The mass of the sun

On Saturday, February 6, 2016 at 6:11:38 PM UTC+8, Poutnik wrote:
Dne 06/02/2016 v 05:06 Peter Riedt napsal(a):
On Friday, February 5, 2016 at 6:31:24 PM UTC+8, Poutnik wrote:
Dne pátek 5. února 2016 7:24:35 UTC+1 Peter Riedt napsal(a):

The second step is to divide GM by the gravitational constant G which was derived by Cavendish in the laboratory in 1798: M=1.327167630E+20/6.674E-11=1.9885640E+30.

While value G.M can be determined with high relative accuracy,
the relative accuracy of Sun mass calculated by dividing by G
is equal to relative accuracy of G.

Yes.

Then error propagation should be reflected in your calculations
by rounding of displayed values, as their ending digits
are of no value in physics.

If we would have a physical quantity equal 1/7,
where value 7 is known with 0.1% accuracy,
than 1/7 is not 0.142857142857... as it is in math.
but 0.14286 +/- 0.00014


--
Poutnik

Yes. Cut off extra decimal places.

Dne 07/02/2016 v 00:30 Peter Riedt napsal(a):


The relative error you quoted is for the standard method. My calculations come out nine times exactly. Nil error.

It is method independent.
Exactness of calculations has nothing to do with physics.

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.

Dne 07/02/2016 v 06:00 Peter Riedt napsal(a):
On Saturday, February 6, 2016 at 6:11:38 PM UTC+8, Poutnik wrote:

Then error propagation should be reflected in your calculations
by rounding of displayed values, as their ending digits
are of no value in physics.

If we would have a physical quantity equal 1/7,
where value 7 is known with 0.1% accuracy,
than 1/7 is not 0.142857142857... as it is in math.
but 0.14286 +/- 0.00014


Yes. Cut off extra decimal places.

You are supposed to do so,
considering errors of input data.

--

Dne 07/02/2016 v 05:59 Peter Riedt napsal(a):


Calculation of G.M is more accurate
from semi major axis and period
than from distance and velocity.

The latter ones are known with lower relative accuracies,
while the former ones already implicitly include error filtering.
.


The semi major axis = distance and period = velocity.

False.
Semi major axis is a one specia kind of distance,
that need no correction for excentricity.

Period and velocity are very different quantities.

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.

Dne 07/02/2016 v 05:59 Peter Riedt napsal(a):

The semi major axis = distance and period = velocity.

Periods are known with accuracy of many orders,
in contrary to velocities, that are changing al the time.

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.

On Sunday, February 7, 2016 at 2:13:01 PM UTC+8, Poutnik wrote:
Dne 07/02/2016 v 06:00 Peter Riedt napsal(a):
On Saturday, February 6, 2016 at 6:11:38 PM UTC+8, Poutnik wrote:

Then error propagation should be reflected in your calculations
by rounding of displayed values, as their ending digits
are of no value in physics.

If we would have a physical quantity equal 1/7,
where value 7 is known with 0.1% accuracy,
than 1/7 is not 0.142857142857... as it is in math.
but 0.14286 +/- 0.00014


Yes. Cut off extra decimal places.

You are supposed to do so,
considering errors of input data.

--

A fixed relationship exists.

Dne 07/02/2016 v 07:26 Peter Riedt napsal(a):
On Sunday, February 7, 2016 at 2:13:01 PM UTC+8, Poutnik wrote:
Dne 07/02/2016 v 06:00 Peter Riedt napsal(a):


Yes. Cut off extra decimal places.

You are supposed to do so,
considering errors of input data.

A fixed relationship exists.

A fixed relationship exists for error propagation as well. :-)

You ignore the essential fact of science,
that all measurements and constant values derived from them
have limited accuracy, some more than others.

Relative accuracy of G is one of the worst - 4.7E-5.

To get better value from astronomical orbiting data,
you need to know masses and distance and related data
with relative accuracy better than 4.7E-5,
as the errors cumulate during G calculation.

And the opposite, if G is used as multiplicator or divider,
no result can have relative accuracy better then 4.7E-5.

It does not matter how accurate the G.M is,
once you divide it by G, relative accuracy of M is 4.7E-5 at the best.

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.

On Sunday, February 7, 2016 at 3:00:01 PM UTC+8, Poutnik wrote:
Dne 07/02/2016 v 07:26 Peter Riedt napsal(a):
On Sunday, February 7, 2016 at 2:13:01 PM UTC+8, Poutnik wrote:
Dne 07/02/2016 v 06:00 Peter Riedt napsal(a):


Yes. Cut off extra decimal places.

You are supposed to do so,
considering errors of input data.

A fixed relationship exists.

A fixed relationship exists for error propagation as well. :-)

You ignore the essential fact of science,
that all measurements and constant values derived from them
have limited accuracy, some more than others.

Relative accuracy of G is one of the worst - 4.7E-5.

To get better value from astronomical orbiting data,
you need to know masses and distance and related data
with relative accuracy better than 4.7E-5,
as the errors cumulate during G calculation.

And the opposite, if G is used as multiplicator or divider,
no result can have relative accuracy better then 4.7E-5.

It does not matter how accurate the G.M is,
once you divide it by G, relative accuracy of M is 4.7E-5 at the best.

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.

The semi major axis of the nine planets given in terms of AU's and converted to km are shown in the following table which also gives the difference in % from the adjusted distances which I have used in my calculations of GM. The problem with the value of AU (149.600.000km) is its variation over the period of a year. This variation is also imported into the semi major axis of every planet and produces an additional distortion to their own eccentricities. My two step method avoids this problem. I am also quite happy about the error factor in G.

sma rkm % diff
MER 57,895,200 57,910,000 -0.025556899
VEN 108,160,800 108,210,000 -0.045467147
EAR 149,600,000 149,600,000 0
MAR 227,990,400 227,920,000 0.030888031
JUP 778,368,800 778,570,000 -0.025842249
SAT 1,426,735,200 1,427,000,000 -0.018556412
URA 2,870,973,600 2,871,000,000 -0.00091954
NEP 4,498,322,400 4,497,100,000 0.027181962
PLU 5,906,507,200 5,913,000,000 -0.109805513

Dne 07/02/2016 v 09:53 Peter Riedt napsal(a):


The semi major axis of the nine planets given in terms of AU's
and converted to km are shown in the following table which also
gives the difference in % from the adjusted distances which I
have used in my calculations of GM. The problem with the value
of AU (149.600.000km) is its variation over the period of a year.
This variation is also imported into the semi major axis of every
planet and produces an additional distortion to their own eccentricities.
My two step method avoids this problem. I am also quite
happy about the error factor in G.


AU does not vary.
AU = 149 597 870 700 m exactly, by definition.
AU (149.600.000km) is wrong number.

Earth orbit semi major axis that is very close to AU
almost does not vary either.

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.

Dne 07/02/2016 v 09:53 Peter Riedt napsal(a):


The semi major axis of the nine planets given in terms of AU's
and converted to km are shown in the following table which also
gives the difference in % from the adjusted distances which I
have used in my calculations of GM. The problem with the value
of AU (149.600.000km) is its variation over the period of a year.
This variation is also imported into the semi major axis of every
planet and produces an additional distortion to their own eccentricities.
My two step method avoids this problem. I am also quite
happy about the error factor in G.


AU does not vary.
AU = 149 597 870 700 m exactly, by definition.

Earth orbit semi major axis vary very little
and over very long time.

Definitely not during the year.

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.