On 3/26/23 11:14 AM, JanPB wrote:
> On Sunday, March 26, 2023 at 7:44:29 AM UTC-7, Edgar L. Owen wrote:
>> Rich, The "physical tangible cause" is the accelerations the space
>> traveling twin experiences. There is no denying that. It's basic
>> physics.

You CLEARLY do not understand very basic physics.

> What if both are free-falling (inertial) through their trips? I'm
> not 100% sure but I think such arrangements are possible in GR (not
> SR).

Yes, in GR it certainly is possible to consider two clocks orbiting a
mass, one in a circular orbit and one in a highly-elliptical orbit, with
the details coordinated so they periodically meet. The elliptical orbit
will display more elapsed proper time between meetings than the
circular orbit.

The twin scenario of SR (with instantaneous accelerations) is just a
triangle. For such timelike paths, path length is just elapsed proper
time. The path length of one side of a triangle is necessarily different
from the sum of the path lengths of the other two sides. The wrinkle is
that in the hyperbolic geometry of SR, those two sides total up to less
than the one side.

Tom Roberts

On Tuesday, 28 March 2023 at 21:19:15 UTC+2, Tom Roberts wrote:
> On 3/26/23 11:14 AM, JanPB wrote:
> > On Sunday, March 26, 2023 at 7:44:29 AM UTC-7, Edgar L. Owen wrote:
> >> Rich, The "physical tangible cause" is the accelerations the space
> >> traveling twin experiences. There is no denying that. It's basic
> >> physics.
>
> You CLEARLY do not understand very basic physics.

That we're FORCED!!!! To THE BEST WAY!!!!!

Tom, the one in the highly elliptical orbit is traveling a further distance through space at an average greater spatial velocity, so wouldn't it display Less rather than More elapsed proper time, contrary to what you say? If I'm wrong please explain why....

Thanks,
Edgar
>
> Yes, in GR it certainly is possible to consider two clocks orbiting a
> mass, one in a circular orbit and one in a highly-elliptical orbit, with
> the details coordinated so they periodically meet. The elliptical orbit
> will display more elapsed proper time between meetings than the
> circular orbit.

>
> Tom Roberts

On Monday, March 27, 2023 at 9:01:25 AM UTC-7, Edgar L. Owen wrote:
> The frame view of Earth/twin A is the only one of the 3 frame views
> that accurately describes the 'actual;' ST distances traveled by both
> twins, because it's the only one that accurately shows the spatial
> velocities produced by their actual tangible accelerations or lack of...

That's untrue. Each of the three inertial coordinate systems (which you are sloppily calling frames) is equally suitable for accurately describing the velocities and the accelerations. In each of the three systems, one twin is unaccelerated the entire time, and the other undergoes acceleration at the middle of his journey, and in each system this is consistent with their velocities, and in each inertial coordinate system x,t the elapsed proper times are given by integrating sqrt(dt^2 - dx^2) along their paths. Do you understand this?

On Wednesday, 29 March 2023 at 02:33:02 UTC+2, Trevor Lange wrote:
> On Monday, March 27, 2023 at 9:01:25 AM UTC-7, Edgar L. Owen wrote:
> > The frame view of Earth/twin A is the only one of the 3 frame views
> > that accurately describes the 'actual;' ST distances traveled by both
> > twins, because it's the only one that accurately shows the spatial
> > velocities produced by their actual tangible accelerations or lack of....
>
> That's untrue. Each of the three inertial coordinate systems (which you are sloppily calling frames) is equally suitable for accurately describing the velocities and the accelerations.

That's untrue. Your tales had never much in common with the reality.

On 2023-03-28 19:59:16 +0000, Maciej Wozniak said:

> On Tuesday, 28 March 2023 at 21:19:15 UTC+2, Tom Roberts wrote:
>> On 3/26/23 11:14 AM, JanPB wrote:> > On Sunday, March 26, 2023 at
>> 7:44:29 AM UTC-7, Edgar L. Owen wrote:> >> Rich, The "physical tangible
>> cause" is the accelerations the space> >> traveling twin experiences.
>> There is no denying that. It's basic> >> physics.>> You CLEARLY do not
>> understand very basic physics.
> That we're FORCED!!!! To THE BEST WAY!!!!!

