The mass of the sun

The mass of the sun

The standard method to calculate the mass of the sun is by the formula
M = 4(3.14159265359)^2*(149597870700)^3/((6.674E-11)(365*24*60*60)^2) with a result of 1.98846548016881E+30 using the standard value of AU of 149,597,870,700 m.

But in the course of a year AU changes from 147,100,176,000 m in January
to 152,103,775,000 m in July because the orbit of the earth is not circular.
The consequence is that the mass of the sun varies by this method of calculation by 10.56% from aphelion to perihelion. It is a major systemic error.

A better method can be used instead in two steps:

First calculate GM by the formula GM = r*v^2 using the distances and velocities of nine solar planets which have been adjusted for the eccentric orbits of the nine planets. The result for GM in each instance is 1.32716E+20.

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.

The calculations of the nine planets in detail a

r(adj) v(adj) GM=r*v^2
MER 57,910,000,000 47872.33119 1.3271582700E+20
VEN 108,210,000,000 35020.92883 1.3271582700E+20
EAR 149,600,000,000 29784.85993 1.3271582700E+20
MAR 227,920,000,000 24130.71224 1.3271582700E+20
JUP 778,570,000,000 13056.07169 1.3271582700E+20
SAT 1,427,000,000,000 9643.82614 1.3271582700E+20
URA 2,871,000,000,000 6798.995639 1.3271582700E+20
NEP 4,497,100,000,000 5432.441852 1.3271582700E+20
PLU 5,913,000,000,000 4737.589411 1.3271582700E+20

Both the orbital velocities and distances from the sun have been adjusted. The differences from the standard velocities are small (from less than 1m/sec to less than 46m/sec). They a

vm(std) v(adj) diff in m
MER 47872.50 47872.331187 -0.16881330990
VEN 35021.40 35020.928829 -0.47117083178
EAR 29785.90 29784.859929 -1.04007056533
MAR 24130.90 24130.712241 -0.18775908649
JUP 13069.70 13056.071691 -13.62830894953
SAT 9672.40 9643.826140 -28.57385987890
URA 6835.20 6798.995639 -36.20436146706
NEP 5477.80 5432.441852 -45.35814816674
PLU 4749.00 4737.589411 -11.41058927037


The differences between the standard and adjusted distances are small;
they range from -0.0073 to 0.112%. They a

r(std) r(adj) diff in %
MER 57,909,175,000 57,910,000,000 0.0014246
VEN 108,208,930,000 108,210,000,000 0.0009888
EAR 149,597,890,000 149,600,000,000 0.0014104
MAR 227,936,640,000 227,920,000,000 -0.0073003
JUP 778,412,010,000 778,570,000,000 0.0202964
SAT 1,426,725,400,000 1,427,000,000,000 0.0192469
URA 2,870,972,200,000 2,871,000,000,000 0.0009683
NEP 4,498,252,900,000 4,497,100,000,000 -0.0256300
PLU 5,906,380,000,000 5,913,000,000,000 0.1120822

You should rather focus on analysis of your ideas,
as I see several misunderstadings, mistakes and errors.

1/Your understanding and usage of AU in formula is wrong.

There should be used semi major axis of Earth orbit,
that is
and M is sum of Sun and Earth mass. Note that the error
due neglegting Earth mass is lower than error of G/

2/ Relative accuracy of result cannot be by principle better
than relative accuracy of G, what is 0.000047.
Therefore result 1.98846548016881E+30 is manifestation of ignorance.

3/ You have used wrong value of Earth orbit period.

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.

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.

On Friday, February 5, 2016 at 6:26:07 PM UTC+8, Poutnik wrote:
You should rather focus on analysis of your ideas,
as I see several misunderstadings, mistakes and errors.

1/Your understanding and usage of AU in formula is wrong.

There should be used semi major axis of Earth orbit,
that is
and M is sum of Sun and Earth mass. Note that the error
due neglegting Earth mass is lower than error of G/

2/ Relative accuracy of result cannot be by principle better
than relative accuracy of G, what is 0.000047.
Therefore result 1.98846548016881E+30 is manifestation of ignorance.

3/ You have used wrong value of Earth orbit period.

