User blog comment:Sirwhiteout/Realmspace astronomy - Orbital periods and distances/@comment-4079189-20180404201013/@comment-1578002-20180404210551

The second discrepancy is that, in Kepler's Third Law, the distance that should be plugged into the equation is the semi-major axis of the orbit. In K'Thoutek's case, that distance is 1 billion miles. So, even using our adjusted parameters, K'Thoutek's period should be closer to 45 years, not 237. If we instead use its aphelion distance of 2 billion miles, we get a much better approximation.

If an orbit is circular or close to circular, this doesn't really make a difference, but in a highly elliptic orbit it is quite relevant. It looks more like a mistake than something done on purpose, unlike the different exponent.

Thanks for the Candlekeep tip! I will take a look at the archives to see if there is something there.