This much repeated catchphrase is becoming as boring as the one about
what clocks measure in the real world. Are you incapable of
constructing a rational argument that consists of more than a short
slogan?

--
athel -- biochemist, not a physicist, but detector of crackpots

On Wednesday, 29 March 2023 at 08:51:36 UTC+2, Athel Cornish-Bowden wrote:
> On 2023-03-28 19:59:16 +0000, Maciej Wozniak said:
>
> > On Tuesday, 28 March 2023 at 21:19:15 UTC+2, Tom Roberts wrote:
> >> On 3/26/23 11:14 AM, JanPB wrote:> > On Sunday, March 26, 2023 at
> >> 7:44:29 AM UTC-7, Edgar L. Owen wrote:> >> Rich, The "physical tangible
> >> cause" is the accelerations the space> >> traveling twin experiences.
> >> There is no denying that. It's basic> >> physics.>> You CLEARLY do not
> >> understand very basic physics.
> > That we're FORCED!!!! To THE BEST WAY!!!!!
> This much repeated catchphrase is becoming as boring as the one about
> what clocks measure in the real world. Are you incapable of
> constructing a rational argument that consists of more than a short
> slogan?

Oh, I present a lot of them, just - being a mindless
fanatic idiot - you're only noticing what you
like to notice.

On 3/29/2023 2:51 AM, Athel Cornish-Bowden wrote:
> On 2023-03-28 19:59:16 +0000, Maciej Wozniak said:
>
>> On Tuesday, 28 March 2023 at 21:19:15 UTC+2, Tom Roberts wrote:
>>> On 3/26/23 11:14 AM, JanPB wrote:> > On Sunday, March 26, 2023 at
>>> 7:44:29 AM UTC-7, Edgar L. Owen wrote:> >> Rich, The "physical
>>> tangible cause" is the accelerations the space> >> traveling twin
>>> experiences. There is no denying that. It's basic> >> physics.>> You
>>> CLEARLY do not understand very basic physics.
>> That we're FORCED!!!! To THE BEST WAY!!!!!
>
> This much repeated catchphrase is becoming as boring as the one about
> what clocks measure in the real world. Are you incapable of constructing
> a rational argument that consists of more than a short slogan?
>
Maciej just had a DNA test and the results were 50% Polish, 50% Macaw
Parrot and 100% retarded. So don't expect anything different.

Den 28.03.2023 21:19, skrev Tom Roberts:
> On 3/26/23 11:14 AM, JanPB wrote:
>> On Sunday, March 26, 2023 at 7:44:29 AM UTC-7, Edgar L. Owen wrote:
>>> Rich, The "physical tangible cause" is the accelerations the space
>>>  traveling twin experiences. There is no denying that. It's basic
>>> physics.
>
> You CLEARLY do not understand very basic physics.
>
>> What if both are free-falling (inertial) through their trips? I'm
>> not 100% sure but I think such arrangements are possible in GR (not
>> SR).
>
> Yes, in GR it certainly is possible to consider two clocks orbiting a
> mass, one in a circular orbit and one in a highly-elliptical orbit, with
> the details coordinated so they periodically meet. The elliptical orbit
> will display more elapsed proper time between meetings than the
> circular orbit.

https://paulba.no/Satellites.html
Scenario: "Twin scenario-kind of"

Screenshot of a run of the simulation:
https://paulba.no/temp/SatelliteRun.pdf

>
> The twin scenario of SR (with instantaneous accelerations) is just a
> triangle. For such timelike paths, path length is just elapsed proper
> time. The path length of one side of a triangle is necessarily different
> from the sum of the path lengths of the other two sides. The wrinkle is
> that in the hyperbolic geometry of SR, those two sides total up to less
> than the one side.
>
> Tom Roberts

--
Paul

https://paulba.no/

On 3/28/23 5:35 PM, Edgar L. Owen wrote:
> Tom, the one in the highly elliptical orbit is traveling a further
> distance through space at an average greater spatial velocity, so
> wouldn't it display Less rather than More elapsed proper time,
> contrary to what you say? If I'm wrong please explain why....

