Here ya go:

Consider a distant observer traveling at 0.867c ( 𝛾 = 2 ) relative to the solar system along the line that is co-linear with the sun's axis of rotation. After taking relativistic doppler into account, the distant observer measures the earth's orbital period around the sun to be 730.5 days according to his own wristwatch, which is in perfect accordance with relativistic time dilation.

But the observer also measures the major and minor axes of the earth's orbit to be identical to its major and minor axes in the solar system's rest frame, where the orbital period is only 365.25 days.

So it appears as if Kepler's 3rd law of planetary motion is only valid in the rest frame of the solar system. Kepler's third law does not survive in it cardinal form

R^3/T^2 = K

when transformed into any other inertial frame of reference other than the rest frame of the planetary system. This is a blatant violation of the sacrosanctity of the first postulate.

Can Kepler's third law be made frame invariant, thereby saving relativity from the ash heap of scientific history? The answer is a resounding and categorical NO! A formal proof of this is constructed below:

To a first approximation Kepler's third law of planetary motion states

𝑅^3/𝑇^2 = 𝐾

where 𝐾 has the numerical value 7.5𝑥10−6 when the orbital period 𝑇 is measured in 𝑑𝑎𝑦𝑠 and the semi-major axis of the orbit 𝑅 is measured in astronomical units 𝐴𝑈.

The earth's orbital period in the solar system's rest frame is

𝑇 = 365𝑑𝑎𝑦𝑠

The Lorentz time dilation for the earth's orbital period between the solar system's rest frame and all other inertial frames is

𝑇' = ( 365𝑑𝑎𝑦𝑠/𝛾 )

The semi-major axis (and the semi-minor axis) of the earth's orbit is identical for all inertial frames where the observer's velocity vector is collinear with the sun's axis of rotation

𝑅′ = 𝑅 = 1𝐴𝑈

Therefore the imputed frame-invariant relativistic version of Kepler's third law when the observer's velocity vector is collinear with the sun's axis of rotation is

1𝐴𝑈^3/( 365𝑑𝑎𝑦𝑠/𝛾)^2 = 7.5×10−6𝐴𝑈^3/𝑑𝑎𝑦𝑠^2

From this if follows that

133333𝑑𝑎𝑦𝑠^2 = ( 365𝑑𝑎𝑦𝑠/𝛾 )^2

365𝑑𝑎𝑦𝑠 = 365𝑑𝑎𝑦𝑠/𝛾

or

365𝑑𝑎𝑦𝑠 − sqrt[ 1 - v^2/c^2 ]365𝑑𝑎𝑦𝑠 = 0

The last equation is only valid in the rest frame of the solar system where the relative velocity is identically zero, v ≡ 0. The equation is invalid in all other inertial frames which is a clear violation of the first postulate of special relativity.

Quod Erat Demonstrandum

On Saturday, January 6, 2024 at 12:21:56 AM UTC-8, patdolan wrote:
> Here ya go:
>
> Consider a distant observer traveling at 0.867c ( 𝛾 = 2 ) relative to the solar system along the line that is co-linear with the sun's axis of rotation. After taking relativistic doppler into account, the distant observer measures the earth's orbital period around the sun to be 730.5 days according to his own wristwatch, which is in perfect accordance with relativistic time dilation.
>
> But the observer also measures the major and minor axes of the earth's orbit to be identical to its major and minor axes in the solar system's rest frame, where the orbital period is only 365.25 days.
>
> So it appears as if Kepler's 3rd law of planetary motion is only valid in the rest frame of the solar system. Kepler's third law does not survive in it cardinal form
>
> R^3/T^2 = K
>
> when transformed into any other inertial frame of reference other than the rest frame of the planetary system. This is a blatant violation of the sacrosanctity of the first postulate.
>
> Can Kepler's third law be made frame invariant, thereby saving relativity from the ash heap of scientific history? The answer is a resounding and categorical NO! A formal proof of this is constructed below:
>
> To a first approximation Kepler's third law of planetary motion states
>
> 𝑅^3/𝑇^2 = 𝐾
>
> where 𝐾 has the numerical value 7.5𝑥10−6 when the orbital period 𝑇 is measured in 𝑑𝑎𝑦𝑠 and the semi-major axis of the orbit 𝑅 is measured in astronomical units 𝐴𝑈.
>
> The earth's orbital period in the solar system's rest frame is
>
> 𝑇 = 365𝑑𝑎𝑦𝑠
>
> The Lorentz time dilation for the earth's orbital period between the solar system's rest frame and all other inertial frames is
>
> 𝑇' = ( 365𝑑𝑎𝑦𝑠/𝛾 )
>
> The semi-major axis (and the semi-minor axis) of the earth's orbit is identical for all inertial frames where the observer's velocity vector is collinear with the sun's axis of rotation
>
> 𝑅′ = 𝑅 = 1𝐴𝑈
>
> Therefore the imputed frame-invariant relativistic version of Kepler's third law when the observer's velocity vector is collinear with the sun's axis of rotation is
>
> 1𝐴𝑈^3/( 365𝑑𝑎𝑦𝑠/𝛾)^2 = 7.5×10−6𝐴𝑈^3/𝑑𝑎𝑦𝑠^2
>
> From this if follows that
>
> 133333𝑑𝑎𝑦𝑠^2 = ( 365𝑑𝑎𝑦𝑠/𝛾 )^2
>
> 365𝑑𝑎𝑦𝑠 = 365𝑑𝑎𝑦𝑠/𝛾
>
> or
>
> 365𝑑𝑎𝑦𝑠 − sqrt[ 1 - v^2/c^2 ]365𝑑𝑎𝑦𝑠 = 0
>
> The last equation is only valid in the rest frame of the solar system where the relative velocity is identically zero, v ≡ 0. The equation is invalid in all other inertial frames which is a clear violation of the first postulate of special relativity.
>
> Quod Erat Demonstrandum

