## You were right: Rotational motion is relative, too, Mr. Einstein!

AAF
AAF

It has been one hundred years since the publication of Einstein's general theory of relativity in May 1916. In a paper recently published in EPJ Plus, Norwegian physicist Øyvind Grøn from the Oslo and Akershus University College of Applied Sciences and his co-author Torkild Jemterud demonstrate that the rotational motion in the universe is also subject to the theory of relativity. Imagine a person at the North pole who doesn't believe the Earth rotates. As she holds a pendulum and can observe the stars in her telescope, she remarks that the swinging plane of the pendulum and the stars rotate together. Newton, who saw the world as a classical physicist, would have pointed out that it is the Earth that rotates. However, if we assume the general principle of relativity is valid, the Earth can be considered as being at rest while the swinging plane of the pendulum and the night sky are rotating. In fact, the rotating mass of the observable part of the universe causes the river of space--which is made up of free particles following the universe's expansion--to rotate together with the stars in the sky. And the swinging plane of the pendulum moves together with the river of space.

https://www.sciencedaily.com/releases/2 ... 120254.htm

"But OK, let's take the simplest possible test case : Say hello to Stanisława from Krakow:

She's the oldest of her sisters, so often known simply by the abbreviation "S_1". In addition, Stanisława is spending a couple of days standing on the the northern surface of S_2 exactly on the axis of rotation - which, of course, leads to her other common nick-name. That's right - Stanisława IS "The North Pole". Now that, of course, means that Stanisława has a constant and low value of H."

Do you mean Stanisława Leszczyńska?

https://en.wikipedia.org/wiki/Stanisława_Leszczyńska

Anyway, you can't see the one, in the picture, from Oslo, if she stands at the North Pole,
because this Stanisława is too short!

Let's assume, for the sake of argument, that Stanisława is 1.75 m tall.

By inserting the above value into this equation:

D = arctan(H/3000),

therefore, we obtain this value of D:

D = arctan(0.00175/3000) = 1.11 x 10-8 degrees.

That is almost equal to zero!

And accordingly, if S_2 is assumed to be spherical, no one can see Stanisława from Oslo.

But let's once again, for the sake of argument, assume that the spherical cap between
Oslo and the North Pole is completely removed; and hence,the flat circle
of Oslo's geometrical latitude is totally exposed.

It's absolutely certain, in this hypothetical case, that a rotating observer,
located in Oslo, will see Stanisława projected on the opposite arc
of the flat circle of Oslo's geometrical latitude, and NOT standing
at the center of the circle on the North Pole as she actually is.

And furthermore, if the rotating observer, located in Oslo, assumes
that he/she is stationary, then he/she will see Stanisława doing all
the circular motion in a big circle centered around Oslo.

Does this well-known optical illusion of circular motion become,
now, very clear?

Ufonaut99
Ufonaut99

It has been one hundred years since the publication of Einstein's general theory of relativity in May 1916. In a paper recently published in EPJ Plus, Norwegian physicist Øyvind Grøn from the Oslo and Akershus University College of Applied Sciences and his co-author Torkild Jemterud demonstrate that the rotational motion in the universe is also subject to the theory of relativity. Imagine a person at the North pole who doesn't believe the Earth rotates. As she holds a pendulum and can observe the stars in her telescope, she remarks that the swinging plane of the pendulum and the stars rotate together. Newton, who saw the world as a classical physicist, would have pointed out that it is the Earth that rotates. However, if we assume the general principle of relativity is valid, the Earth can be considered as being at rest while the swinging plane of the pendulum and the night sky are rotating. In fact, the rotating mass of the observable part of the universe causes the river of space--which is made up of free particles following the universe's expansion--to rotate together with the stars in the sky. And the swinging plane of the pendulum moves together with the river of space.