The highly-elliptical orbit spends most of its proper time at a higher
gravitational potential than the circular orbit. This is more important
than the effect of its varying velocity (relative to the inertial frame
of the mass), and causes it to accumulate more elapsed proper time
between meetings than the circular orbit.

Attempting to think in terms of "distance through space" is hopeless --
GR simply does not work that way; one must integrate the metric over the
actual paths.

Tom Roberts

>> Yes, in GR it certainly is possible to consider two clocks
>> orbiting a mass, one in a circular orbit and one in a
>> highly-elliptical orbit, with the details coordinated so they
>> periodically meet. The elliptical orbit will display more elapsed
>> proper time between meetings than the circular orbit.
>
>>
>> Tom Roberts

On Wednesday, March 29, 2023 at 10:07:04 AM UTC-7, Paul B. Andersen wrote:
>
> Screenshot of a run of the simulation:
> https://paulba.no/temp/SatelliteRun.pdf

Very nice!

--
Jan

Den 29.03.2023 00:35, skrev Edgar L. Owen:
> Tom, the one in the highly elliptical orbit is traveling a further distance through space at an average greater spatial velocity, so wouldn't it display Less rather than More elapsed proper time, contrary to what you say? If I'm wrong please explain why....
>
> Thanks,
> Edgar

See my previous posting.

https://paulba.no/Satellites.html
Scenario: "Twin scenario-kind of"

Screenshot of a run of the simulation:
https://paulba.no/temp/SatelliteRun.pdf

The speed of the red satellite is constant 6,460 m/s.
The altitude is constant 3,183 km.
The apparent rate of its clock is 1 relative to UTC.

At apogee the speed of the green satellite is 2,025 m/s,
less than 1/3 of the speed of the red satellite.
The altitude is 32,212 km, more than 10 times the altitude
of the red satellite.
The apparent rate of the clock will be ≈(1+5.6E-10) relative
to UTC, which is faster than the apparent rate of the red
satellite clock.

At perigee the speed of the green satellite will be 8,170 m/s,
1.25 times faster than the red satellite.
The altitude is 3,183 km, same as the altitude of the red satellite.
The apparent rate of the clock will be ≈(1-1.4E-10) relative to
UTC, which is slower than the apparent rate of the red satellite clock.

On average the speed of the green satellite is slower than the speed
of the red satellite, and the average altitude of the green satellite
is much higher than the altitude of the red satellite, so the green
satellite clock will on average appear to run faster than the clock
in the red satellite.
The net result is that the green satellite clock will gain ≈15.5 μs
on the red satellite clock between each time they meet.
The green satellite clock will on average appear to run faster
than the clock in the red satellite.

--
Paul

https://paulba.no/

On Wednesday, March 29, 2023 at 11:50:01 AM UTC-7, Paul B. Andersen wrote:
> Den 29.03.2023 00:35, skrev Edgar L. Owen:
> > Tom, the one in the highly elliptical orbit is traveling a further distance through space at an average greater spatial velocity, so wouldn't it display Less rather than More elapsed proper time, contrary to what you say? If I'm wrong please explain why....
> >
> > Thanks,
> > Edgar
>
>
> See my previous posting.
> https://paulba.no/Satellites.html" rel="nofollow" target="_blank">https://paulba.no/Satellites.html
> Scenario: "Twin scenario-kind of"
> Screenshot of a run of the simulation:
> https://paulba.no/temp/SatelliteRun.pdf
> The speed of the red satellite is constant 6,460 m/s.
> The altitude is constant 3,183 km.
> The apparent rate of its clock is 1 relative to UTC.
>
> At apogee the speed of the green satellite is 2,025 m/s,
> less than 1/3 of the speed of the red satellite.
> The altitude is 32,212 km, more than 10 times the altitude
> of the red satellite.
> The apparent rate of the clock will be ≈(1+5.6E-10) relative
> to UTC, which is faster than the apparent rate of the red
> satellite clock.
>
> At perigee the speed of the green satellite will be 8,170 m/s,
> 1.25 times faster than the red satellite.
> The altitude is 3,183 km, same as the altitude of the red satellite.
> The apparent rate of the clock will be ≈(1-1.4E-10) relative to
> UTC, which is slower than the apparent rate of the red satellite clock.
>
> On average the speed of the green satellite is slower than the speed
> of the red satellite, and the average altitude of the green satellite
> is much higher than the altitude of the red satellite, so the green
> satellite clock will on average appear to run faster than the clock
> in the red satellite.
> The net result is that the green satellite clock will gain ≈15.5 μs
> on the red satellite clock between each time they meet.
> The green satellite clock will on average appear to run faster
> than the clock in the red satellite.
>
> --
> Paul
>
> https://paulba.no/
Very nice! If I may suggest, try arranging such the average speed of the two satellites are equal, so the only differentiation in total elapsed proper time comes from the differences in altitude.

