Kepler's 3rd with adjusted periods and radii

Kepler's 3rd with adjusted periods and radii

Kepler's third law in the form t2/r3 gives a constant for solar objects such as planets and asteroids. It is a precise law but applying it with the measured values for the orbital periods in seconds for t and the measured semi major axis in metres for r produces results with small differences.

It suggests that the measured numbers for t and/or r are incorrect. However a small adjustment to the orbital periods or the semi major axis achieves an identical constant for all nine planets. The adjustments to the orbital periods are in the range of -0.065% to 0.002% and for the semi major axis from -0.003% to 0.043%.

Measured t and r
measured t measured r t2/r3
MER 7,600,752 57,909,175,000 2.9748905E-19
VEN 19,414,681 108,208,930,000 2.9748919E-19
EAR 31,558,150 149,597,890,000 2.9747831E-19
MAR 59,356,661 227,936,640,000 2.9750653E-19
JUP 374,365,908 778,412,010,000 2.9714197E-19
SAT 929,317,806 1,426,725,400,000 2.9737697E-19
URA 2,651,442,610 2,870,972,200,000 2.9708279E-19
NEP 5,200,560,940 4,498,252,900,000 2.9714524E-19
PLU 7,823,994,908 5,906,380,000,000 2.9709337E-19

Adjusted t, measured r
adjusted t measured r t2/r3
MER 7,600,552 57,909,175,000 2.974734E-19
VEN 19,414,164 108,208,930,000 2.974734E-19
EAR 31,558,202 149,597,890,000 2.974734E-19
MAR 59,353,354 227,936,640,000 2.974734E-19
JUP 374,574,616 778,412,010,000 2.974734E-19
SAT 929,468,424 1,426,725,400,000 2.974734E-19
URA 2,653,184,989 2,870,972,200,000 2.974734E-19
NEP 5,203,431,644 4,498,252,900,000 2.974734E-19
PLU 7,828,997,025 5,906,380,000,000 2.974734E-19

Measured t, adjusted r
measured t adjusted r t2/r3
MER 7,600,752 57,910,192,390 2.974734E-19
VEN 19,414,681 108,210,849,270 2.974734E-19
EAR 31,558,464 149,598,717,700 2.974734E-19
MAR 59,356,661 227,945,107,140 2.974734E-19
JUP 374,365,908 778,122,836,410 2.974734E-19
SAT 929,317,806 1,426,571,264,970 2.974734E-19
URA 2,651,442,610 2,869,715,128,020 2.974734E-19
NEP 5,200,560,940 4,496,598,308,700 2.974734E-19
PLU 7,823,994,908 5,903,863,923,800 2.974734E-19


Peter Riedt

Dne 16/02/2016 v 01:00 Peter Riedt napsal(a):



Kepler's 3rd with adjusted periods and radii

You mean tampered.

Adjusted t, measured r

...is tampering t to assure r^3/t^2 fits G.Ms.


Measured t, adjusted r

...is tampering r to assure r^3/t^2 fits G.Ms.

Such practice is not acceptable in science.

--
Poutnik ( the Czech word for a wanderer )

Peter Riedt wrote:
Kepler's 3rd with adjusted periods and radii

Kepler's third law in the form t2/r3 gives a constant for solar
objects such as planets and asteroids. It is a precise law but
applying it with the measured values for the orbital periods in
seconds for t and the measured semi major axis in metres for r
produces results with small differences.

Kepler's third law, in a more general form, involves the SUM of the masses
of the two bodies:

(M1+M2)P^2 = a^3 (using units of solar masses, years, and AUs)

Hence for more massive planets like Jupiter you have to take this into
account (Jupiter's mass is around 1/1000 of the Sun's mass). Just fiddling
with numbers is not correct, and inadequate!


It suggests that the measured numbers for t and/or r are incorrect.
However a small adjustment to the orbital periods or the semi major
axis achieves an identical constant for all nine planets. The
adjustments to the orbital periods are in the range of -0.065% to
0.002% and for the semi major axis from -0.003% to 0.043%.

Measured t and r
measured t measured r t2/r3
MER 7,600,752 57,909,175,000 2.9748905E-19
VEN 19,414,681 108,208,930,000 2.9748919E-19
EAR 31,558,150 149,597,890,000 2.9747831E-19
MAR 59,356,661 227,936,640,000 2.9750653E-19
JUP 374,365,908 778,412,010,000 2.9714197E-19
SAT 929,317,806 1,426,725,400,000 2.9737697E-19
URA 2,651,442,610 2,870,972,200,000 2.9708279E-19
NEP 5,200,560,940 4,498,252,900,000 2.9714524E-19
PLU 7,823,994,908 5,906,380,000,000 2.9709337E-19