https://www.sciencedaily.com/releases/2 ... 120254.htm

AAF: Do you mean Stanisława Leszczyńska? https://en.wikipedia.org/wiki/Stanisława_Leszczyńska
Wow, what a lady. To see someone standing for goodness, in the face of such evil, really shows our own petty troubles in context.
AAF: a rotating observer, located in Oslo, will see Stanisława projected on the opposite arc .... Does this well-known optical illusion of circular motion become, now, very clear?
No - it remains blatantly false. The "opposite arc" of Oslo is Alaska, so the rotating observer will see Stanisława ALWAYS fixed stationary against Alaska throughout S_2's entire rotation (though again, we're supposed to be concerned solely with S_1 and S_2, not any background).
AAF: if the city of Brisbane is located on the eastern horizon .. S_1, sometime, seems to be over Brisbane ... Surely, S_1 is always '3000Km straight ahead
From where I am, real-life Brisbane CBD is due north, and the Pacific is to the east. While I am standing (not moving a muscle) facing due North :
- There is NO optical illusion (let alone any "well-known" one (*)) that will put Brisbane CBD over the Pacific.
- There is NO optical illusion (let alone any "well-known" one (*)) that will result in the Pacific ever being straight ahead of me.

Any reader could substitute their own landmarks, to see that these will always be self-evidently true - and would remain true even if Brisbane was actually at the north pole (Brrrr, please no !)

These have been long threads, and IMHO, this claim is the central core point of difference between us, upon which your remaining arguments are hinged.
I have repeatedly asked for clear justification of this claim, but we're still not progressing from the above statements, so it's time to call a halt.

In summary, I see our respective positions, as stated above and what I said in my previous post :
I go instead with the commonsense straightforward view that anything that remains on (or directly above) the north pole remains due north of our observer. Since our observer is always facing due north, then he sees that object fixed in front of him. THAT is what makes perfect sense.

In contrast, you claim that an object positioned at/above the north pole travels until it's due EAST of our observer (.... and so continues until that NORTH pole object is due SOUTH of him, yes?) However, even though the observer remains facing north, you reckon this object (that is now East of him) is not off to his right - No, you say it's still straight ahead of him !!
I'm happy to leave any other readers to decide the relative credibility of these positions, and consequently the merit of all your arguments against Einstein in these threads

(*) Going incredibly cross-eyed doesn't count !

AAF
AAF

It has been one hundred years since the publication of Einstein's general theory of relativity in May 1916. In a paper recently published in EPJ Plus, Norwegian physicist Øyvind Grøn from the Oslo and Akershus University College of Applied Sciences and his co-author Torkild Jemterud demonstrate that the rotational motion in the universe is also subject to the theory of relativity. Imagine a person at the North pole who doesn't believe the Earth rotates. As she holds a pendulum and can observe the stars in her telescope, she remarks that the swinging plane of the pendulum and the stars rotate together. Newton, who saw the world as a classical physicist, would have pointed out that it is the Earth that rotates. However, if we assume the general principle of relativity is valid, the Earth can be considered as being at rest while the swinging plane of the pendulum and the night sky are rotating. In fact, the rotating mass of the observable part of the universe causes the river of space--which is made up of free particles following the universe's expansion--to rotate together with the stars in the sky. And the swinging plane of the pendulum moves together with the river of space.

https://www.sciencedaily.com/releases/2 ... 120254.htm

Oh, so you've decided suddenly to suspend it; just like
Ted Cruz after losing the Indiana primary:

Well; speaking for myself, it's too late,
for me, to quit now . . .

I still have a huge file full of unpublished posts related

…..................................................................................................................................................................

""if the city of Brisbane is located on the eastern horizon and the city of Oslo is located on the western horizon of the rotating observer, then S_1 will, sometimes, appear over the city of Brisbane; and it will appear, at some other times, over the city of Oslo." Surely it's commonsense that the North Pole will always be due North - yes? .... so please explain clearly, with maths, exactly: how and why you reckon our camera sees The North Pole over at Brisbane due .... East ???? And then, of course, how you reckon that The North Pole swings over to Oslo due West ????"

The North Pole, by definition, does not swing over to Oslo due west.

