Dne 19/02/2016 v 13:30 Peter Riedt napsal(a):
K3 revision3

By popular demand I revised the calculation of Kepler's third law constant using only data I cannot accused of to have tampered with. The data (orbital period in earth years and semi major axis in AU) was sourced from https://www.princeton.edu/~willman/planetary with the comment that all orbital characteristics are specified with respect to the Solar system's barycenter and the J2000.0 ecliptic.

opy SMA(AU) t2/r3
MER 0.240847 0.3870993 1.000
VEN 0.615197 0.7233360 1.000
EAR 1.000017 1.0000030 1.000
MAR 1.880816 1.5237100 1.000
JUP 11.862615 5.2029000 0.999
SAT 29.447498 9.5370000 1.000
URA 84.016846 19.1890000 0.999
NEP 164.791320 30.0699000 0.999
PLU 248.020800 39.4821000 0.999

Peter Riedt

Now imagine our Sun is not alone,
but is a twin binary star of the same masses
with circular orbits around common barycentre.

You will realize the simplified Kepler 3rd law
does not fit well the requirement of equality of
gravitation acceleration G.Ms/(2R)^2 , 2R = distance
and centripetal acceleration v^2/R = 4.pi^2.R

E.g. if the strar distance is 2 AU, so orbit radius is 1 AU,
the period is not 1 year, but 2 years.

Note the generalized 3rd kepler law
G.(M1+M2) = 4pi^2 . a^3/T^2 is valid for coordinate system with center
in object, not in barycenter.

By analysis of circular orbits with M1 = M2 = M,
it is
G.2M = 4pi^2 . D^3/T^2
or
G.M/4= 4pi^2 . R^3/T^2

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.