## 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

"...I can still remember being surprised at how inquisitive and friendly
this thing was - it was actively looking around, and seeing what
was going on. Interesting creatures.... An observer who moves has
never been in question; I am disputing your claim that an observer
who does NOT move will see see an up/down motion of S_1. THAT claim,
since travel “along the periphery of a big circle” includes an up/down
component. Let’s say the radius of your supposed circle is X degrees.
It is clear from the illustration that S_1 is ALWAYS 3,000km straight
ahead of the camera, and ALWAYS 4,000km above the camera. It’s line of
sight, by simple trigonometry, is therefore ALWAYS at an angle of 53 degrees.
Except you claim it’s not. You claim that that 3,000km 4,000km right-angled
triangle sometimes has an angle of 53+X degrees, and sometimes has an angle
of 53-X degrees, even though (by definition from the illustration) the lengths
of the triangle never change. THAT is the claim I am asking you to justify."

Of course, the carpet python is very inquisitive and friendly, when it's young and tiny like this:

Even Jack the Ripper was so lovely and friendly,
when he was a kid:

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

I presume!

But we have to wait, until its size becomes slightly gigantic like this::

O.K. . .

The observer on S_2, as depicted in the above illustration, is always at rest
in the same location.

Now, S_2 is either rotating or at rest:

[1.] If S_2 is at rest, then S_1 will appear, to the observer,
to be at rest as well.

[2.] But if S_2 is rotating around its geometrical axis, then S_1
will appear, to the same observer, to be in orbital motion
around absolutely nothing.

What is the justification for the last one?

Well; it's obvious . . .

The observer, in the latter case, thinks he's at rest; but he's, actually,
constantly moving along the circumference of a huge circle
whose diameter is equal to 6,000 km.

And furthermore, the angle of 53 degrees,between the observer and S_1,
is not a 2-dimensional, plane angle, but a 3-dimensional,
solid angle, like this one:

And therefore, S_1 has no other scenario beside appearing, to the observer
on S_2, to be traveling constantly along the circumference of a humongous
circle on the sky and centered around the North Pole.

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

Actually, young jungle pythons can be quite aggressive and snappy - maybe because they are so small and vulnerable. My son’s also tend to stay out of their hides more than others, which probably also contributes. As they get older, they mellow (a little!) - maybe because they’re bigger and/or maybe because they get used to being handled.
AAF: The observer on S_2, as depicted in the above illustration, is always at rest in the same location. …. The observer, in the latter case, thinks he's at rest; but he's, actually, constantly moving along the circumference of a huge circle whose diameter is equal to 6,000 km. And furthermore, the angle of 53 degrees,between the observer and S_1, is not a 2-dimensional, plane angle, but a 3-dimensional, solid angle, like this one:
Yes. So in that picture, our camera is travelling around the upper slice, and S_1 is the point at the centre of the sphere, so forming a downward-pointing cone.
AAF: And therefore, S_1 has no other scenario beside appearing, to the observer on S_2, to be traveling constantly along the circumference of a humongous circle on the sky and centered around the North Pole.
And no. Again, just another unsubstantiated repetition of the claim.

If I regard myself as stationary, then by definition I regard everything else that is stationary-relative-to-me as also being stationary. So, where is S_1 relative to me? IT IS STATIONARY. It is always at exactly 3,000km straight in front and 4,000km up from me. It is at that location regardless of whether I am stationary or whether I am moving - there is no change. To take the cone picture, my camera is whizzing around the circle at the base of the cone looking up (or down!) at the tip. If my camera is stationary, then I regard the cone as rotating, but that does not translate into my seeing the tip moving. (*)

Your pictures are flawed, because you are neglecting to take into account that S_1 is along the axis of rotation. You are actually arguing the general case of bodies at OTHER locations, but repeatedly refuse to apply the mathematics to our special case of a body positioned along the axis. For example, taking the cone again, if we were to be looking at the general case of a star that is away from the axis, then that cone would be lopsided. The camera being stationary and the cone rotating would then certainly result in our seeing the tip moving. For our special case of a body positioned along the axis, however, the cone is symmetrical, and so the tip does not move.