But the external object S_1 does swing over to Oslo due west.

And also, the external object S_1 does swing over to Brisbane due east.

How do we explain it exactly with math?

Very simple!

Firstly, we calculate the angle D between the S_1, the rotating observer, and the North Pole,
by using this equation: D = arctan(H/3000).

And since the height of S_1 over the North Pole is equal to 4,000 km,
then D is equal to about 53 degrees.

And secondly, we rotate the straight line between the observer and S_1 at
a 53-degree angle across the sky.

And finally, by simply assuming that observer is stationary, we make S_1 appear to travel
in a circle at about 53 degrees over the stationary circle of the observer's horizon.

It's that simple!

Ufonaut99
Ufonaut99

It has been one hundred years since the publication of Einstein's general theory of relativity in May 1916. In a paper recently published in EPJ Plus, Norwegian physicist Øyvind Grøn from the Oslo and Akershus University College of Applied Sciences and his co-author Torkild Jemterud demonstrate that the rotational motion in the universe is also subject to the theory of relativity. Imagine a person at the North pole who doesn't believe the Earth rotates. As she holds a pendulum and can observe the stars in her telescope, she remarks that the swinging plane of the pendulum and the stars rotate together. Newton, who saw the world as a classical physicist, would have pointed out that it is the Earth that rotates. However, if we assume the general principle of relativity is valid, the Earth can be considered as being at rest while the swinging plane of the pendulum and the night sky are rotating. In fact, the rotating mass of the observable part of the universe causes the river of space--which is made up of free particles following the universe's expansion--to rotate together with the stars in the sky. And the swinging plane of the pendulum moves together with the river of space.

https://www.sciencedaily.com/releases/2 ... 120254.htm

AAF: Oh, so you've decided suddenly to suspend it; just like Ted Cruz after losing the Indiana primary:
Oh no !!! If I'm Ted Cruz, that means you regard yourself as Donald Trump <img alt="Shocked eyes" width="55" height="60" src="http://www.sherv.net/cm/emoticons/shock ... oticon.gif">

OK, you put a bit more detail into that post, so lets give it another shot

So, from what you described in the final section of your post, seemed to imply the following :

1) Let's say that, as per the graphic, at 1am we point our camera directly at S_1, that is positioned fixed at a constant height H above the north pole.
2) Let's also say Mizar happens to also be in the camera's frame (although ignored by our observers ).

3) Now, we agree that S_2 has actual rotation about it's axis (although again, not known by our observers )
4) However, assuming our camera-observer is stationary, then it will remain stationary throughout the rotation
5) (and so, consequently, always remain pointing towards Mizar)
6) while S_2's rotation means S_2 will be rotating about it.
7) That is, although at 1am the north pole is directly ahead of the camera, at other times the pole will be rotating around (and at 1pm, be behind) it.
8) All of which means, whatever is above S_2's north pole will also be effectively rotating around the camera
9) which results in S_1 being seen travelling by our observer "in a big circle in the sky", such that Parallax can be applied.

So is that a fair summary of your position ?

Pending your confirmation, it's worth pointing out that that position is totally inconsistent with the idea that "the external object S_1 does swing over to Brisbane due east" (Actually, your repetition of those "S_1 over Brisbane" claims is one of the reasons I've been thinking you couldn't have that model in mind.)
but that's minor issue

AAF
AAF

It has been one hundred years since the publication of Einstein's general theory of relativity in May 1916. In a paper recently published in EPJ Plus, Norwegian physicist Øyvind Grøn from the Oslo and Akershus University College of Applied Sciences and his co-author Torkild Jemterud demonstrate that the rotational motion in the universe is also subject to the theory of relativity. Imagine a person at the North pole who doesn't believe the Earth rotates. As she holds a pendulum and can observe the stars in her telescope, she remarks that the swinging plane of the pendulum and the stars rotate together. Newton, who saw the world as a classical physicist, would have pointed out that it is the Earth that rotates. However, if we assume the general principle of relativity is valid, the Earth can be considered as being at rest while the swinging plane of the pendulum and the night sky are rotating. In fact, the rotating mass of the observable part of the universe causes the river of space--which is made up of free particles following the universe's expansion--to rotate together with the stars in the sky. And the swinging plane of the pendulum moves together with the river of space.

https://www.sciencedaily.com/releases/2 ... 120254.htm

I hope we all will, someday, be as good at making BIG money
as Mr. Trump:

….............................................................................................................................................

