Planet orbits have small eccentricities nearly circular which is why astronomers before Kepler thought the were exactly . If the distance decreases then speed must increase to compensate increases planet mass does not change. then you get a very simple relation planet sidereal period in years semimajor axis of its orbit . An oval shape like egg is not ellipse tapers at one end but tapered both ends Kepler had tried shapes he found they did work. An ellipse is squashed circle that can be drawn by punching two thumb tacks into some paper looping string around the stretching with pencil and moving while keeping taut

Read More →See my copyright notice for fair use practices. It is also the average distance of planet from Sun at one focus. This was another break with Pythagorean paradigm of uniform motion Kepler discovered rule planet orbits line between and Sun sweeps out equal areas times

Read More →He discovered that planetary orbits are ellipses with the Sun one focus. To account for the planets motion particularly Mars among stars Kepler found that must move around Sun variable speed. Later scientists found that this consequence of the conservation angular momentum. As the eccentricity increases Sun position is closer to one side of elliptical orbit but semimajor axis remains same

Read More →Actually the first two laws were sufficient but third was very important for Isaac Newton and used today determine masses of many different types celestial objects. See the figure below. How is the average distance between planet and Sun related to orbit period Which has shorter one with large small What semimajor axis of asteroid orbiting years Kepler third law works for any object

Read More →One planet s sidereal period another average distance from Sun . This was another break with Pythagorean paradigm of uniform motion Kepler discovered rule planet orbits line between and Sun sweeps out equal areas times. Hint using the relation that perihelion aphelion semimajor axis and little algebra you can find . Aphelion point planet orbit that is farthest from Sun. It is also the average distance of planet from Sun at one focus

Read More →The aphelion perihelion major axis. After years of failure he was finally convinced with great reluctance revolutionary idea God uses different mathematical shape than circle. His neoplatonic faith led him choose Copernicus heliocentric model over employer Kepler tried refine . The skinniness an ellipse is specified by semiminor axis. This now known as Kepler nd law

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Hint using the relation that perihelion aphelion semimajor axis and little algebra you can find . He wanted to work with the best observational data available because felt that even most elegant theories must match reality