So, leave those words, and instead concentrate on the plain simple maths that is clearly shown in the illustration :
- S_1 is always 3,000km straight ahead and 4,000km up from the camera
- That results in the line-of-sight always being at a 53 degree angle
- You claim that, at say the bottom of the supposed circle, the line of sight will be less than 53 degrees

Please describe in concise mathematical detail how you reckon this is possible.

(*) For completeness sake, it’s worth mentioning that an alternate picture - that of the cone rotating “around” (from in-front, to behind, to in front again) the camera - is not applicable for this scenario, as it is in stark contradiction to the illustration where S_1 is always in front of the camera

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

"Actually, young jungle pythons can be quite aggressive and snappy . . . . Yes. So in that picture, our camera is travelling around the upper slice, and S_1 is the point at the centre of the sphere, so forming a downward-pointing cone. "And therefore, S_1 has no other scenario beside appearing, to the observer on S_2, to be traveling constantly along the circumference of a humongous circle on the sky and centered around the North Pole". And no. Again, just another unsubstantiated repetition of the claim. If I regard myself as stationary, then by definition I regard everything else that is stationary-relative-to-me as also being stationary. So, where is S_1 relative to me? IT IS STATIONARY. It is always at exactly 3,000km straight in front and 4,000km up from me. It is at that location regardless of whether I am stationary or whether I am moving - there is no change. To take the cone picture, my camera is whizzing around the circle at the base of the cone looking up (or down!) at the tip. If my camera is stationary, then I regard the cone as rotating, but that does not translate into my seeing the tip moving. (*) Your pictures are flawed, because you are neglecting to take into account that S_1 is along the axis of rotation. You are actually arguing the general case of bodies at OTHER locations, but repeatedly refuse to apply the mathematics to our special case of a body positioned along the axis. For example, taking the cone again, if we were to be looking at the general case of a star that is away from the axis, then that cone would be lopsided. The camera being stationary and the cone rotating would then certainly result in our seeing the tip moving. For our special case of a body positioned along the axis, however, the cone is symmetrical, and so the tip does not move. So, leave those words, and instead concentrate on the plain simple maths that is clearly shown in the illustration: - S_1 is always 3,000km straight ahead and 4,000km up from the camera - That results in the line-of-sight always being at a 53 degree angle - You claim that, at say the bottom of the supposed circle, the line of sight will be less than 53 degrees. Please describe in concise mathematical detail how you reckon this is possible. (*) For completeness sake, it’s worth mentioning that an alternate picture - that of the cone rotating “around” (from in-front, to behind, to in front again) the camera - is not applicable for this scenario, as it is in stark contradiction to the illustration where S_1 is always in front of the camera."

YEP . . .

They can be quite snappy:

http://www.acreptiles.com/main/index.ph ... Itemid=140

In this illustration:

S_1 is only 4,000 km over the North Pole.

And so, if the observer, on the rotating S_2, looks at S_1 from the east, S_1 will appear in the west.

And if the observer, on the rotating S_2, looks at S_1 from the west, S_1 will appear in the east.

And because the observer, on the rotating S_2, is traveling along a big circle, the end result of
changing perspective, in this particular case, is a big circle, on the sky, along which
S_1 appears to travel around the North Pole.

But why doesn't S_1, in this scenario, behave like the star Polaris and stay stationary over the
North Pole?

It's because S_1 is only 4,000 km over the North Pole.

While the star Polaris, by contrast, is more than 323 light-years over the same North Pole.

And therefore, the angle between the observer and the star Polaris is much greater than 53 degrees;
and almost equal to 90 degrees.

In short, in order to make S_1 appear stationary, the observer must stand right smack on the exact
geometrical point of the North Pole.

Right?

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: YEP . . . They can be quite snappy:
Heh, he hasn’t got snapped like that. They do have teeth and can draw blood - so that guy would have had an interesting story to dine out on

Mind you, it could have been worse ..