"finally agreed"????? I never disagreed (beyond the earlier correction); I said it was irrelevant to the effect you were claiming (which it is). "And if the observer moves in a circle, then he/she will see the external object moving in a circle." Let's take a simple every day example - but first give a warm welcome to Stanisława's brother Szczepan. He's the oldest son, so also affectionately known as "S_1" He has a habit of climbing on top of things that are in the middle of something - so yes, he's nicknamed "The Central Pole". Now, imagine someone - "Alice" - standing on the outer edge of a spinning 3-metre radius merry-go-round in the middle of a grassy park. She is not moving a muscle, but looking inwards (so always looking inwards) towards Szczepan, who is (also without moving a muscle) standing on top of the central NON-rotating 4-metre pole that the merry-go-round goes round. Someone's painted a couple of words on the merry-go-round - "Brisbane in the east" to Alice's right, "Oslo in the west" to her left. I claim that: As Alice is rotating on the merry-go-round, she will always see the central pole ("S_1" - Szczepan ... and, of course, the metal thing he's on) straight-ahead in her line of sight. He remains always fixed at exactly the same place in her view throughout the rotation, moving neither to the left nor right, and never leaving her view. As the merry-go-round spins, she see his front, then his left-side, then his back, then his right-side, then front again - in clear apparent rotation around his central axis."

The consequences of the equation:

D = arctan(H/3000) are relevant and very important!

So, Alice is standing on the outer edge of a spinning 3-metre radius merry-go-round
looking inwards towards Szczepan; right?

Of course, I got it right?

Since Szczepan is stationary at the center of the spinning 3-metre radius merry-go-round,
then Alice, standing on the outer edge of the spinning 3-metre radius merry-go-round and
looking inwards towards him, must always see Szczepan, NOT stationary as he actually
is, but projected on the other outer edge of the spinning 3-metre radius merry-go-round
and constantly rotating in a circle around Alice herself.

Do you agree with this result?

Of course, everyone must agree with this result.

And that is because the above 'stationary Szczepan - rotating Alice' system
is very similar to the 'stationary Sun – rotating Earth' system, which had
fooled very smart astronomers into deducing the exact opposite what is really going
on, for hundreds of years.

Ufonaut99
Ufonaut99

It has been one hundred years since the publication of Einstein's general theory of relativity in May 1916. In a paper recently published in EPJ Plus, Norwegian physicist Øyvind Grøn from the Oslo and Akershus University College of Applied Sciences and his co-author Torkild Jemterud demonstrate that the rotational motion in the universe is also subject to the theory of relativity. Imagine a person at the North pole who doesn't believe the Earth rotates. As she holds a pendulum and can observe the stars in her telescope, she remarks that the swinging plane of the pendulum and the stars rotate together. Newton, who saw the world as a classical physicist, would have pointed out that it is the Earth that rotates. However, if we assume the general principle of relativity is valid, the Earth can be considered as being at rest while the swinging plane of the pendulum and the night sky are rotating. In fact, the rotating mass of the observable part of the universe causes the river of space--which is made up of free particles following the universe's expansion--to rotate together with the stars in the sky. And the swinging plane of the pendulum moves together with the river of space.

https://www.sciencedaily.com/releases/2 ... 120254.htm

AAF: I hope we all will, someday, be as good at making BIG money as Mr. Trump:
I once made a \$1,000,000,000 note printed on my printer - does that count ?
AAF: Since Szczepan is stationary at the center of the spinning 3-metre radius merry-go-round, then Alice ... looking inwards towards him, must always see Szczepan ... constantly rotating in a circle around Alice herself.
Nonsense.

