sun to a planet sweeps out equal areas in equal times. The square of the period of revolution of a planet is proportional to the cube of the length of the major axis of its orbit. Isaac Newton later realized that Kepler's laws are merely the biproduct of his 2nd law of motion and his law on universal gravitation. I use Newton’s laws to derive Kepler's laws, while making extensive use of vector functions, calculus, and the polar equation of an ellipse. Later in the video, I calculate the distance a satellite needs to be from the equator of the Earth to have a geosynchronous orbit, in which the orbit of the satellite around the Earth is in sync with Earth's rotation. This type of orbit is sometimes…

People in this episode

Host: Math Easy Solutions

Topics covered

  • planetary motion
  • Kepler's laws
  • Newton's laws
  • astronomy
  • satellite orbits

Keywords

  • Kepler's laws
  • planetary motion
  • Newton's second law
  • universal gravitation
  • geosynchronous orbit

Mentioned in this episode

Books & works: 2001: A Space Odyssey

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