I the last remaining days of this forum, I am interested in, and do hereby formally request Legion's response to this airtight proof against special relativity which demonstrates the violation of THE CORE POSTULATE, indeed the very postulate from which the principle of relativity gets its name.

Legion, where have you gone? Please come back for one last, glorious battle. You too Bodkin, wherever you are. Damed ol' Dirk is a lost cause. But at least Dirk lived long enough to see the fall of the empire he serves so loyally since his 10th year of life.

On Saturday, January 6, 2024 at 12:21:56 AM UTC-8, patdolan wrote:
> Here ya go:
>
> Consider a distant observer traveling at 0.867c ( 𝛾 = 2 ) relative to the solar system along the line that is co-linear with the sun's axis of rotation. After taking relativistic doppler into account, the distant observer measures the earth's orbital period around the sun to be 730.5 days according to his own wristwatch, which is in perfect accordance with relativistic time dilation.
>
> But the observer also measures the major and minor axes of the earth's orbit to be identical to its major and minor axes in the solar system's rest frame, where the orbital period is only 365.25 days.
>
> So it appears as if Kepler's 3rd law of planetary motion is only valid in the rest frame of the solar system. Kepler's third law does not survive in it cardinal form
>
> R^3/T^2 = K
>
> when transformed into any other inertial frame of reference other than the rest frame of the planetary system. This is a blatant violation of the sacrosanctity of the first postulate.
>
> Can Kepler's third law be made frame invariant, thereby saving relativity from the ash heap of scientific history? The answer is a resounding and categorical NO! A formal proof of this is constructed below:
>
> To a first approximation Kepler's third law of planetary motion states
>
> 𝑅^3/𝑇^2 = 𝐾
>
> where 𝐾 has the numerical value 7.5𝑥10−6 when the orbital period 𝑇 is measured in 𝑑𝑎𝑦𝑠 and the semi-major axis of the orbit 𝑅 is measured in astronomical units 𝐴𝑈.
>
> The earth's orbital period in the solar system's rest frame is
>
> 𝑇 = 365𝑑𝑎𝑦𝑠
>
> The Lorentz time dilation for the earth's orbital period between the solar system's rest frame and all other inertial frames is
>
> 𝑇' = ( 365𝑑𝑎𝑦𝑠/𝛾 )
>
> The semi-major axis (and the semi-minor axis) of the earth's orbit is identical for all inertial frames where the observer's velocity vector is collinear with the sun's axis of rotation
>
> 𝑅′ = 𝑅 = 1𝐴𝑈
>
> Therefore the imputed frame-invariant relativistic version of Kepler's third law when the observer's velocity vector is collinear with the sun's axis of rotation is
>
> 1𝐴𝑈^3/( 365𝑑𝑎𝑦𝑠/𝛾)^2 = 7.5×10−6𝐴𝑈^3/𝑑𝑎𝑦𝑠^2
>
> From this if follows that
>
> 133333𝑑𝑎𝑦𝑠^2 = ( 365𝑑𝑎𝑦𝑠/𝛾 )^2
>
> 365𝑑𝑎𝑦𝑠 = 365𝑑𝑎𝑦𝑠/𝛾
>
> or
>
> 365𝑑𝑎𝑦𝑠 − sqrt[ 1 - v^2/c^2 ]365𝑑𝑎𝑦𝑠 = 0
>
> The last equation is only valid in the rest frame of the solar system where the relative velocity is identically zero, v ≡ 0. The equation is invalid in all other inertial frames which is a clear violation of the first postulate of special relativity.
>
> Quod Erat Demonstrandum

In the last remaining days of this forum, I am interested in, and do hereby formally request Legion's response to this airtight proof against special relativity which demonstrates the violation of THE CORE POSTULATE, indeed the very postulate from which the theory of relativity gets its name.