Since Alice is ALWAYS looking "inwards towards him", then BY DEFINITION Szczepan is ALWAYS in front of her, in her field of view. I do not understand how can you disagree with something so straightforward.

But OK, you claim that he is making a "big circle" around her, which means sometimes he will be positioned behind her - yes? So please describe - clearly and with maths - when you claim that Szczepan will be behind Alice, and so out of Alice's field of view (bearing in mind we've both agreed that he is ALWAYS in front of her).

Briefly, your whole claim seems to be based on wanting BOTH that she is always looking inwards (as per our graphics), AND that she is seeing the roundabout rotate around her (which is only possble if she is rotating on-the-spot herself), and ignoring the fact that those statements are in CONTRADCTION.
AAF: And that is because the above 'stationary Szczepan - rotating Alice' system is very similar to the 'stationary Sun – rotating Earth' system, which had fooled very smart astronomers into deducing the exact opposite what is really going on, for hundreds of years.
As I have said before : The Sun is NOT - repeat NOT - a valid substitution for S_1 nor Szczepan.
S_1 and Szczepan are along the axis of our observer's rotation. The Sun is NOT (of Earth's daily rotation, which is our analogue for S_2's rotation)

So YET AGAIN : Your pictures are flawed, because you are neglecting to take into account that S_1 is along the axis of rotation. You … repeatedly refuse to apply the mathematics to our special case of a body positioned along the axis.

AAF
AAF

It has been one hundred years since the publication of Einstein's general theory of relativity in May 1916. In a paper recently published in EPJ Plus, Norwegian physicist Øyvind Grøn from the Oslo and Akershus University College of Applied Sciences and his co-author Torkild Jemterud demonstrate that the rotational motion in the universe is also subject to the theory of relativity. Imagine a person at the North pole who doesn't believe the Earth rotates. As she holds a pendulum and can observe the stars in her telescope, she remarks that the swinging plane of the pendulum and the stars rotate together. Newton, who saw the world as a classical physicist, would have pointed out that it is the Earth that rotates. However, if we assume the general principle of relativity is valid, the Earth can be considered as being at rest while the swinging plane of the pendulum and the night sky are rotating. In fact, the rotating mass of the observable part of the universe causes the river of space--which is made up of free particles following the universe's expansion--to rotate together with the stars in the sky. And the swinging plane of the pendulum moves together with the river of space.

https://www.sciencedaily.com/releases/2 ... 120254.htm

YEP . . .

Printing a \$1,000,000,000 note is half the job . . .

The other half of the job is to convince the Reserve Bank of Australia:

http://www.rba.gov.au

that the printed \$1,000,000,000 note is genuine!

…...........................................................................................................................................

"In contrast, you claim that an object positioned at/above the north pole travels until it's due EAST of our observer (.... and so continues until that NORTH pole object is due SOUTH of him, yes?) However, even though the observer remains facing north, you reckon this object (that is now East of him) is not off to his right - No, you say it's still straight ahead of him!! All based on some idea that The projected circle is the circle of the rotating observer's latitude as seen by the same observer projected on an external object like S_1. In other words, rather than simply calculating line-of-sight directly with maths, you're basing the whole thing on some flawed idea that "if he sees me moving in a "big circle", then I must see him moving in one as well" (*) - an absurd proposition that is clearly contradicted by the everyday experience of riders viewing central poles of merry-go-rounds. And you reckon all that "makes perfect sense" ????? (*) Heh, reminded me of The Ravenous Bug-Blatter Beast of Traal, that believes that if you can't see it, then it can't see you - so the best way to escape it is to wrap a towel around your head."

An object positioned at/above the north pole must travel in a circle,
if the observer is rotating in a circle.

And if the observer decides to divide and segment that circle to east, west,
south, and north, then he/she can do it in any way he/she likes it to be.

