On 5/9/2022 6:54 AM, whodat wrote:
> On 5/9/2022 1:03 AM, Richard Hertz wrote:
>> On Monday, May 9, 2022 at 2:39:57 AM UTC-3, whodat wrote:
>>> On 5/8/2022 11:15 PM, Richard Hertz wrote:
>>>> I wonder at which distance from the Sun GR curving space fail and
>>>> Newton's
>>>> Law take over.
>>> <snip>
>>>
>>> Give some consideration to the possibility that all of space is curved.
>>>
>>> How would you know?
>>>
>>> This isn't a premise from me, simply something to think about.
>>
>> Read GR main premises about the compromise between
>> Ricci-Civita-Grossman curved spacetime and Newton's euclidean space.
>>
>> It was clearly stated by Einstein in his two last 1915 papers, in
>> particular the one about Mercury's problem.
>>
>> GR curved spacetime vanishes at "enough" distance of massive celestial
>> bodies, and become fully newtonian.
>
> Other han an appeal to authority (see fallacies) how would you know
> that's true? What's the test?

It looks like you don't have and answer, or perhaps you don't want to
answer. No problem. No partial credit.

On Wednesday, 11 May 2022 at 06:12:51 UTC+2, whodat wrote:
> On 5/9/2022 6:54 AM, whodat wrote:
> > On 5/9/2022 1:03 AM, Richard Hertz wrote:
> >> On Monday, May 9, 2022 at 2:39:57 AM UTC-3, whodat wrote:
> >>> On 5/8/2022 11:15 PM, Richard Hertz wrote:
> >>>> I wonder at which distance from the Sun GR curving space fail and
> >>>> Newton's
> >>>> Law take over.
> >>> <snip>
> >>>
> >>> Give some consideration to the possibility that all of space is curved.
> >>>
> >>> How would you know?
> >>>
> >>> This isn't a premise from me, simply something to think about.
> >>
> >> Read GR main premises about the compromise between
> >> Ricci-Civita-Grossman curved spacetime and Newton's euclidean space.
> >>
> >> It was clearly stated by Einstein in his two last 1915 papers, in
> >> particular the one about Mercury's problem.
> >>
> >> GR curved spacetime vanishes at "enough" distance of massive celestial
> >> bodies, and become fully newtonian.
> >
> > Other han an appeal to authority (see fallacies) how would you know
> > that's true? What's the test?
> It looks like you don't have and answer,

Neither you have it. You only abandoned 2000-years old
math because your idiot guru was waving his arms very
impressively.

On Wednesday, May 11, 2022 at 1:12:51 AM UTC-3, whodat wrote:

<snip>

> >> It was clearly stated by Einstein in his two last 1915 papers, in particular the one about Mercury's problem.
> >>
> >> GR curved spacetime vanishes at "enough" distance of massive celestial bodies, and become fully newtonian.

> > Other han an appeal to authority (see fallacies) how would you know that's true? What's the test?

> It looks like you don't have and answer, or perhaps you don't want to answer. No problem. No partial credit.

Excerpts from Schwarzschild's paper, answering to Einstein and developing his famous metric (to be corrected by Hilbert in 1917)

On the Gravitational Field of a Mass Point according to Einstein’s Theory †
by K. Schwarzschild
(Communicated January 13th, 1916 [see above p. 42].)
translation‡ and foreword by S. Antoci∗ and A. Loinger∗∗

*****************************************************
Then, according to Mr. Einstein’s list, loc. cit. p. 833, the following conditions must be fulfilled too:

1. All the components are independent of the time x4. (NOTE 1: time is not used in the spacetime calculation of GR in vacuum)
2. The equations g4 = g4 = 0 hold exactly for  = 1, 2, 3. (NOTE 2: this reduces the problem to 3D flat space - Euclidean)
3. The solution is spatially symmetric with respect to the origin of the co-ordinate system in the
sense that one finds again the same solution when x1, x2, x3 are subjected to an orthogonal transformation (rotation).

4. The g_uv vanish at infinity, with the exception of the following four limits different from zero:

g44 = 1, g11 = g22 = g33 = −1.

(NOTE 3: With this point, the influence of gravitational potential on space curvature goes to ZERO at enough distance from 0,0,0)

The problem is to find out a line element with coefficients such that the field equations, the equation
of the determinant and these four requirements are satisfied.

§2. Mr. Einstein showed that this problem, in first approximation, leads to Newton’s law
and that the second approximation correctly reproduces the known anomaly in the motion of the
perihelion of Mercury. The following calculation yields the exact solution of the problem. It is
always pleasant to avail of exact solutions of simple form. More importantly, the calculation proves
also the uniqueness of the solution, about which Mr. Einstein’s treatment still left doubt, and
which could have been proved only with great difficulty, in the way shown below, through such an
approximation method. The following lines therefore let Mr. Einstein’s result shine with increased clearness.
*****************************************************

If you have any doubt, should study Einstein's Nov.18, 1915 paper. I'll not repeat the 4 conditions cited by Schwarzschild.