Legion, where have you gone? Please come back for one last, glorious battle.. You too Bodkin, wherever you are. Damed ol' Dirk is a lost cause. But at least Dirk lived long enough to see the fall of the empire he served so loyally since his 10th year of life.

On Saturday, January 6, 2024 at 12:21:56 AM UTC-8, patdolan wrote:
> Here ya go:
>
> Consider a distant observer traveling at 0.867c ( 𝛾 = 2 ) relative to the solar system along the line that is co-linear with the sun's axis of rotation. After taking relativistic doppler into account, the distant observer measures the earth's orbital period around the sun to be 730.5 days according to his own wristwatch, which is in perfect accordance with relativistic time dilation.
>
> But the observer also measures the major and minor axes of the earth's orbit to be identical to its major and minor axes in the solar system's rest frame, where the orbital period is only 365.25 days.
>
> So it appears as if Kepler's 3rd law of planetary motion is only valid in the rest frame of the solar system. Kepler's third law does not survive in it cardinal form
>
> R^3/T^2 = K
>
> when transformed into any other inertial frame of reference other than the rest frame of the planetary system. This is a blatant violation of the sacrosanctity of the first postulate.
>
> Can Kepler's third law be made frame invariant, thereby saving relativity from the ash heap of scientific history? The answer is a resounding and categorical NO! A formal proof of this is constructed below:
>
> To a first approximation Kepler's third law of planetary motion states
>
> 𝑅^3/𝑇^2 = 𝐾
>
> where 𝐾 has the numerical value 7.5𝑥10−6 when the orbital period 𝑇 is measured in 𝑑𝑎𝑦𝑠 and the semi-major axis of the orbit 𝑅 is measured in astronomical units 𝐴𝑈.
>
> The earth's orbital period in the solar system's rest frame is
>
> 𝑇 = 365𝑑𝑎𝑦𝑠
>
> The Lorentz time dilation for the earth's orbital period between the solar system's rest frame and all other inertial frames is
>
> 𝑇' = ( 365𝑑𝑎𝑦𝑠/𝛾 )
>
> The semi-major axis (and the semi-minor axis) of the earth's orbit is identical for all inertial frames where the observer's velocity vector is collinear with the sun's axis of rotation
>
> 𝑅′ = 𝑅 = 1𝐴𝑈
>
> Therefore the imputed frame-invariant relativistic version of Kepler's third law when the observer's velocity vector is collinear with the sun's axis of rotation is
>
> 1𝐴𝑈^3/( 365𝑑𝑎𝑦𝑠/𝛾)^2 = 7.5×10−6𝐴𝑈^3/𝑑𝑎𝑦𝑠^2
>
> From this if follows that
>
> 133333𝑑𝑎𝑦𝑠^2 = ( 365𝑑𝑎𝑦𝑠/𝛾 )^2
>
> 365𝑑𝑎𝑦𝑠 = 365𝑑𝑎𝑦𝑠/𝛾
>
> or
>
> 365𝑑𝑎𝑦𝑠 − sqrt[ 1 - v^2/c^2 ]365𝑑𝑎𝑦𝑠 = 0
>
> The last equation is only valid in the rest frame of the solar system where the relative velocity is identically zero, v ≡ 0. The equation is invalid in all other inertial frames which is a clear violation of the first postulate of special relativity.
>
> Quod Erat Demonstrandum

( ( ( ( crickets again ) ) ) )

Yep, the KP is a tough paradox to even approach, let alone argue against, if you are a relativists. That's because there are no tensors hanging about.. In the case of the BBP a relativist could at least argue, though not calculate, that the Riemann tensor did its tensorey thing and some how allowed the earth to remain aloft even at half the necessary speed. But there are no such tensor to be found in the Kepler paradox. The KP is pure SR.