But the fact of the matter is that, come hell or high water, an object positioned
at/above the north pole must travel in a circle, if the observer
is rotating in a circle.

And so, now, let's, please, take our hats off, for the first time,
to the great Aristarchus, the original discoverer
of the solar parallax:

Because ancient Aristarchus of Samos, for certain, was, way more scientific,
visionary, and extremely smarter than modern Albert Einstein!

Ufonaut99
Ufonaut99

It has been one hundred years since the publication of Einstein's general theory of relativity in May 1916. In a paper recently published in EPJ Plus, Norwegian physicist Øyvind Grøn from the Oslo and Akershus University College of Applied Sciences and his co-author Torkild Jemterud demonstrate that the rotational motion in the universe is also subject to the theory of relativity. Imagine a person at the North pole who doesn't believe the Earth rotates. As she holds a pendulum and can observe the stars in her telescope, she remarks that the swinging plane of the pendulum and the stars rotate together. Newton, who saw the world as a classical physicist, would have pointed out that it is the Earth that rotates. However, if we assume the general principle of relativity is valid, the Earth can be considered as being at rest while the swinging plane of the pendulum and the night sky are rotating. In fact, the rotating mass of the observable part of the universe causes the river of space--which is made up of free particles following the universe's expansion--to rotate together with the stars in the sky. And the swinging plane of the pendulum moves together with the river of space.

https://www.sciencedaily.com/releases/2 ... 120254.htm

AAF: An object positioned at/above the north pole must travel in a circle, if the observer is rotating in a circle.
And still just another bland repetition of the claim, with NOTHING given in support of it.

It doesn't even need to be at/above the North Pole. As before :

If I am standing due south of Brisbane CBD, then by definition Brisbane CBD is due North of me. Throughout Earth's rotation, with me not moving a muscle, Brisbane CBD will ALWAYS remain due North of me - and ALWAYS fixed stationary at THE EXACT SAME PLACE in my field of view. NO CIRCLE !.
That remains so clearly, obviously, blatantly, self-evidently true for ANY object that is due North of ANY northward-facing observer (including objects at/above the North Pole), I have no idea how or why you could possibly question it.

Sorry, but your claim remains ludicrous, no matter how many times you repeat it.
AAF: take our hats off, for the first time, to the great Aristarchus
Love that Star; Also made me think of that song Putting on the Ritz

AAF
AAF

It has been one hundred years since the publication of Einstein's general theory of relativity in May 1916. In a paper recently published in EPJ Plus, Norwegian physicist Øyvind Grøn from the Oslo and Akershus University College of Applied Sciences and his co-author Torkild Jemterud demonstrate that the rotational motion in the universe is also subject to the theory of relativity. Imagine a person at the North pole who doesn't believe the Earth rotates. As she holds a pendulum and can observe the stars in her telescope, she remarks that the swinging plane of the pendulum and the stars rotate together. Newton, who saw the world as a classical physicist, would have pointed out that it is the Earth that rotates. However, if we assume the general principle of relativity is valid, the Earth can be considered as being at rest while the swinging plane of the pendulum and the night sky are rotating. In fact, the rotating mass of the observable part of the universe causes the river of space--which is made up of free particles following the universe's expansion--to rotate together with the stars in the sky. And the swinging plane of the pendulum moves together with the river of space.

https://www.sciencedaily.com/releases/2 ... 120254.htm

What are EXACTLY the odds of convincing the Reserve Bank of Australia that
OUR printed \$1,000,000,000 note is genuine?

Although I haven't done any math for it, I shall assume, at once, that the CHANCES,
here, are slightly better than those of selecting & sending UKIP Leader, Nigel Farage,
as an EU chief ambassador to Civilization #2 on Planet #7
around the star Alpha Centauri:

http://www.ukip.org/statement_from_ukip ... esignation

….................................................................................................................................