AAF: S_1 is only 4,000 km over the North Pole.
ONLY 4,000 km ???? Hey, I think it’s a long way down to the chemists ……..
AAF: And so, if the observer, on the rotating S_2, looks at S_1 from the east, S_1 will appear in the west.
And if the observer, on the rotating S_2, looks at S_1 from the west, S_1 will appear in the east.
I don’t see what that’s got to do with up/down motion that we were discussing, but OK, its you want to add Left/Right motion (which, of course, is equally implicit in circular motion) to the question ….

- when the observer is to the West, he is looking due East, and S_1 all also appear due East - ie. S_1 appears exactly in front of him.
- when the observer is to the South, he is looking due North, and S_1 all also appear due North - ie. S_1 appears exactly in front of him.
- when the observer is to the East, he is looking due West, and S_1 all also appear due West - ie. S_1 appears exactly in front of him.
- when the observer is to the North, he is looking due South, and S_1 all also appear due South - ie. S_1 appears exactly in front of him.

So, in addition to when the observer sees S_1 move Up/Down, we can now add the question : when and how you reckon he sees S_1 move Left/Right ?
AAF: But why doesn't S_1, in this scenario, behave like the star Polaris and stay stationary over the North Pole? It's because S_1 is only 4,000 km over the North Pole. While the star Polaris, by contrast, is more than 323 light-years over the same North Pole. And therefore, the angle between the observer and the star Polaris is much greater than 53 degrees; and almost equal to 90 degrees.
Utterly irrelevant. The maths remains the same, whatever the value for the height. Let’s replace that 4,000km with a variable H km.
Consequently, our line of sight angle of 53 degrees is simply arctan(H/3,000) - let’s call it D.

So, make H however large you like, the question remains : when and how you reckon he sees S_1 move above/below D ?
AAF: In short, in order to make S_1 appear stationary, the observer must stand right smack on the exact geometrical point of the North Pole. Right?
Blatantly wrong. Not according to the maths (nor the illustration) he doesn’t.

So again, you are just making claims some “Big Circle” with words instead of maths - and those words are blatantly wrong. As I said before : don’t just claim it …. SHOW IT, yes?

SHOW how something that is always 3000Km straight ahead, and 4000Km up, can be at anything other than that 53 degree angle in the sky.

SHOW how something that is always straight ahead of the camera, can appear to move to the Left or Right.

SHOW WITH MATHS, not just word claims.

Right ?

As an aside, it’s worthwhile considering what an effect a 4,000km height instead of a 323 light year height would have. The 4,000km will appear lower in the sky than Polaris. The other existing far stars, of course (assuming they could be seen ), would of course be entirely unaffected by this, and continue to produce their existing circular star trails. This would mean that those circles would not be centred on our 4,000km object. That’s irrelevant of course, since we are discussing S_1 staying at the same point in the sky, not staying at the centre of star-trails. S_1 will appear motionless, just as the centre pole of a merry-go-round that I’m riding appears motionless to me, even though that’s nowhere near even the 4,000km high

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

"ONLY 4,000 km ???? Hey, I think it’s a long way down to the chemists …….. I don’t see what that’s got to do with up/down motion that we were discussing, but OK, its you want to add Left/Right motion (which, of course, is equally implicit in circular motion) to the question …. - when the observer is to the West, he is looking due East, and S_1 all also appear due East - ie. S_1 appears exactly in front of him. - when the observer is to the South, he is looking due North, and S_1 all also appear due North - ie. S_1 appears exactly in front of him. - when the observer is to the East, he is looking due West, and S_1 all also appear due West - i.e. S_1 appears exactly in front of him. - when the observer is to the North, he is looking due South, and S_1 all also appear due South - ie. S_1 appears exactly in front of him. So, in addition to when the observer sees S_1 move Up/Down, we can now add the question : when and how you reckon he sees S_1 move Left/Right?"

YEP!