Bench warmers like Volroney, Gary Harnagel and Muttons are fond of screaming "Frame Jumping!" at this point. But another term for frame jumping is Lorentz transforming. Those clocks REALLY DO run slower, chumps. That earth REALLY DOES orbit slower too--it just happens to be traveling at the same time it is orbiting from many points of view. So when you three clowns cry frame jumping, I respond with my cry of claim jumping. You three stooges are claiming something Einstein never claimed. If all the LTs did was let us calculate what the "real" situation is in the rest frame then what's the point of the theory of relativity in the first place? Galilean relativity does that. SR states in the plainest terms that the same laws (or canonical forms of them) operative in the rest frame are also operative at high velocity. That is the principle of relativity. And that principle has been demolished by the Kepler Paradox. Hell, the damned thing is sooooo simple that there is not enough algebra for even Sylvia to sink her teeth in. The KP is much purer reasoning than the BBP. But the BBP is far more eye-catching because it is far more dramatic. I'm not sure which I will choose to put on my tomb stone. I don't have room for both, with all my other achievements.

On Sunday, January 7, 2024 at 7:45:21 PM UTC-8, patdolan wrote:
> On Saturday, January 6, 2024 at 12:21:56 AM UTC-8, patdolan wrote:
> > Here ya go:
> >
> > Consider a distant observer traveling at 0.867c ( 𝛾 = 2 ) relative to the solar system along the line that is co-linear with the sun's axis of rotation. After taking relativistic doppler into account, the distant observer measures the earth's orbital period around the sun to be 730.5 days according to his own wristwatch, which is in perfect accordance with relativistic time dilation.
> >
> > But the observer also measures the major and minor axes of the earth's orbit to be identical to its major and minor axes in the solar system's rest frame, where the orbital period is only 365.25 days.
> >
> > So it appears as if Kepler's 3rd law of planetary motion is only valid in the rest frame of the solar system. Kepler's third law does not survive in it cardinal form
> >
> > R^3/T^2 = K
> >
> > when transformed into any other inertial frame of reference other than the rest frame of the planetary system. This is a blatant violation of the sacrosanctity of the first postulate.
> >
> > Can Kepler's third law be made frame invariant, thereby saving relativity from the ash heap of scientific history? The answer is a resounding and categorical NO! A formal proof of this is constructed below:
> >
> > To a first approximation Kepler's third law of planetary motion states
> >
> > 𝑅^3/𝑇^2 = 𝐾
> >
> > where 𝐾 has the numerical value 7.5𝑥10−6 when the orbital period 𝑇 is measured in 𝑑𝑎𝑦𝑠 and the semi-major axis of the orbit 𝑅 is measured in astronomical units 𝐴𝑈.
> >
> > The earth's orbital period in the solar system's rest frame is
> >
> > 𝑇 = 365𝑑𝑎𝑦𝑠
> >
> > The Lorentz time dilation for the earth's orbital period between the solar system's rest frame and all other inertial frames is
> >
> > 𝑇' = ( 365𝑑𝑎𝑦𝑠/𝛾 )
> >
> > The semi-major axis (and the semi-minor axis) of the earth's orbit is identical for all inertial frames where the observer's velocity vector is collinear with the sun's axis of rotation
> >
> > 𝑅′ = 𝑅 = 1𝐴𝑈
> >
> > Therefore the imputed frame-invariant relativistic version of Kepler's third law when the observer's velocity vector is collinear with the sun's axis of rotation is
> >
> > 1𝐴𝑈^3/( 365𝑑𝑎𝑦𝑠/𝛾)^2 = 7.5×10−6𝐴𝑈^3/𝑑𝑎𝑦𝑠^2
> >
> > From this if follows that
> >
> > 133333𝑑𝑎𝑦𝑠^2 = ( 365𝑑𝑎𝑦𝑠/𝛾 )^2
> >
> > 365𝑑𝑎𝑦𝑠 = 365𝑑𝑎𝑦𝑠/𝛾
> >
> > or
> >
> > 365𝑑𝑎𝑦𝑠 − sqrt[ 1 - v^2/c^2 ]365𝑑𝑎𝑦𝑠 = 0
> >
> > The last equation is only valid in the rest frame of the solar system where the relative velocity is identically zero, v ≡ 0. The equation is invalid in all other inertial frames which is a clear violation of the first postulate of special relativity.
> >
> > Quod Erat Demonstrandum
> ( ( ( ( crickets again ) ) ) )
>
> Yep, the KP is a tough paradox to even approach, let alone argue against, if you are a relativists. That's because there are no tensors hanging about. In the case of the BBP a relativist could at least argue, though not calculate, that the Riemann tensor did its tensorey thing and some how allowed the earth to remain aloft even at half the necessary speed. But there are no such tensor to be found in the Kepler paradox. The KP is pure SR.
>
> Bench warmers like Volroney, Gary Harnagel and Muttons are fond of screaming "Frame Jumping!" at this point. But another term for frame jumping is Lorentz transforming. Those clocks REALLY DO run slower, chumps. That earth REALLY DOES orbit slower too--it just happens to be traveling at the same time it is orbiting from many points of view. So when you three clowns cry frame jumping, I respond with my cry of claim jumping. You three stooges are claiming something Einstein never claimed. If all the LTs did was let us calculate what the "real" situation is in the rest frame then what's the point of the theory of relativity in the first place? Galilean relativity does that. SR states in the plainest terms that the same laws (or canonical forms of them) operative in the rest frame are also operative at high velocity.. That is the principle of relativity. And that principle has been demolished by the Kepler Paradox. Hell, the damned thing is sooooo simple that there is not enough algebra for even Sylvia to sink her teeth in. The KP is much purer reasoning than the BBP. But the BBP is far more eye-catching because it is far more dramatic. I'm not sure which I will choose to put on my tomb stone. I don't have room for both, with all my other achievements.

