Kepler and the dwarf

Kepler’s third law A recent article from Smithsonian magazine says a new dwarf planet candidate is 46 times further from the sun as earth is, and it takes 281.1 years to orbit the sun. I did a back-of-the-envelope calculation and thought something was wrong. Kepler’s third law says T² = c a³. Here T is the orbital period and a is the semimajor axis. If T is measured in years and a is measured in astronomical units (AU) then the proportionality constant c equals 1. If T = 281.1 years, then a = 42.91 AU, not 46 AU. Eccentricity The difference between 46 AU and 42.91 AU is only a contradiction if we assume the dwarf planet is in a circular orbit. The semimajor axis a is the the maximum distance to the center of the orbit, not the distance to the sun. In an elliptical orbit, the focus of the ellipse where the sun sits is not at the center. The orbit is eccentric, meaning off-center. Assume the dwarf planet candidate ED138 iis in an orbit with semimajor axis 42.91 AU. What does the article…

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