""AFF: Oh, yeah . . . That is what the Sun is doing everyday"! Utterly irrelevant. The Sun is NOT a valid candidate for S_1. Yet again: Your pictures are flawed, because you are neglecting to take into account that S_1 is along the axis of rotation. You … repeatedly refuse to apply the mathematics to our special case of a body positioned along the axis. "AAF: On the other hand, if the value of H is NOT so large, then S_1 will always appear to be moving, as one single unit, in a circle over the North Pole." And STILL just another empty repetition of the claim, with absolutely no basis or support (let alone any maths) given. Again: Don’t just claim it …. SHOW IT, yes? SHOW WITH MATHS, not just word claims."

The Sun, too, has daily parallax, which is the angle subtended by the mean equatorial
radius of the Earth at a distance of one astronomical unit:

http://www.thefreedictionary.com/solar+parallax

http://www.didaktik.physik.uni-due.de/~ ... s/Idea.htm

The daily rising and setting of the Sun is NOT the solar parallax.

I repeat once again:

The daily rising and setting of the stars is NOT the stellar parallax.

The vast majority of people, who have ever lived on the face of the earth,
have and must have noticed the daily rising and setting
of celestial bodies very well.

But, at the same time, those people could have never noticed or even suspected
the presence of the solar and stellar parallax.

It's just unbelievably strange and too abstract for them . . .

Even the illustrious genius called 'Albert Einstein' never suspected,
in all his entire life, the existence of the S_1 parallax.

the discoverer of the solar parallax:

Because Aristarchus, for sure, is so many light-years ahead of Einstein!

Anyway, the daily rising and setting of celestial bodies are caused by the angular
displacement due to the observer's angular velocity; that is to say, if the observer
is rotating at an angular velocity omega, then, in every interval of time equal
to delta_t, the celestial bodies will appear to rotate by an angle
equal to omega times delta_t.

While the solar and stellar parallax are caused by the linear displacement due to the
observer's linear velocity; that is say, if the observer is traveling at a linear
velocity equal to v, then, in every interval of time equal to delta_t, the celestial
bodies will appear to make an angular displacement equal to
theta = arctan([v x delta_t]/d); where d is the distance
between the observer and the celestial body in question.

Ufonaut99
Ufonaut99

It has been one hundred years since the publication of Einstein's general theory of relativity in May 1916. In a paper recently published in EPJ Plus, Norwegian physicist Øyvind Grøn from the Oslo and Akershus University College of Applied Sciences and his co-author Torkild Jemterud demonstrate that the rotational motion in the universe is also subject to the theory of relativity. Imagine a person at the North pole who doesn't believe the Earth rotates. As she holds a pendulum and can observe the stars in her telescope, she remarks that the swinging plane of the pendulum and the stars rotate together. Newton, who saw the world as a classical physicist, would have pointed out that it is the Earth that rotates. However, if we assume the general principle of relativity is valid, the Earth can be considered as being at rest while the swinging plane of the pendulum and the night sky are rotating. In fact, the rotating mass of the observable part of the universe causes the river of space--which is made up of free particles following the universe's expansion--to rotate together with the stars in the sky. And the swinging plane of the pendulum moves together with the river of space.

https://www.sciencedaily.com/releases/2 ... 120254.htm

AAF: What are EXACTLY the odds of convincing the Reserve Bank of Australia that OUR printed \$1,000,000,000 note is genuine?
Probably better than the odds that people were giving Iceland !
AAF: Nigel Farage, as an EU chief ambassador to Civilization #2 on Planet #7 around the star Alpha Centauri:
I can picture another Civilization that would vie against that one
<blockquote><blockquote><blockquote>Ufonaut99: Utterly irrelevant. The Sun is NOT a valid candidate for S_1. Yet again: Your pictures are flawed, because you are neglecting to take into account that S_1 is along the axis of rotation. You … repeatedly refuse to apply the mathematics to our special case of a body positioned along the axis.
AAF: if the value of H is NOT so large, then S_1 will always appear to be moving, as one single unit, in a circle over the North Pole. </blockquote>
Ufonaut99: And STILL just another empty repetition of the claim, with absolutely no basis or support (let alone any maths) given. Again: Don’t just claim it …. SHOW IT, yes? SHOW WITH MATHS, not just word claims." </blockquote>
AAF: The Sun, too, has daily parallax ... </blockquote>

Utterly irrelevant to "S_1 will always appear to be moving, as one single unit, in a circle over the North Pole" ... or, indeed, to anything in OUR SPECIFIC SCENARIO.