Tom Roberts <tjoberts137@sbcglobal.net> wrote:

> On 3/26/23 11:14 AM, JanPB wrote:
> > On Sunday, March 26, 2023 at 7:44:29?AM UTC-7, Edgar L. Owen wrote:
> >> Rich, The "physical tangible cause" is the accelerations the space
> >> traveling twin experiences. There is no denying that. It's basic
> >> physics.
>
> You CLEARLY do not understand very basic physics.
>
> > What if both are free-falling (inertial) through their trips? I'm
> > not 100% sure but I think such arrangements are possible in GR (not
> > SR).
>
> Yes, in GR it certainly is possible to consider two clocks orbiting a
> mass, one in a circular orbit and one in a highly-elliptical orbit, with
> the details coordinated so they periodically meet. The elliptical orbit
> will display more elapsed proper time between meetings than the
> circular orbit.

Beware. You can have the kissing elliptical orbit outside,
so with a > r, or inside, with a < r.

Jan

Paul B. Andersen <paul.b.andersen@paulba.no> wrote:

> Den 28.03.2023 21:19, skrev Tom Roberts:
> > On 3/26/23 11:14 AM, JanPB wrote:
> >> On Sunday, March 26, 2023 at 7:44:29?AM UTC-7, Edgar L. Owen wrote:
> >>> Rich, The "physical tangible cause" is the accelerations the space
> >>> traveling twin experiences. There is no denying that. It's basic
> >>> physics.
> >
> > You CLEARLY do not understand very basic physics.
> >
> >> What if both are free-falling (inertial) through their trips? I'm
> >> not 100% sure but I think such arrangements are possible in GR (not
> >> SR).
> >
> > Yes, in GR it certainly is possible to consider two clocks orbiting a
> > mass, one in a circular orbit and one in a highly-elliptical orbit, with
> > the details coordinated so they periodically meet. The elliptical orbit
> > will display more elapsed proper time between meetings than the
> > circular orbit.
>
> https://paulba.no/Satellites.html
> Scenario: "Twin scenario-kind of"
>
> Screenshot of a run of the simulation:
> https://paulba.no/temp/SatelliteRun.pdf

Hmmm. If you take gravitational time shift into account
you should also take apsidal precession into account.
This will not influence proper time over an orbit,
but it will have an effect on their comparison
of elapsed proper times at their next meeting.

Jan
(needs to think some more)

On 3/29/23 3:06 PM, J. J. Lodder wrote:
> Tom Roberts <tjoberts137@sbcglobal.net> wrote:
>> Yes, in GR it certainly is possible to consider two clocks
>> orbiting a mass, one in a circular orbit and one in a
>> highly-elliptical orbit, with the details coordinated so they
>> periodically meet. The elliptical orbit will display more elapsed
>> proper time between meetings than the circular orbit.
>
> Beware. You can have the kissing elliptical orbit outside, so with a
>> r, or inside, with a < r.