If nobody here will tackle Kepler's Paradox then let's look at what others have said on other platforms. Here's the highest rated answer to Kepler's Paradox on physics.stackexchange:

"No. It just means that Kepler’s laws are not actually laws of physics. Instead, they are approximations to the laws of physics in the non-relativistic limit"

Incredible. These relativistic-woke maniacs, at the drop of a hat, stripped Kepler's laws of their legitimacy as a true laws of nature and relegated them to mere non-relativistic approximations of some more correct, yet unknown version of Kepler's Laws. They threw in the towel for Kepler and ruled it a TKO victory for me! I wrote the following response which was cancelled within 10 minutes:

"Does anyone else share my opinion that the first answer is circular reasoning? The first answer tacitly accepts that Kepler's third law of planetary motion falsifies the principle of relativity because it is demonstrated to be valid only in the rest frame of the solar system. But because of this demonstration the conclusion is reached that Kepler's Laws can't be laws anymore. Instead, they are relegated to the status of non-relativistic approximations of other, as yet unknown relativistic laws--laws which presumably will not falsify the principle of relativity. In lieu of these new laws of planetary motion are we not justified in remaining convinced that Kepler's third law has indeed falsified the principle of relativity?"

On Monday, January 8, 2024 at 9:30:19 PM UTC-8, patdolan wrote:
> On Sunday, January 7, 2024 at 7:45:21 PM UTC-8, patdolan wrote:
> > On Saturday, January 6, 2024 at 12:21:56 AM UTC-8, patdolan wrote:
> > > Here ya go:
> > >
> > > Consider a distant observer traveling at 0.867c ( 𝛾 = 2 ) relative to the solar system along the line that is co-linear with the sun's axis of rotation. After taking relativistic doppler into account, the distant observer measures the earth's orbital period around the sun to be 730.5 days according to his own wristwatch, which is in perfect accordance with relativistic time dilation.
> > >
> > > But the observer also measures the major and minor axes of the earth's orbit to be identical to its major and minor axes in the solar system's rest frame, where the orbital period is only 365.25 days.
> > >
> > > So it appears as if Kepler's 3rd law of planetary motion is only valid in the rest frame of the solar system. Kepler's third law does not survive in it cardinal form
> > >
> > > R^3/T^2 = K
> > >
> > > when transformed into any other inertial frame of reference other than the rest frame of the planetary system. This is a blatant violation of the sacrosanctity of the first postulate.
> > >
> > > Can Kepler's third law be made frame invariant, thereby saving relativity from the ash heap of scientific history? The answer is a resounding and categorical NO! A formal proof of this is constructed below:
> > >
> > > To a first approximation Kepler's third law of planetary motion states
> > >
> > > 𝑅^3/𝑇^2 = 𝐾
> > >
> > > where 𝐾 has the numerical value 7.5𝑥10−6 when the orbital period 𝑇 is measured in 𝑑𝑎𝑦𝑠 and the semi-major axis of the orbit 𝑅 is measured in astronomical units 𝐴𝑈.
> > >
> > > The earth's orbital period in the solar system's rest frame is
> > >
> > > 𝑇 = 365𝑑𝑎𝑦𝑠
> > >
> > > The Lorentz time dilation for the earth's orbital period between the solar system's rest frame and all other inertial frames is
> > >
> > > 𝑇' = ( 365𝑑𝑎𝑦𝑠/𝛾 )
> > >
> > > The semi-major axis (and the semi-minor axis) of the earth's orbit is identical for all inertial frames where the observer's velocity vector is collinear with the sun's axis of rotation
> > >
> > > 𝑅′ = 𝑅 = 1𝐴𝑈
> > >
> > > Therefore the imputed frame-invariant relativistic version of Kepler's third law when the observer's velocity vector is collinear with the sun's axis of rotation is
> > >
> > > 1𝐴𝑈^3/( 365𝑑𝑎𝑦𝑠/𝛾)^2 = 7.5×10−6𝐴𝑈^3/𝑑𝑎𝑦𝑠^2
> > >
> > > From this if follows that
> > >
> > > 133333𝑑𝑎𝑦𝑠^2 = ( 365𝑑𝑎𝑦𝑠/𝛾 )^2
> > >
> > > 365𝑑𝑎𝑦𝑠 = 365𝑑𝑎𝑦𝑠/𝛾
> > >
> > > or
> > >