AGAIN : THE SUN IS NOT - REPEAT <font size="+1">NOT - S_1</font>

Look, We are SUPPOSED to be discussing Einstein's Scenario.

S_1 and S_2 are clearly defined in Einstein's scenario as being positioned along a common central axis of rotation.

Discussions about bodies that are NOT so positioned along a common central axis of rotation, are therefore NOT discussions about Einstein's scenario.

If you think that there is some issue about the Sun, Parallax, etc that is applicable to Einstein's scenario, then you should be able to APPLY it TO Einstein's scenario, referencing only S_1 and S_2.
If you cannot apply that issue to Einstein's scenario, then by definition that issue is IRRELEVANT to Einstein's scenario, and therefore to our discussion.

Thus far, over both these threads, you have NEVER followed through and applied anything about the sun nor Parallax to S_1, S_2; You have simply referenced them, but never applied the maths TO OUR SCENARIO.

Case in point :
AAF: While the solar and stellar parallax are caused by the linear displacement due to the observer's linear velocity; that is say, if the observer is traveling at a linear velocity equal to v, then, in every interval of time equal to delta_t, the celestial bodies will appear to make an angular displacement equal to theta = arctan([v x delta_t]/d); where d is the distance between the observer and the celestial body in question.
Yes, that equation theta = arctan([v x delta_t]/d) does give the change in line of sight for parallax - for an observer in STRAIGHT-LINE motion.

S_2 is NOT straight-line motion; It is CIRCULAR.

Look, imagine a car driving in a straight line left-to-right past our merry-go-round, camera out the side window. One moment the central pole is to the right of the camera, next it's to the left. That's Parallax, as given by that equation. Fine.
However, that does NOT describe Alice, who is rotating round with the merry-go-round always looking straight at the central pole. That pole is ALWAYS straight in front of her, not to her left nor right. That is exactly what we expect from common-sense and see by looking at both merry-go-rounds and Polaris. Your claims that the central pole in that merry-go-round scenario would swing to her left and to her right remain ludicrous despite the mathematics of straight-line motion.

Again: Your pictures are flawed, because you are neglecting to take into account that S_1 is along the axis of rotation. You repeatedly refuse to apply the mathematics to our special case of a body positioned along the axis.

PLEASE: apply any points and maths to S_1 and S_2, preferably referencing our graphic. There was nothing in your previous post that did.

Now, let's put some actual figures into your claim - eg. say that our camera has a field of view of a square 1 degree (so nice big telephoto lens ).
We agree that :
- D = arctan(H / 3000) , where D is the angle of line of sight from our camera to the centre of S_1
- H is constant throughout S_2's revolution - let's take our graphic, with H = 4,000km
- Consequently :
[color=#FF0000" size="+1]D = arctan(H / 3000) = arctan( 0.75 ) = 53 degrees[/color] (-ish!)

However, you claim that it will be observed travelling in "big circles in the sky" - say 5 degrees radius, OK? So at the top of the circle it's at 58 degrees, at the bottom at 48 degrees.

So what we have is (as seen by a human behind our camera) is the following - our camera's field of view being the bit in Yellow :

So I say S_1 is always at that D=53 degrees line, by definition.

You claim that, even though neither the H nor the 3,000 values change, that the line of sight to S_1 - that [color=#FF0000" size="+1]D = arctan( 0.75 ) sometimes = 58, and sometimes = 48 !!![/color]

THAT is what I am still waiting for you to come up with some justification for.

Height in the sky is the angle D by defintion - and also by definition, D is constant in our scenario. Your wordy descriptions of "projected circles", etc are wrong.