That's why I said HIGHLY elliptical, so the elliptical clock spends more
time outside the circular orbit. I implicitly assumed speed << c so the
effect of velocity is much less than that of gravitation; I don't know
how this works out for orbital speeds approaching c.

> [... precession]

Yes -- this can be more complicated than I implied in my initial post. I
should have said that it is possible to set it up as I described, but
other results are possible.

[For instance, if the orbits are not in the same plane,
precession will prevent them from intersecting again
until the elliptical orbit has precessed 360 degrees,
and even then an intersection will require fine tuning.]

Tom Roberts

On Wednesday, March 29, 2023 at 1:38:36 PM UTC-7, J. J. Lodder wrote:
> Paul B. Andersen <paul.b....@paulba.no> wrote:
>
> > Den 28.03.2023 21:19, skrev Tom Roberts:
> > > On 3/26/23 11:14 AM, JanPB wrote:
> > >> On Sunday, March 26, 2023 at 7:44:29?AM UTC-7, Edgar L. Owen wrote:
> > >>> Rich, The "physical tangible cause" is the accelerations the space
> > >>> traveling twin experiences. There is no denying that. It's basic
> > >>> physics.
> > >
> > > You CLEARLY do not understand very basic physics.
> > >
> > >> What if both are free-falling (inertial) through their trips? I'm
> > >> not 100% sure but I think such arrangements are possible in GR (not
> > >> SR).
> > >
> > > Yes, in GR it certainly is possible to consider two clocks orbiting a
> > > mass, one in a circular orbit and one in a highly-elliptical orbit, with
> > > the details coordinated so they periodically meet. The elliptical orbit
> > > will display more elapsed proper time between meetings than the
> > > circular orbit.
> >
> > https://paulba.no/Satellites.html
> > Scenario: "Twin scenario-kind of"
> >
> > Screenshot of a run of the simulation:
> > https://paulba.no/temp/SatelliteRun.pdf
> Hmmm. If you take gravitational time shift into account
> you should also take apsidal precession into account.
> This will not influence proper time over an orbit,
> but it will have an effect on their comparison
> of elapsed proper times at their next meeting.

Wouldn't this effect be an order (or more) of magnitude smaller?
The answer is in calculating this but I'm too lazy...

--
Jan

On Wednesday, 29 March 2023 at 20:50:01 UTC+2, Paul B. Andersen wrote:
> Den 29.03.2023 00:35, skrev Edgar L. Owen:
> > Tom, the one in the highly elliptical orbit is traveling a further distance through space at an average greater spatial velocity, so wouldn't it display Less rather than More elapsed proper time, contrary to what you say? If I'm wrong please explain why....
> >
> > Thanks,
> > Edgar
>
>
> See my previous posting.
> https://paulba.no/Satellites.html
> Scenario: "Twin scenario-kind of"
> Screenshot of a run of the simulation:
> https://paulba.no/temp/SatelliteRun.pdf
> The speed of the red satellite is constant 6,460 m/s.
> The altitude is constant 3,183 km.
> The apparent rate of its clock is 1 relative to UTC.
>
> At apogee the speed of the green satellite is 2,025 m/s,
> less than 1/3 of the speed of the red satellite.
> The altitude is 32,212 km, more than 10 times the altitude
> of the red satellite.
> The apparent rate of the clock will be ≈(1+5.6E-10) relative
> to UTC, which is faster than the apparent rate of the red
> satellite clock.
>
> At perigee the speed of the green satellite will be 8,170 m/s,
> 1.25 times faster than the red satellite.
> The altitude is 3,183 km, same as the altitude of the red satellite.
> The apparent rate of the clock will be ≈(1-1.4E-10) relative to
> UTC, which is slower than the apparent rate of the red satellite clock.
>
> On average the speed of the green satellite is slower than the speed
> of the red satellite, and the average altitude of the green satellite
> is much higher than the altitude of the red satellite, so the green
> satellite clock will on average appear to run faster than the clock
> in the red satellite.
> The net result is that the green satellite clock will gain ≈15.5 μs
> on the red satellite clock between each time they meet.

No, it doesn't. Anyone can check GPS to see your
insane bullshit is just some insane bullshit.