Adjusted t, measured r
adjusted t measured r t2/r3
MER 7,600,552 57,909,175,000 2.974734E-19
VEN 19,414,164 108,208,930,000 2.974734E-19
EAR 31,558,202 149,597,890,000 2.974734E-19
MAR 59,353,354 227,936,640,000 2.974734E-19
JUP 374,574,616 778,412,010,000 2.974734E-19
SAT 929,468,424 1,426,725,400,000 2.974734E-19
URA 2,653,184,989 2,870,972,200,000 2.974734E-19
NEP 5,203,431,644 4,498,252,900,000 2.974734E-19
PLU 7,828,997,025 5,906,380,000,000 2.974734E-19

Measured t, adjusted r
measured t adjusted r t2/r3
MER 7,600,752 57,910,192,390 2.974734E-19
VEN 19,414,681 108,210,849,270 2.974734E-19
EAR 31,558,464 149,598,717,700 2.974734E-19
MAR 59,356,661 227,945,107,140 2.974734E-19
JUP 374,365,908 778,122,836,410 2.974734E-19
SAT 929,317,806 1,426,571,264,970 2.974734E-19
URA 2,651,442,610 2,869,715,128,020 2.974734E-19
NEP 5,200,560,940 4,496,598,308,700 2.974734E-19
PLU 7,823,994,908 5,903,863,923,800 2.974734E-19


Peter Riedt

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

On Tuesday, February 16, 2016 at 4:03:53 PM UTC+8, Mike Dworetsky wrote:
Peter Riedt wrote:
Kepler's 3rd with adjusted periods and radii

Kepler's third law in the form t2/r3 gives a constant for solar
objects such as planets and asteroids. It is a precise law but
applying it with the measured values for the orbital periods in
seconds for t and the measured semi major axis in metres for r
produces results with small differences.

Kepler's third law, in a more general form, involves the SUM of the masses
of the two bodies:

(M1+M2)P^2 = a^3 (using units of solar masses, years, and AUs)

Hence for more massive planets like Jupiter you have to take this into
account (Jupiter's mass is around 1/1000 of the Sun's mass). Just fiddling
with numbers is not correct, and inadequate!


I have used your formula (M1+M2)P^2 = a^3 and got the following results. Can you explain where I used the wrong data or arithmetic?

P M1 M2
MER 0.2408467000 1.988550E+30 3.302200E+23
VEN 0.6151972600 1.988550E+30 4.868500E+24
EAR 1.0000000000 1.988550E+30 5.973600E+24
MAR 1.8808476000 1.988550E+30 6.418500E+23
JUP 11.8626150000 1.988550E+30 1.898600E+27
SAT 29.4474980000 1.988550E+30 5.684600E+26
URA 84.0168460000 1.988550E+30 8.681000E+25
NEP 164.7913200000 1.988550E+30 1.024300E+26
PLU 247.9206500000 1.988550E+30 1.250000E+22

(M1+M2)P^2 AU AU^3
MER 1.9885503.E+30 3.8709893.E-01 5.8005064.E-02
VEN 1.9885549.E+30 7.2333199.E-01 3.7845393.E-01
EAR 1.9885560.E+30 1.0000001.E+00 1.0000003.E+00
MAR 1.9885506.E+30 1.5236623.E+00 3.5372534.E+00
JUP 1.9904486.E+30 5.2033630.E+00 1.4088098.E+02
SAT 1.9891185.E+30 9.5370703.E+00 8.6745101.E+02
URA 1.9886368.E+30 1.9191264.E+01 7.0682310.E+03
NEP 1.9886524.E+30 3.0068963.E+01 2.7186630.E+04
PLU 1.9885500.E+30 3.9482000.E+01 6.1545660.E+04

Dne úterý 16. února 2016 14:22:00 UTC+1 Peter Riedt napsal(a):
On Tuesday, February 16, 2016 at 4:03:53 PM UTC+8, Mike Dworetsky wrote:
Peter Riedt wrote:
Kepler's 3rd with adjusted periods and radii

Kepler's third law in the form t2/r3 gives a constant for solar
objects such as planets and asteroids. It is a precise law but
applying it with the measured values for the orbital periods in
seconds for t and the measured semi major axis in metres for r
produces results with small differences.

Kepler's third law, in a more general form, involves the SUM of the masses
of the two bodies:

(M1+M2)P^2 = a^3 (using units of solar masses, years, and AUs)

Hence for more massive planets like Jupiter you have to take this into
account (Jupiter's mass is around 1/1000 of the Sun's mass). Just fiddling
with numbers is not correct, and inadequate!


I have used your formula (M1+M2)P^2 = a^3 and got the following results.. Can you explain where I used the wrong data or arithmetic?

