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:
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 referred to as the Arthur C. Clarke orbit, named after the famous author of 2001: A Space Odyssey, who popularized the orbit in a fictional novel in 1945. I also go over some very interesting connections surrounding Arthur C. Clarke, so buckle up!
#math #vectors #calculus #astronomy #keplerslaws
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