It's June 2 – Yell "Fudge" at the Cobras in North America Day:

http://every-day-is-special.blogspot.co ... north.html

We are not discussing 'up/down' motion anymore, because you said earlier that the observer
is not allowed to approach or recede from the North Pole!

And so, the observer, on the rotating S_2, can only travel along a circle with a radius equal
to 3,000 km.

In short, our current scenario is just like as if you tie one end of a very long rope to the top
of this Uluru (Ayers Rock):

http://amazingdubaigu.blogspot.com/2013 ... pMJMK.dpbs

and then you stretch it and hold its other end and begin moving in a big circle around
that giant rock.

Now, if you assume that you are stationary, then you must accept that Uluru (Ayers Rock)
is really moving in a big circle around you;
right?

And the MATH of it, of course, is next time ...

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: It's June 2 – Yell "Fudge" at the Cobras in North America Day:
Mmmm, Fudge I wonder if that’s how St Patrick got all the snakes out of Ireland ?? Wish it would work against Cane Toads, though
But not the maroon cane toads - they’re great at crushing the blue cockroaches
AAF: We are not discussing 'up/down' motion anymore, because you said earlier that the observer is not allowed to approach or recede from the North Pole!
We most certainly ARE still discussing up/down motion; As I clearly stated : “I am disputing your claim that an observer who does NOT move will see an up/down motion of S_1

From the illustration and basic trigonometry, S_1 at height H km will always appear in the sky at angle arctan(H/3,000) - let’s call it D degrees.

But you claim that our observer stationary on S_2 will see S_1 make a circular orbit in the sky - let’s say with radius R degrees.

That would mean that our stationary observer sometimes sees S_1 at D+R degrees, and sometimes at D-R degrees.

So yet again : don’t just claim it …. SHOW IT, yes?

SHOW how something that is always 3000Km straight ahead, and H km up, can ever be at anything other than that D degree angle in the sky.

SHOW how a right-angled-triangle with base 3,000km and height H km, can have that angle being D-R degrees.

Take our H=4,000km straight from the illustration if you like - SHOW how and when our observer sees S_1 at less than 53 degrees

SHOW WITH MATHS, not just word claims.

Next post, yes?

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

Hi, Ufonaut99:

It is not just Ireland; but, also, New Zealand, Hawaii, Greenland, Iceland, and Antarctica don’t have snakes:

http://www.popsci.com/why-doesnt-ireland-have-snakes

Just take a closer look at this thing:

It's called the 'hooded malpolon'.

And although harmless, it's playing the role of the cobra so well, that Indian and
Australian soldiers in Montgomery's army, fighting in the Sahara desert in 1942,
were more scared of it than of Erwin Rommel himself and his tanks!

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

"Utterly irrelevant. The maths remains the same, whatever the value for the height. Let’s replace that 4,000km with a variable H km. Consequently, our line of sight angle of 53 degrees is simply arctan(H/3,000) - let’s call it D. So, make H however large you like, the question remains : when and how you reckon he sees S_1 move above/below D? Blatantly wrong. Not according to the maths (nor the illustration) he doesn’t. So again, you are just making claims some “Big Circle” with words instead of maths - and those words are blatantly wrong. As I said before : don’t just claim it …. SHOW IT, yes? SHOW how something that is always 3000Km straight ahead, and 4000Km up, can be at anything other than that 53 degree angle in the sky. SHOW how something that is always straight ahead of the camera, can appear to move to the Left or Right. SHOW WITH MATHS, not just word claims. Right? As an aside, it’s worthwhile considering what an effect a 4,000km height instead of a 323 light year height would have. The 4,000km will appear lower in the sky than Polaris. The other existing far stars, of course (assuming they could be seen), would of course be entirely unaffected by this, and continue to produce their existing circular star trails. This would mean that those circles would not be centred on our 4,000km object. That’s irrelevant of course, since we are discussing S_1 staying at the same point in the sky, not staying at the centre of star-trails. S_1 will appear motionless, just as the centre pole of a merry-go-round that I’m riding appears motionless to me, even though that’s nowhere near even the 4,000km high".

