The picture showing area and time looked extreme. Do any planets have that great a difference between closest and farthest points from the Sun?
Yes, that picture of an elliptical orbit showed a rather large eccentricity. The orbits of most of our traditional planets are very nearly circular and have small eccentricies, although Mercury has an eccentricity of 0.2, and Pluto (planet or no) has an eccentricity of 0.25. (Here’s a link with a table that has eccentricities listed.) However there are plenty of solar system objects, like comets, that have extremely elliptical orbits, with eccentricities much larger than shown in the figure. Note that Kepler’s laws apply to any object object the Sun, not just planets.
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