JanPB <filmart@gmail.com> wrote:

> On Wednesday, March 29, 2023 at 1:38:36?PM UTC-7, J. J. Lodder wrote:
> > Paul B. Andersen <paul.b....@paulba.no> wrote:
> >
> > > Den 28.03.2023 21:19, skrev Tom Roberts:
> > > > On 3/26/23 11:14 AM, JanPB wrote:
> > > >> On Sunday, March 26, 2023 at 7:44:29?AM UTC-7, Edgar L. Owen wrote:
> > > >>> Rich, The "physical tangible cause" is the accelerations the space
> > > >>> traveling twin experiences. There is no denying that. It's basic
> > > >>> physics.
> > > >
> > > > You CLEARLY do not understand very basic physics.
> > > >
> > > >> What if both are free-falling (inertial) through their trips? I'm
> > > >> not 100% sure but I think such arrangements are possible in GR (not
> > > >> SR).
> > > >
> > > > Yes, in GR it certainly is possible to consider two clocks orbiting a
> > > > mass, one in a circular orbit and one in a highly-elliptical orbit, with
> > > > the details coordinated so they periodically meet. The elliptical orbit
> > > > will display more elapsed proper time between meetings than the
> > > > circular orbit.
> > >
> > > https://paulba.no/Satellites.html
> > > Scenario: "Twin scenario-kind of"
> > >
> > > Screenshot of a run of the simulation:
> > > https://paulba.no/temp/SatelliteRun.pdf
> > Hmmm. If you take gravitational time shift into account
> > you should also take apsidal precession into account.
> > This will not influence proper time over an orbit,
> > but it will have an effect on their comparison
> > of elapsed proper times at their next meeting.
>
> Wouldn't this effect be an order (or more) of magnitude smaller?
> The answer is in calculating this but I'm too lazy...

Don't know. (and lazy too)
Anyway, your calculations are fine
as far as time over an orbit is concerned.
But since you are using Newtonian orbits you are in error
on where (or whether) they will meet again,

Jan

Tom Roberts <tjoberts137@sbcglobal.net> wrote:

> On 3/29/23 3:06 PM, J. J. Lodder wrote:
> > Tom Roberts <tjoberts137@sbcglobal.net> wrote:
> >> Yes, in GR it certainly is possible to consider two clocks
> >> orbiting a mass, one in a circular orbit and one in a
> >> highly-elliptical orbit, with the details coordinated so they
> >> periodically meet. The elliptical orbit will display more elapsed
> >> proper time between meetings than the circular orbit.
> >
> > Beware. You can have the kissing elliptical orbit outside,
> > so with a > r, or inside, with a < r.
>
> That's why I said HIGHLY elliptical, so the elliptical clock spends more
> time outside the circular orbit. I implicitly assumed speed << c so the
> effect of velocity is much less than that of gravitation; I don't know
> how this works out for orbital speeds approaching c.

You didn't see the point. [1]
The inside kissing orbit can be highly elliptical too.

Jan

Example: start at Earth orbit. Give it a // boost
such that the orbital period becomes two years.
They'll meet again in two years time.
Or: give it an anti-// boost such that the orbital period
becomes half a year. The orbit will be a kissing ellipse
entirely inside the circular orbit.

Den 29.03.2023 22:37, skrev J. J. Lodder:
> Paul B. Andersen <paul.b.andersen@paulba.no> wrote:
>
>> Den 28.03.2023 21:19, skrev Tom Roberts:
>>> On 3/26/23 11:14 AM, JanPB wrote:
>>>> On Sunday, March 26, 2023 at 7:44:29?AM UTC-7, Edgar L. Owen wrote:
>>>>> Rich, The "physical tangible cause" is the accelerations the space
>>>>> traveling twin experiences. There is no denying that. It's basic
>>>>> physics.
>>>
>>> You CLEARLY do not understand very basic physics.
>>>
>>>> What if both are free-falling (inertial) through their trips? I'm
>>>> not 100% sure but I think such arrangements are possible in GR (not
>>>> SR).
>>>
>>> Yes, in GR it certainly is possible to consider two clocks orbiting a
>>> mass, one in a circular orbit and one in a highly-elliptical orbit, with
>>> the details coordinated so they periodically meet. The elliptical orbit
>>> will display more elapsed proper time between meetings than the
>>> circular orbit.
>>
>> https://paulba.no/Satellites.html
>> Scenario: "Twin scenario-kind of"
>>
>> Screenshot of a run of the simulation:
>> https://paulba.no/temp/SatelliteRun.pdf
>
> Hmmm. If you take gravitational time shift into account
> you should also take apsidal precession into account.
> This will not influence proper time over an orbit,
> but it will have an effect on their comparison
> of elapsed proper times at their next meeting.
>
> Jan
> (needs to think some more)