The height of S_1, over the North Pole, is very important.

Because the diameter of the projected circle of the observer's latitude, on the sky,
is inversely proportional to the height of S_1 over the North Pole; i.e., the larger
the height; the smaller the subtended circle;
and vice versa.

As for the math, here, it's exactly the same as the math of parallax:

http://www.esa.int/Our_Activities/Space ... a/Parallax

But whether S_1 is assumed to be too close or faraway, Einstein's assumption
of relative rotation is always false.

And that is because, if S_1 is nearby, then it must appear to travel along a huge circle,
because its parallax is big.

And if S_1 is faraway, then it must appear to be non-rotating and stationary, because
its parallax is so tiny and very close to nil.

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

Hey AAF
AAF: It is not just Ireland; but, also, New Zealand, Hawaii, Greenland, Iceland, and Antarctica don’t have snakes:
http://www.investigatemagazine.co.nz/In ... ents/”>Not native snakes, no

That hooded malpolon looks fierce - I can certainly understand why even brave soldiers got jittery Equally fierce looking is this one - love that array of bulging teeth :

When I first arrived in Australia, I thought I’d take up Scuba diving. After getting my licence, I thought “What’s a good first dive to do?”, and it just so happened a local dice shop was having a Shark-Dive So we drove up to Seal Rocks, and dived to see these (that photo’s nothing to do with me, though ! ) These are “Grey Nurse” sharks, and are actually quite docile - beautiful creatures. Unfortunately, their appearance led to them getting a bad reputation - even as man eaters - and they were hunted, so they’re still on the endangered list today

Let’s clarify the last point first :
AAF: if S_1 is faraway, then it must appear to be non-rotating and stationary, because its parallax is so tiny and very close to nil
Sorry, but I couldn’t care less about “very close to nil” I’m talking about the maths - and maths is not dependent on the resolving power of our telescope. Either S_1 is in EXACTLY the same position in the sky, or it is not. So let’s leave the fudge factor of “so tiny” out of it; that is not what we are talking about - right ?

And that, in turn, means The height of S_1, over the North Pole, is still totally unimportant.

Which brings us to :
AAF: As for the math, here, it's exactly the same as the math of parallax:
Really ??? Because that page you linked to, that has that graphic, describes Parallax as : “<font>Now open the other eye, and close the first. Your finger appears to move against the more distant objects, even though you haven’t moved it. This is parallax!</font>” …. but our scenario explicitly does not have any “more distant objects”, remember ? So no, it can’t be the same as that.

What about the “close the first [eye]” bit? Again no, that’s a different scenario from ours, since “your finger” is not on any axis of rotation (unless you have very weird eyes !!), so the maths can’t be the same as that one either.

So what I said earlier still holds : 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.

I am asking you, to make a clear case, in your own words, on OUR explicit scenario. That’s actually one of the main reasons I’ve been repeatedly asking “SHOW WITH MATHS, not just word claims”, because that it’s only by the maths - APPLIED TO THIS SCENARIO - that your argument becomes clear and unambiguous.

So again, for OUR scenario where S_1 is positioned along the axis of rotation :

D = arctan( H / 3000 ) is the equation, and for a given H and a stationary observer, that angle D does NOT change during S_2’s revolution …… except, of course, you claim that it does.

SHOW how something that is always 3000Km straight ahead, and H km up, can ever be at anything other than that D degree angle in the sky.

SHOW how a right-angled-triangle with base 3,000km and height H km, can have that angle being D-R degrees.

Take our H=4,000km straight from the illustration if you like - SHOW how and when our observer sees S_1 at less than 53 degrees

SHOW WITH MATHS, not just word claims - Yes ?

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!