Explanation of the Perihelion Motion of Mercury from General Relativity Theory
Albert Einstein

*****************************************************
Introduction
In an earlier version of the work appearing in this journal, I have presented
the field equations of gravity, which are covariant under corresponding transformations
having a determinant equals unity. In an Addendum to this work,
I have shown that each of the field equations is generally covariant when the
scalar of the energy tensor of the matter vanishes, and I have thereby shown
from the introduction of this hypothesis, through which time and space are
robbed of the last vestige of objective reality, that in principle there are no
doubts standing against this assertion.
............................
We place a point mass (the Sun) at the origin of the coordinate system.
The gravitational field, which this mass point produces, can be calculated
from these equations through successive approximations.
............................................
As one sees from (4b), our theory brings with it that in the case of a
slowly moving mass the components g11 to g33 already appear to the non-zero
magnitude of first order. We will see later that hereby there is no difference
between Newton’s law (in the first order approximation).
...............................
From this equation, it follows that the Newton motion equation is obtained
as a first approximation. Namely, when the speed of a point particle is small
with respect to the speed of light, so dx1 , dx2 , dx3 are small against dx4.
...................................
Besides, it should be remarked that (7b) and (9) for the case of an orbital motion give
no deviation from Kepler’s third law.
From (7b) next follows the exactly valid form of the equation
r^2 dφ/ds = B (10)
where B means a constant.

(NOTE: Angular momentum is conserved. Pure Newton)
..................
By the determination of the orbital form, one now goes forth exactly as in
the Newtonian case. From (7c) one next obtains

(NOTE: At Eq. 7c Einstein magically changes the gravitational potential used until then).

It's changed from Φ = - 1/2 α/r to Φ = - 1/2 α/r (1 + B²/r²) *** GEOMETRICAL UNITS

Φ= - GMm/r [1 + B²/(m²c²r²)] = -1/2 α m/r [1 + B²/(m²c²r²)] *** PHYSICAL UNITS

*****************************************************

Can you understand how did Einstein played his fallacies on the paper between Newton and his GR?

No? I'm sorry. Learn more.

I'm going back to the original posting that you've deleted in an attempt
to foist off a response that does not reply to the question raised.
Perhaps you're used to arguing with others who give up easily.

Here's the original posting and the few initial replies:
=========================================================================

On 5/9/2022 1:03 AM, Richard Hertz wrote:
> On Monday, May 9, 2022 at 2:39:57 AM UTC-3, whodat wrote:
>> On 5/8/2022 11:15 PM, Richard Hertz wrote:
>>> I wonder at which distance from the Sun GR curving space fail and
Newton's
>>> Law take over.
>> <snip>
>>
>> Give some consideration to the possibility that all of space is curved.
>>
>> How would you know?

>>
>> This isn't a premise from me, simply something to think about.
>
> Read GR main premises about the compromise between Ricci-Civita-
> Grossman curved spacetime and Newton's euclidean space.
>
> It was clearly stated by Einstein in his two last 1915 papers, in
particular the one about Mercury's problem.
>
> GR curved spacetime vanishes at "enough" distance of massive celestial
> bodies, and become fully newtonian.

Other han an appeal to authority (see fallacies) how would you know >
that's true? What's the test?

===========================================================================

Your reply, below after the line of &'s is just another appeal to
authority and an attempt to belittle my mental capacity. Of course
you're free to do that, but it is not anywhere near the answer that
was requested, so why fake a reply?

As I've asked before, and you have failed to reply,

WHERE'S THE TEST"

You don't have one because apparently nobody has approached the question
I asked that us simply:

"Give some consideration to the possibility that all of space is curved."

No problem, you're not an expert on new/novel questions. But thanks for
playing. The correct answer, if there must be one, is simply that the
question has not been considered. There are lots of questions that have
not been considered as yet. It appears that curvature o0f space is
local. But I cannot cite any7 test that validates that premise either.

