KEPLER'S LAW OF PLANETARY MOTION
Updated: 1/9/2021
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• Hello everyone, I'm Angelo B. Duco
• Today we are going to be learning about "Kepler's law of planetary motion."
• In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits and epicycles with elliptical trajectories, and explaining how planetary velocities vary. The three laws state that:
• 1. The orbit of a planet is an ellipse with the Sun at one of the two foci.
• 2. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
• 3. The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit.
• Isaac Newton showed in 1687 that relationships like Kepler's would apply in the Solar System to a good approximation, as a consequence of his own laws of motion and law of universal gravitation.
• Johannes Kepler's laws improved the model of Copernicus. If the eccentricities of the planetary orbits are taken as zero, then Kepler basically agreed with Copernicus:
• The planetary orbit is a circle.The Sun is at the center of the orbit.The speed of the planet in the orbit is constant.
• 2. The Sun is not at the center but at a focal point of the elliptical orbit.
• The planetary orbit is not a circle, but an ellipse.
• The eccentricities of the orbits of those planets known to Copernicus and Kepler are small, so the foregoing rules give fair approximations of planetary motion, but Kepler's laws fit the observations better than does the model proposed by Copernicus. Kepler's corrections are:
• Neither the linear speed nor the angular speed of the planet in the orbit is constant, but the area speed (closely linked historically with the concept of angular momentum) is constant.