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#1




Kepler's 3rd revision3
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 
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#2




Kepler's 3rd revision3
Dne pátek 19. února 2016 13:30:06 UTC+1 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 And what is the new information ? 
#3




Kepler's 3rd revision3
On Friday, February 19, 2016 at 9:03:11 PM UTC+8, Poutnik wrote:
Dne pátek 19. února 2016 13:30:06 UTC+1 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 And what is the new information ? Ockham's razor. 
#4




Kepler's 3rd revision3
Dne 20/02/2016 v 01:31 Peter Riedt napsal(a):
On Friday, February 19, 2016 at 9:03:11 PM UTC+8, Poutnik wrote: Dne pátek 19. února 2016 13:30:06 UTC+1 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 And what is the new information ? Ockham's razor. I do not think so, as the table content is obvious and useless. Deviations of simplified Kepler law cause by its ignoring of influence of planet/Solar mass ratios are comparable(Jupiter) or smaller then rounding errors.  Poutnik ( the Czech word for a wanderer ) Knowledge makes great men humble, but small men arrogant. 
#5




Kepler's 3rd revision3
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. 
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