Since apsidal precession of the satellite in elliptic orbit
would make its perigee move along the orbit of the satellite
in circular orbit, the proper time of the latter satellite
between the meetings would be affected.

The proper time is calculated by integration
of the Schwarzschild metric, but Newton's gravitational
acceleration is used in the simulation of the orbits.
And since the effects from the Sun and Moon are ignored,
there is no apsidal precession.

It would be however be interesting to use the post-Newtonian
approximation of the gravitational acceleration predicted by GR
in the simulation.
https://paulba.no/pdf/GRPerihelionAdvance.pdf
Equation (3)

I am however pretty sure that the effect of the apsidal precession
on the proper time would be miniscule.

--
Paul

Den 30.03.2023 15:57, skrev Paul B. Andersen:
> Den 29.03.2023 22:37, skrev J. J. Lodder:
>> Paul B. Andersen <paul.b.andersen@paulba.no> wrote:
>>
>>> Den 28.03.2023 21:19, skrev Tom Roberts:
>>>> On 3/26/23 11:14 AM, JanPB wrote:
>>>>> On Sunday, March 26, 2023 at 7:44:29?AM UTC-7, Edgar L. Owen wrote:
>>>>>> Rich, The "physical tangible cause" is the accelerations the space
>>>>>>   traveling twin experiences. There is no denying that. It's basic
>>>>>> physics.
>>>>
>>>> You CLEARLY do not understand very basic physics.
>>>>
>>>>> What if both are free-falling (inertial) through their trips? I'm
>>>>> not 100% sure but I think such arrangements are possible in GR (not
>>>>> SR).
>>>>
>>>> Yes, in GR it certainly is possible to consider two clocks orbiting a
>>>> mass, one in a circular orbit and one in a highly-elliptical orbit,
>>>> with
>>>> the details coordinated so they periodically meet. The elliptical orbit
>>>> will display more elapsed proper time between meetings than the
>>>> circular orbit.
>>>
>>> https://paulba.no/Satellites.html
>>> Scenario: "Twin scenario-kind of"
>>>
>>> Screenshot of a run of the simulation:
>>> https://paulba.no/temp/SatelliteRun.pdf
>>
>> Hmmm. If you take gravitational time shift into account
>> you should also take apsidal precession into account.
>> This will not influence proper time over an orbit,
>> but it will have an effect on their comparison
>> of elapsed proper times at their next meeting.
>>
>> Jan
>> (needs to think some more)
>
>
> Since apsidal precession of the satellite in elliptic orbit
> would make its perigee move along the orbit of the satellite
> in circular orbit, the proper time of the latter satellite
> between the meetings would be affected.

On second thought, they wouldn't meet at all.
The orbital time of the circular orbit would have to
be adjusted a bit.

>
> The proper time is calculated by integration
> of the Schwarzschild metric, but Newton's gravitational
> acceleration is used  in the simulation of the orbits.
> And since the effects from the Sun and Moon are ignored,
> there is no apsidal precession.
>
> It would be however be interesting to use the post-Newtonian
> approximation of the gravitational acceleration predicted by GR
> in the simulation.
> https://paulba.no/pdf/GRPerihelionAdvance.pdf
> Equation (3)
>
> I am however pretty sure that the effect of the apsidal precession
> on the proper time would be miniscule.
>

--
Paul