- Missing gravitational constant and 4.pi^2 factor.
G.(M1+M2). P^2 = 4.pi^2 . a^3

- Missing either conversion to meters and seconds,
either conversion of the gravitational constant for AUs and years.

- Persistent ignoring of rules of processing inaccurate data.

On Wednesday, February 17, 2016 at 1:17:00 AM UTC+8, Poutnik wrote:
Dne úterý 16. února 2016 14:22:00 UTC+1 Peter Riedt napsal(a):
On Tuesday, February 16, 2016 at 4:03:53 PM UTC+8, Mike Dworetsky wrote:
Peter Riedt wrote:
Kepler's 3rd with adjusted periods and radii

Kepler's third law in the form t2/r3 gives a constant for solar
objects such as planets and asteroids. It is a precise law but
applying it with the measured values for the orbital periods in
seconds for t and the measured semi major axis in metres for r
produces results with small differences.

Kepler's third law, in a more general form, involves the SUM of the masses
of the two bodies:

(M1+M2)P^2 = a^3 (using units of solar masses, years, and AUs)

Hence for more massive planets like Jupiter you have to take this into
account (Jupiter's mass is around 1/1000 of the Sun's mass). Just fiddling
with numbers is not correct, and inadequate!


I have used your formula (M1+M2)P^2 = a^3 and got the following results. Can you explain where I used the wrong data or arithmetic?

- Missing gravitational constant and 4.pi^2 factor.
G.(M1+M2). P^2 = 4.pi^2 . a^3

- Missing either conversion to meters and seconds,
either conversion of the gravitational constant for AUs and years.

- Persistent ignoring of rules of processing inaccurate data.

The formula was posted by Mike. Read his post in this thread.

On 16/02/2016 13:21, Peter Riedt wrote:
On Tuesday, February 16, 2016 at 4:03:53 PM UTC+8, Mike Dworetsky wrote:
Peter Riedt wrote:
Kepler's 3rd with adjusted periods and radii

Kepler's third law in the form t2/r3 gives a constant for solar
objects such as planets and asteroids. It is a precise law but
applying it with the measured values for the orbital periods in
seconds for t and the measured semi major axis in metres for r
produces results with small differences.

Kepler's third law, in a more general form, involves the SUM of the masses
of the two bodies:

(M1+M2)P^2 = a^3 (using units of solar masses, years, and AUs)

*UNITS!!!* ^^^^^^^^^^^^

Hence for more massive planets like Jupiter you have to take this into
account (Jupiter's mass is around 1/1000 of the Sun's mass). Just fiddling
with numbers is not correct, and inadequate!


I have used your formula (M1+M2)P^2 = a^3 and got the following results. Can you explain where I used the wrong data or arithmetic?

P M1 M2
MER 0.2408467000 1.988550E+30 3.302200E+23
VEN 0.6151972600 1.988550E+30 4.868500E+24
EAR 1.0000000000 1.988550E+30 5.973600E+24
MAR 1.8808476000 1.988550E+30 6.418500E+23
JUP 11.8626150000 1.988550E+30 1.898600E+27
SAT 29.4474980000 1.988550E+30 5.684600E+26
URA 84.0168460000 1.988550E+30 8.681000E+25
NEP 164.7913200000 1.988550E+30 1.024300E+26
PLU 247.9206500000 1.988550E+30 1.250000E+22

(M1+M2)P^2 AU AU^3
MER 1.9885503.E+30 3.8709893.E-01 5.8005064.E-02
VEN 1.9885549.E+30 7.2333199.E-01 3.7845393.E-01
EAR 1.9885560.E+30 1.0000001.E+00 1.0000003.E+00
MAR 1.9885506.E+30 1.5236623.E+00 3.5372534.E+00
JUP 1.9904486.E+30 5.2033630.E+00 1.4088098.E+02
SAT 1.9891185.E+30 9.5370703.E+00 8.6745101.E+02
URA 1.9886368.E+30 1.9191264.E+01 7.0682310.E+03
NEP 1.9886524.E+30 3.0068963.E+01 2.7186630.E+04
PLU 1.9885500.E+30 3.9482000.E+01 6.1545660.E+04

Using the correct units where Msun = 1.0

P M1 M2
MER 0.2408467 1.00E+00 1.66E-07 0.058007143
VEN 0.61519726 1.00E+00 2.45E-06 0.378468595
EAR 1.0000000 1.00E+00 3.00E-06 1.000003004
MAR 1.8808476 1.00E+00 3.23E-07 3.537588836
JUP 11.862615 1.00E+00 9.55E-04 140.8559909
SAT 29.447498 1.00E+00 2.86E-04 867.4030291
URA 84.016846 1.00E+00 4.37E-05 7059.138564
NEP 164.79132 1.00E+00 5.15E-05 27157.57796
PLU 247.92065 1.00E+00 6.29E-09 61464.64908

And ratios

Ratio
MER 0.999964168
VEN 0.999961251
EAR 0.999997296
MAR 0.999905179
JUP 1.000177409
SAT 1.000055316
URA 1.001288038
NEP 1.001069758
PLU 1.001318008

Seems like a systematic drift high with increasing orbital period.

