I Didn't Know that; Planets and the Law of 3

Did you know how neatly the sum of the days all planets take to orbit the Sun, 196,324.8, breaks down into a function of 3 and the squaring of 2?  I used my trusty ephemeris myself to find the average orbit of the 9 planets to derive 196,324.8 ('verify all things):

In other words, divide 196,324.8 by 2 a succession of times until you arrive at 3.  

Then I used 3 and 2 raised to successive exponents to recreate the progression and imply that the true number of days it takes (because I used average orbits and my ephemeris could only calculate 1 orbit of Pluto, etc) is really 196,608.

Some memorable numbers in that harmonic (doubling/halving, as in the octave) progression from nothing to 196,608.  

Law of 3?  So where's the subordinate Law of 7?  Where's G when I need him?  [I feel a sequel coming on.]

Jim