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Kepler's 3rd revision3



 
 
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  #1  
Old February 19th 16, 12:30 PM posted to sci.astro
Peter Riedt
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Posts: 83
Default 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  
Old February 19th 16, 01:03 PM posted to sci.astro
Poutnik[_5_]
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Posts: 68
Default 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  
Old February 20th 16, 12:31 AM posted to sci.astro
Peter Riedt
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Posts: 83
Default 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  
Old February 20th 16, 08:57 AM posted to sci.astro
Poutnik[_5_]
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Posts: 68
Default 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  
Old February 20th 16, 09:39 AM posted to sci.astro
Poutnik[_5_]
external usenet poster
 
Posts: 68
Default 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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