How precisely are the orbital periods of the outer planets known
experimentally?

--
Regards,
Martin Brown

Dne 16/02/2016 v 19:36 Peter Riedt napsal(a):
On Wednesday, February 17, 2016 at 1:17:00 AM UTC+8, Poutnik wrote:
Dne úterý 16. února 2016 14:22:00 UTC+1 Peter Riedt napsal(a):
On Tuesday, February 16, 2016 at 4:03:53 PM UTC+8, Mike Dworetsky wrote:
Peter Riedt wrote:
Kepler's 3rd with adjusted periods and radii

Kepler's third law in the form t2/r3 gives a constant for solar
objects such as planets and asteroids. It is a precise law but
applying it with the measured values for the orbital periods in
seconds for t and the measured semi major axis in metres for r
produces results with small differences.

Kepler's third law, in a more general form, involves the SUM of the masses
of the two bodies:

(M1+M2)P^2 = a^3 (using units of solar masses, years, and AUs)

Hence for more massive planets like Jupiter you have to take this into
account (Jupiter's mass is around 1/1000 of the Sun's mass). Just fiddling
with numbers is not correct, and inadequate!


I have used your formula (M1+M2)P^2 = a^3 and got the following results. Can you explain where I used the wrong data or arithmetic?

- Missing gravitational constant and 4.pi^2 factor.
G.(M1+M2). P^2 = 4.pi^2 . a^3

- Missing either conversion to meters and seconds,
either conversion of the gravitational constant for AUs and years.

- Persistent ignoring of rules of processing inaccurate data.

The formula was posted by Mike. Read his post in this thread.

I am aware of it very well.


--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.

On Wednesday, February 17, 2016 at 5:20:28 AM UTC+8, Poutnik wrote:
Dne 16/02/2016 v 19:36 Peter Riedt napsal(a):
On Wednesday, February 17, 2016 at 1:17:00 AM UTC+8, Poutnik wrote:
Dne úterý 16. února 2016 14:22:00 UTC+1 Peter Riedt napsal(a):
On Tuesday, February 16, 2016 at 4:03:53 PM UTC+8, Mike Dworetsky wrote:
Peter Riedt wrote:
Kepler's 3rd with adjusted periods and radii

Kepler's third law in the form t2/r3 gives a constant for solar
objects such as planets and asteroids. It is a precise law but
applying it with the measured values for the orbital periods in
seconds for t and the measured semi major axis in metres for r
produces results with small differences.

Kepler's third law, in a more general form, involves the SUM of the masses
of the two bodies:

(M1+M2)P^2 = a^3 (using units of solar masses, years, and AUs)

Hence for more massive planets like Jupiter you have to take this into
account (Jupiter's mass is around 1/1000 of the Sun's mass). Just fiddling
with numbers is not correct, and inadequate!


I have used your formula (M1+M2)P^2 = a^3 and got the following results. Can you explain where I used the wrong data or arithmetic?

- Missing gravitational constant and 4.pi^2 factor.
G.(M1+M2). P^2 = 4.pi^2 . a^3

- Missing either conversion to meters and seconds,
either conversion of the gravitational constant for AUs and years.

- Persistent ignoring of rules of processing inaccurate data.

The formula was posted by Mike. Read his post in this thread.

I am aware of it very well.


--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.

Your formula is incomplete just as Mike's. The correct formula should be
G*(M1+M2)P^2 = 4pi^2*r^3/tsec^2. P is in AU and r in m.

Dne 17/02/2016 v 04:27 Peter Riedt napsal(a):


- Missing gravitational constant and 4.pi^2 factor.
G.(M1+M2). P^2 = 4.pi^2 . a^3



Your formula is incomplete just as Mike's. The correct formula should be
G*(M1+M2)P^2 = 4pi^2*r^3/tsec^2. P is in AU and r in m.


Dimensional analysis of equation I provided fits.
Dimensional analysis of equation you provided
is wrong by factor s^-2 .


[G] = [N . m^2 . kg^-2] = [kg . m . s^-2 . m^2 . kg^-2]
= [s^-2 . m^3 . kg^-1]

[G.(M1+M2). P^2] = [s^-2 . m^3 . kg^-1 . kg . s^2] = [m^3]

[4.pi^2 . a^3 ] = [m^3]

[m^3] = [m^3]

--
Poutnik ( the Czech word for a wanderer )

Knowledge makes great men humble, but small men arrogant.