It looks as fiercesome & fearsome as its cousin, the great white shark:

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

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

"We most certainly ARE still discussing up/down motion; As I clearly stated : “I am disputing your claim that an observer who does NOT move will see an up/down motion of S_1”. From the illustration and basic trigonometry, S_1 at height H km will always appear in the sky at angle arctan(H/3,000) - let’s call it D degrees. But you claim that our observer stationary on S_2 will see S_1 make a circular orbit in the sky - let’s say with radius R degrees. That would mean that our stationary observer sometimes sees S_1 at D+R degrees, and sometimes at D-R degrees. So yet again : don’t just claim it …. SHOW IT, yes? SHOW how something that is always 3000Km straight ahead, and H km up, can ever be at anything other than that D degree angle in the sky. SHOW how a right-angled-triangle with base 3,000km and height H km, can have that angle being D-R degrees. Take our H=4,000km straight from the illustration if you like - SHOW how and when our observer sees S_1 at less than 53 degrees. SHOW WITH MATHS, not just word claims."

An observer who does not move, can see nothing:

No up/down motion & no circular motion!

But the rotating observer, on S_2, can see that S_1 is making a circle, on the sky,
directly proportional to the circle, along which he/she is moving; and inversely
proportional to the distance between S_1 & S_2.

Surely, S_1 is always '3000Km straight ahead, and H km up'.

Nonetheless, the straight line between the observer & S_1 is constantly sweeping the sky
and drawing a huge circle, along which S_1 appears to be continuously and tirelessly
moving around the North Pole.

What about the math of it?

Well; the math has already been worked out by the astronomers:

http://www.math.nus.edu.sg/aslaksen/gem ... rallax.pdf

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: It looks as fiercesome & fearsome as its cousin, the great white shark: https://en.wikipedia.org/wiki/Sand_tiger_shark
Typo :https://en.wikipedia.org/wiki/Great_white_shark
No kidding, if I saw a great white while I was diving, I’d be jumping out of that water faster than a stingray !
Grey Nurses are nice, though. I remember one dive, we turned up where there were 4 or 5, so they decided just to go away ... except one came back just to have a look at us (not to eat us ! )
AAF: Surely, S_1 is always '3000Km straight ahead, and H km up'.

Now, ’3000Km straight ahead, and H km up' is ALWAYS the same triangle, as shown in our graphic - and therefore by definition, S_1 is always at angle D = arctan( H / 3000 ) straight ahead (neither left nor right) to our observer.

Not D + R nor D - R; ALWAYS just plain D.

By definition.
AAF:But the rotating observer, on S_2, can see that S_1 is making a circle
THEN SHOW IT ! Don’t just keep claiming it - show it with maths, and not just words - yes ?

As I said before : 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.

Speaking of neglecting to take into account S_1 being on the axis of rotation .....
AAF: Well; the math has already been worked out by the astronomers:
Yes - and that maths in that paper is full of scenarios like :
- “your finger” in front of “your” eye - NOT APPLICABLE TO THIS EXPLICIT SCENARIO
- Calculating distances using Parallax - NOT APPLICABLE TO THIS EXPLICIT SCENARIO
- Simultaneous measurements from two locations - NOT APPLICABLE TO THIS EXPLICIT SCENARIO
- Appearance shifting against background of stars - NOT APPLICABLE TO THIS EXPLICIT SCENARIO

Those scenarios (and more) are all applicable and incredibly useful with real-life Earth-based Parallax calculations - but that does NOT make them applicable to THIS EXPLICIT SCENARIO.

Seriously, I asked you to make a clear case, in your own words, on OUR explicit scenario. That’s actually one of the main reasons I’ve been repeatedly asking “SHOW WITH MATHS, not just word claims”, because that it’s only by the maths - APPLIED TO THIS SCENARIO - that your argument becomes clear and unambiguous.

Instead, you just point to some 50 page document, leaving all readers to guess which - if any - of the maths you think is applicable.

So no more links to random pages on Parallax, which will be full of those scenarios not applicable to us - OK ? If you continue to think that Parallax is somehow applicable, then you should be able to SHOW it here - right ? After all, ours is not a complex scenario, so easy to describe with no reason to link off anywhere else.