> > > 365𝑑𝑎𝑦𝑠 − sqrt[ 1 - v^2/c^2 ]365𝑑𝑎𝑦𝑠 = 0
> > >
> > > The last equation is only valid in the rest frame of the solar system where the relative velocity is identically zero, v ≡ 0. The equation is invalid in all other inertial frames which is a clear violation of the first postulate of special relativity.
> > >
> > > Quod Erat Demonstrandum
> > ( ( ( ( crickets again ) ) ) )
> >
> > Yep, the KP is a tough paradox to even approach, let alone argue against, if you are a relativists. That's because there are no tensors hanging about. In the case of the BBP a relativist could at least argue, though not calculate, that the Riemann tensor did its tensorey thing and some how allowed the earth to remain aloft even at half the necessary speed. But there are no such tensor to be found in the Kepler paradox. The KP is pure SR.
> >
> > Bench warmers like Volroney, Gary Harnagel and Muttons are fond of screaming "Frame Jumping!" at this point. But another term for frame jumping is Lorentz transforming. Those clocks REALLY DO run slower, chumps. That earth REALLY DOES orbit slower too--it just happens to be traveling at the same time it is orbiting from many points of view. So when you three clowns cry frame jumping, I respond with my cry of claim jumping. You three stooges are claiming something Einstein never claimed. If all the LTs did was let us calculate what the "real" situation is in the rest frame then what's the point of the theory of relativity in the first place? Galilean relativity does that. SR states in the plainest terms that the same laws (or canonical forms of them) operative in the rest frame are also operative at high velocity. That is the principle of relativity. And that principle has been demolished by the Kepler Paradox. Hell, the damned thing is sooooo simple that there is not enough algebra for even Sylvia to sink her teeth in. The KP is much purer reasoning than the BBP. But the BBP is far more eye-catching because it is far more dramatic. I'm not sure which I will choose to put on my tomb stone. I don't have room for both, with all my other achievements.
> If nobody here will tackle Kepler's Paradox then let's look at what others have said on other platforms. Here's the highest rated answer to Kepler's Paradox on physics.stackexchange:
>
> "No. It just means that Kepler’s laws are not actually laws of physics. Instead, they are approximations to the laws of physics in the non-relativistic limit"
>
> Incredible. These relativistic-woke maniacs, at the drop of a hat, stripped Kepler's laws of their legitimacy as a true laws of nature and relegated them to mere non-relativistic approximations of some more correct, yet unknown version of Kepler's Laws. They threw in the towel for Kepler and ruled it a TKO victory for me! I wrote the following response which was cancelled within 10 minutes:
>
> "Does anyone else share my opinion that the first answer is circular reasoning? The first answer tacitly accepts that Kepler's third law of planetary motion falsifies the principle of relativity because it is demonstrated to be valid only in the rest frame of the solar system. But because of this demonstration the conclusion is reached that Kepler's Laws can't be laws anymore. Instead, they are relegated to the status of non-relativistic approximations of other, as yet unknown relativistic laws--laws which presumably will not falsify the principle of relativity. In lieu of these new laws of planetary motion are we not justified in remaining convinced that Kepler's third law has indeed falsified the principle of relativity?"

Tom Roberts, Sylvia, Legion, Jan(s), Gary Harnagel, Prokary, Pyth, Dirk, how can you let the Kepler paradox go un-opposed? Because it leaves you with a horrendous choice:

Either 1) Kepler's third law of planetary motion is not a law of physics

or

2) the principle of relativity is falsified.

[I just happened to see this.]

On 1/12/24 12:10 PM, patdolan wrote:
> Tom Roberts, Sylvia, Legion, Jan(s), Gary Harnagel, Prokary, Pyth,
> Dirk, how can you let the Kepler paradox go un-opposed?