I agree the standard method calculating the mass of the sun is deficient. My two step method establishes GM and G precisely. It confirms the official value of G by Codata nine times exactly using the data of 18 different values of nine planets.

Dne 06/02/2016 v 07:28 Peter Riedt napsal(a):
On Friday, February 5, 2016 at 6:26:07 PM UTC+8, Poutnik wrote:
You should rather focus on analysis of your ideas,
as I see several misunderstadings, mistakes and errors.

1/Your understanding and usage of AU in formula is wrong.

There should be used semi major axis of Earth orbit,
that is
and M is sum of Sun and Earth mass. Note that the error
due neglegting Earth mass is lower than error of G/

2/ Relative accuracy of result cannot be by principle better
than relative accuracy of G, what is 0.000047.
Therefore result 1.98846548016881E+30 is manifestation of ignorance.

3/ You have used wrong value of Earth orbit period.

I agree the standard method calculating the mass of the sun is deficient. My two step method establishes GM and G precisely.

The standard method is fine.

What is deficient is your approach to it,
turning good procedure into crap.

There is NO way
you can establish G and by consequence M precisely.

Relative error of known value of G is 4.7E-5
and therefore relative error of M calculated with G
CANNOT be better.

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.

Dne 05/02/2016 v 07:24 Peter Riedt napsal(a):
The mass of the sun

The standard method to calculate the mass of the sun is by the formula
M = 4(3.14159265359)^2*(149597870700)^3/((6.674E-11)(365*24*60*60)^2) with a result of 1.98846548016881E+30 using the standard value of AU of 149,597,870,700 m.

But in the course of a year AU changes from 147,100,176,000 m in January
to 152,103,775,000 m in July because the orbit of the earth is not circular.
The consequence is that the mass of the sun varies by this method of calculation by 10.56% from aphelion to perihelion. It is a major systemic error.

A better method can be used instead in two steps:

First calculate GM by the formula GM = r*v^2 using the distances and velocities of nine solar planets which have been adjusted for the eccentric orbits of the nine planets. The result for GM in each instance is 1.32716E+20.

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.


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.
..

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.

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

On Saturday, February 6, 2016 at 3:46:45 PM UTC+8, Poutnik wrote:
Dne 06/02/2016 v 07:28 Peter Riedt napsal(a):
On Friday, February 5, 2016 at 6:26:07 PM UTC+8, Poutnik wrote:
You should rather focus on analysis of your ideas,
as I see several misunderstadings, mistakes and errors.

1/Your understanding and usage of AU in formula is wrong.

There should be used semi major axis of Earth orbit,
that is
and M is sum of Sun and Earth mass. Note that the error
due neglegting Earth mass is lower than error of G/

2/ Relative accuracy of result cannot be by principle better
than relative accuracy of G, what is 0.000047.
Therefore result 1.98846548016881E+30 is manifestation of ignorance.

3/ You have used wrong value of Earth orbit period.

I agree the standard method calculating the mass of the sun is deficient. My two step method establishes GM and G precisely.

The standard method is fine.

What is deficient is your approach to it,
turning good procedure into crap.

There is NO way
you can establish G and by consequence M precisely.

Relative error of known value of G is 4.7E-5
and therefore relative error of M calculated with G
CANNOT be better.

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.

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

On Saturday, February 6, 2016 at 5:38:55 PM UTC+8, Poutnik wrote:
Dne 05/02/2016 v 07:24 Peter Riedt napsal(a):
The mass of the sun

The standard method to calculate the mass of the sun is by the formula
M = 4(3.14159265359)^2*(149597870700)^3/((6.674E-11)(365*24*60*60)^2) with a result of 1.98846548016881E+30 using the standard value of AU of 149,597,870,700 m.

But in the course of a year AU changes from 147,100,176,000 m in January
to 152,103,775,000 m in July because the orbit of the earth is not circular.
The consequence is that the mass of the sun varies by this method of calculation by 10.56% from aphelion to perihelion. It is a major systemic error.

A better method can be used instead in two steps:

First calculate GM by the formula GM = r*v^2 using the distances and velocities of nine solar planets which have been adjusted for the eccentric orbits of the nine planets. The result for GM in each instance is 1.32716E+20.

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.


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.
.

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.

The semi major axis = distance and period = velocity.