trouble choosing between models — r^2 set:
0.999991869, 0.999987017, 0.999987844, 0.999989971, 0.999992955
so I’ve been looking at physical parameters to help discern
something I noticed:
mass
J / S = 189.9 / 56.846 = 3.34060444
1/(radius^2)
J / S = 0.036962337 / 0.010996863 = 3.361171098
and of course there’s the obvious one we’ve seen pointed out countless times forever:
period:
S / J = 29.447498 / 11.862615 = 2.482378295 ~= 5/2
Given the √5 coming up, notice that
(2 * 2.482378295)^(3/2) = 11.06233845
Of the models based on √5, φ, & 11.06233845 none are uniformly better. Each performs better in a certain segment of the solar system. With r^2 so high, the general pattern is nailed, but even though the residuals are small, they’re sufficiently systematic to demand more scrutinizing attention.
I’m not one to get carried away with details. I like exploring first-order aggregate structure. So I may just report all models side-by-side and leave it there for others to go explore the roots of the subtle but systematic structural nuances. I want to work out and illustrate the geometry before reporting just tables, which are by orders of magnitude inferior to illustrations on the information assimilability scale.
I’m going to rewrite this from above since it’s probably more intuitive reorganized this way:
(φ^5)^(2/3)) ~= 5
2π*5/(2√2) = 2π*5/(2^(3/2)) = 11.10720735
~= φ^5 = 11.09016994
(11.10720735)*(11.09016994) / ( (11.10720735 + 11.09016994) / 2 ) = 11.09868211
2*(11.09868211) = 22.19736421
(1/(J+S)) / (1/(V+E)) = 8.456145629 / 0.380883098 = 22.20141997
5 = 5
2 = 2
φ = 1.61803398874989
1/φ = Φ = 0.618033988749895
2φ = 3.23606797749979
1/2φ = 0.309016994374947
arccos(1/2φ) = 1.25663706143592
(5/2)*arccos(1/2φ) = 3.14159265358979
π = 3.14159265358979
2π = 6.28318530717959
2π/5 = 1.25663706143592
cos(2π/5) = 0.309016994374947
1/cos(2π/5) = 3.23606797749979
2cos(2π/5) = 0.618033988749895
1/(2cos(2π/5)) = 1.61803398874989
1/(2cos(2π/5)) = φ
(5/2)*arccos(1/2φ) = π
الفقرة السابقة
أول 