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

On 5/11/2022 1:09 AM, Richard Hertz wrote:
> On Wednesday, May 11, 2022 at 1:12:51 AM UTC-3, whodat wrote:
>
> <snip>
>
>>>> It was clearly stated by Einstein in his two last 1915 papers, in particular the one about Mercury's problem.
>>>>
>>>> GR curved spacetime vanishes at "enough" distance of massive celestial bodies, and become fully newtonian.
>
>>> Other han an appeal to authority (see fallacies) how would you know that's true? What's the test?
>
>> It looks like you don't have and answer, or perhaps you don't want to answer. No problem. No partial credit.
>
> Excerpts from Schwarzschild's paper, answering to Einstein and developing his famous metric (to be corrected by Hilbert in 1917)
>
>
> On the Gravitational Field of a Mass Point according to Einstein’s Theory †
> by K. Schwarzschild
> (Communicated January 13th, 1916 [see above p. 42].)
> translation‡ and foreword by S. Antoci∗ and A. Loinger∗∗
>
> *****************************************************
> Then, according to Mr. Einstein’s list, loc. cit. p. 833, the following conditions must be fulfilled too:
>
> 1. All the components are independent of the time x4. (NOTE 1: time is not used in the spacetime calculation of GR in vacuum)
> 2. The equations g4 = g4 = 0 hold exactly for  = 1, 2, 3. (NOTE 2: this reduces the problem to 3D flat space - Euclidean)
> 3. The solution is spatially symmetric with respect to the origin of the co-ordinate system in the
> sense that one finds again the same solution when x1, x2, x3 are subjected to an orthogonal transformation (rotation).
>
> 4. The g_uv vanish at infinity, with the exception of the following four limits different from zero:
>
> g44 = 1, g11 = g22 = g33 = −1.
>
> (NOTE 3: With this point, the influence of gravitational potential on space curvature goes to ZERO at enough distance from 0,0,0)
>
> The problem is to find out a line element with coefficients such that the field equations, the equation
> of the determinant and these four requirements are satisfied.
>
> §2. Mr. Einstein showed that this problem, in first approximation, leads to Newton’s law
> and that the second approximation correctly reproduces the known anomaly in the motion of the
> perihelion of Mercury. The following calculation yields the exact solution of the problem. It is
> always pleasant to avail of exact solutions of simple form. More importantly, the calculation proves
> also the uniqueness of the solution, about which Mr. Einstein’s treatment still left doubt, and
> which could have been proved only with great difficulty, in the way shown below, through such an
> approximation method. The following lines therefore let Mr. Einstein’s result shine with increased clearness.
> *****************************************************
>
> If you have any doubt, should study Einstein's Nov.18, 1915 paper. I'll not repeat the 4 conditions cited by Schwarzschild.
>
> Explanation of the Perihelion Motion of Mercury from General Relativity Theory
> Albert Einstein
>
> *****************************************************
> Introduction
> In an earlier version of the work appearing in this journal, I have presented
> the field equations of gravity, which are covariant under corresponding transformations
> having a determinant equals unity. In an Addendum to this work,
> I have shown that each of the field equations is generally covariant when the
> scalar of the energy tensor of the matter vanishes, and I have thereby shown
> from the introduction of this hypothesis, through which time and space are
> robbed of the last vestige of objective reality, that in principle there are no
> doubts standing against this assertion.
> ...........................
> We place a point mass (the Sun) at the origin of the coordinate system.
> The gravitational field, which this mass point produces, can be calculated
> from these equations through successive approximations.
> ...........................................
> As one sees from (4b), our theory brings with it that in the case of a
> slowly moving mass the components g11 to g33 already appear to the non-zero
> magnitude of first order. We will see later that hereby there is no difference
> between Newton’s law (in the first order approximation).
> ..............................
> From this equation, it follows that the Newton motion equation is obtained
> as a first approximation. Namely, when the speed of a point particle is small
> with respect to the speed of light, so dx1 , dx2 , dx3 are small against dx4.
> ..................................
> Besides, it should be remarked that (7b) and (9) for the case of an orbital motion give
> no deviation from Kepler’s third law.
> From (7b) next follows the exactly valid form of the equation
> r^2 dφ/ds = B (10)
> where B means a constant.
>
> (NOTE: Angular momentum is conserved. Pure Newton)
> .................
> By the determination of the orbital form, one now goes forth exactly as in
> the Newtonian case. From (7c) one next obtains
>
> (NOTE: At Eq. 7c Einstein magically changes the gravitational potential used until then).
>
> It's changed from Φ = - 1/2 α/r to Φ = - 1/2 α/r (1 + B²/r²) *** GEOMETRICAL UNITS
>
>
> Φ= - GMm/r [1 + B²/(m²c²r²)] = -1/2 α m/r [1 + B²/(m²c²r²)] *** PHYSICAL UNITS
>
> *****************************************************
>
> Can you understand how did Einstein played his fallacies on the paper between Newton and his GR?
>
> No? I'm sorry. Learn more.

Whose fool do you think the readers of this newsgroup are? Who could the
fool in this discussion actually be? Why the person who faked an
answer, of course.

Sigh, you've become too accustomed to arguing where there's no real
cause to argue.