You have posted hundreds of times around here without ever saying
anything correct or valid. All you ever do is display your personal
misconceptions about various aspects of physics.

I have no expectation of anything else from this.

> Because it leaves you with a horrendous choice: Either 1) Kepler's
> third law of planetary motion is not a law of physics or 2) the
> principle of relativity is falsified.

That's easy: Kepler's laws (all of them) are quite clearly not laws of
physics, they are at best approximations. Indeed, in a purely Newtonian
universe (which ours is not), they are exact only for a very massive sun
and A SINGLE PLANET [#]. In the universe we inhabit, they are CLEARLY
just approximations.

[#] Unlike Kepler's original formulation, one must use the
sun+planet barycenter, not the sun, as the origin.

But I doubt that you understand this, and I doubt even more that your
"Kepler paradox" comes anywhere close to being useful.

Hint: the principle of relativity is also an approximation.

Once again you merely display your personal misunderstanding and lack of
knowledge of very basic physics. You have proven many times that you are
completely ineducable, so I generally ignore you.

Tom Roberts

On Friday, January 12, 2024 at 3:18:21 PM UTC-8, Tom Roberts wrote:
> [I just happened to see this.]
> On 1/12/24 12:10 PM, patdolan wrote:
> > Tom Roberts, Sylvia, Legion, Jan(s), Gary Harnagel, Prokary, Pyth,
> > Dirk, how can you let the Kepler paradox go un-opposed?
> You have posted hundreds of times around here without ever saying
> anything correct or valid. All you ever do is display your personal
> misconceptions about various aspects of physics.
>
> I have no expectation of anything else from this.
> > Because it leaves you with a horrendous choice: Either 1) Kepler's
> > third law of planetary motion is not a law of physics or 2) the
> > principle of relativity is falsified.
> That's easy: Kepler's laws (all of them) are quite clearly not laws of
> physics, they are at best approximations.

Then tell this forum, Tom Roberts, what are the laws of planetary motion that Einstein promised us which are true in all inertial frames of reference? Show them to us.

Indeed, in a purely Newtonian
> universe (which ours is not), they are exact only for a very massive sun
> and A SINGLE PLANET [#]. In the universe we inhabit, they are CLEARLY
> just approximations.
>
> [#] Unlike Kepler's original formulation, one must use the
> sun+planet barycenter, not the sun, as the origin.
>
> But I doubt that you understand this, and I doubt even more that your
> "Kepler paradox" comes anywhere close to being useful.
>
> Hint: the principle of relativity is also an approximation.
>
> Once again you merely display your personal misunderstanding and lack of
> knowledge of very basic physics. You have proven many times that you are
> completely ineducable, so I generally ignore you.
>
> Tom Roberts

On Friday, January 12, 2024 at 6:11:35 PM UTC-8, patdolan wrote:
> On Friday, January 12, 2024 at 3:18:21 PM UTC-8, Tom Roberts wrote:
> > [I just happened to see this.]
> > On 1/12/24 12:10 PM, patdolan wrote:
> > > Tom Roberts, Sylvia, Legion, Jan(s), Gary Harnagel, Prokary, Pyth,
> > > Dirk, how can you let the Kepler paradox go un-opposed?
> > You have posted hundreds of times around here without ever saying
> > anything correct or valid. All you ever do is display your personal
> > misconceptions about various aspects of physics.
> >
> > I have no expectation of anything else from this.
> > > Because it leaves you with a horrendous choice: Either 1) Kepler's
> > > third law of planetary motion is not a law of physics or 2) the
> > > principle of relativity is falsified.
> > That's easy: Kepler's laws (all of them) are quite clearly not laws of
> > physics, they are at best approximations.
> Then tell this forum, Tom Roberts, what are the laws of planetary motion that Einstein promised us which are true in all inertial frames of reference? Show them to us.

And resist the urge, in the dying days of this forum, to degrade yourself to the level of a Muttonchops or Volroney by cutting and pasting the E. field equations and calling it good. No, you need to give us the canonical form of the substitute for Kepler 3 that which is true in all inertial frames

> Indeed, in a purely Newtonian
> > universe (which ours is not), they are exact only for a very massive sun
> > and A SINGLE PLANET [#]. In the universe we inhabit, they are CLEARLY
> > just approximations.
> >
> > [#] Unlike Kepler's original formulation, one must use the
> > sun+planet barycenter, not the sun, as the origin.
> >
> > But I doubt that you understand this, and I doubt even more that your
> > "Kepler paradox" comes anywhere close to being useful.
> >
> > Hint: the principle of relativity is also an approximation.
> >
> > Once again you merely display your personal misunderstanding and lack of
> > knowledge of very basic physics. You have proven many times that you are
> > completely ineducable, so I generally ignore you.
> >
> > Tom Roberts

"you boys"????

only girls talk like dat..

On 1/12/24 8:11 PM, patdolan wrote:
> On Friday, January 12, 2024 at 3:18:21 PM UTC-8, Tom Roberts wrote:
>> That's easy: Kepler's laws (all of them) are quite clearly not
>> laws of physics, they are at best approximations.
>
> Then tell this forum, Tom Roberts, what are the laws of planetary
> motion that Einstein promised us which are true in all inertial
> frames of reference? Show them to us.

For the case of a very massive sun and planets of negligible mass, which
is an approximation that is very good in the solar system, then each
planet follows a geodesic in the spacetime defined by the sun:

D_v v = 0

where v is the 4-velocity of the planet (i.e. the tangent 4-vector of
its path), and D_v is the covariant derivative along v.

Note this equation is completely independent of coordinates, and can be
projected onto any coordinate system you wish, not just (locally)
inertial frames.

If you want to avoid that approximation, then you must use the Einstein
field equation:

G + Λ g = T

where G is the Einstein curvature tensor, g is the metric tensor, Λ is
the cosmological constant, and T is the energy-momentum tensor for sun
and planets (units have 8 π G = c = 1, where this G is Newton's
gravitational constant). It is infeasible to solve this analytically for
even a two-body system, much less the solar system, but it can be solved
numerically to essentially arbitrary precision. Like the previous
equation, this equation is completely independent of coordinates, and
can be projected onto any coordinate system you wish, not just (locally)
inertial frames.

[Don't expect me to explain this further, as it is quite
clear you do not understand the requisite physics or
the underlying mathematics.]

Tom Roberts

On Friday, January 12, 2024 at 9:21:43 PM UTC-8, Tom Roberts wrote:
> On 1/12/24 8:11 PM, patdolan wrote:
> > On Friday, January 12, 2024 at 3:18:21 PM UTC-8, Tom Roberts wrote:
> >> That's easy: Kepler's laws (all of them) are quite clearly not
> >> laws of physics, they are at best approximations.
> >
> > Then tell this forum, Tom Roberts, what are the laws of planetary
> > motion that Einstein promised us which are true in all inertial
> > frames of reference? Show them to us.
> For the case of a very massive sun and planets of negligible mass, which
> is an approximation that is very good in the solar system, then each
> planet follows a geodesic in the spacetime defined by the sun:
>
> D_v v = 0
>
> where v is the 4-velocity of the planet (i.e. the tangent 4-vector of
> its path), and D_v is the covariant derivative along v.
>
> Note this equation is completely independent of coordinates, and can be
> projected onto any coordinate system you wish, not just (locally)
> inertial frames.
>
> If you want to avoid that approximation, then you must use the Einstein
> field equation:
>
> G + Λ g = T
>
> where G is the Einstein curvature tensor, g is the metric tensor, Λ is
> the cosmological constant, and T is the energy-momentum tensor for sun
> and planets (units have 8 π G = c = 1, where this G is Newton's
> gravitational constant). It is infeasible to solve this analytically for
> even a two-body system, much less the solar system, but it can be solved
> numerically to essentially arbitrary precision. Like the previous
> equation, this equation is completely independent of coordinates, and
> can be projected onto any coordinate system you wish, not just (locally)
> inertial frames.
>
> [Don't expect me to explain this further, as it is quite
> clear you do not understand the requisite physics or
> the underlying mathematics.]
>
> Tom Roberts
This submission of your, Tom Roberts, is absolutely useless garbage. Not a damned word of it addresses the scientific relationship between a planet's orbital period and it's semi-major axis.

Far from dissuading me from further pursuing my gospel of anti-relativity, it only reinforces my conviction that I reasoned correctly and you have reasoned wrongly in choosing the correct beliefs wrt to Herr Einstein's theories from early last century.

Einstein promised that every law of mechanics and every law of electrodynamics existed in simple form in every inertial system. I have proven him wrong. My discovery would have earned me a doctorate in any major European University right up until 1910. And I fully expect to be awarded one posthumously, if needs be.

On Friday, January 12, 2024 at 8:39:17 PM UTC-8, The Starmaker wrote:
> "you boys"????
>
> only girls talk like dat..
https://youtu.be/BYD-nN3ehPA?si=EqFCo-9VsGvy-MJR&t=13