[Astrophysics]

The unshakable method of science sounds like "Science is refutable." Details:
https://en.wikipedia.org/wiki/Falsifiability
Same thing: "Science is possible to refute." Why then not to take opportunity? It is just like possibility of opening the can of fish. It is possible to open can, why then not?! "The theory is Scientific, if it can be shown, that theory is wrong." Why nobody is laughing at this Popper's idea?
Perhaps theory is Science, if it can be rather proven or at least confirmed several times? The Popper's idea is not the same as saying "Possibly, the Science is refutable." Latter rejects the Popper as established, unshakable method of Science.

More: https://www.theflatearthsociety.org/forum/index.php?topic=78569.0

[Rama Set]

I don’t know what this “Dark Force” you refer to is. Can you link to anything describing it?

[rabinoz]

Consider in your imagination three bullets, which fly on a ring orbit around the Sun. The distance between the bullets is just couple decimeters. The bullets A and B are non-rotating bullets, but bullet C rotates around own axis of symmetry W. The segment AB has same direction as the axis W.

Let's ignore you "bullets A and B" as they are they would orbit on their own or if close to the earth would just fall to earth.

According to Newton the inertial frame is such reference system, where free objects (our bullets A and B, and even C) hold the constant position (or velocity vectors, and angular momentum vector (of C)).

No, there is nothing to say that "according to Newton" "free objects (our bullets A and B, and even C) hold the constant position" because they are subject to very slightly different forces.

Thus, there is no global huge inertial frame. Why? Because in addition to Newton's contribution, the Einstein has found out, that Gravity is not a force, thus, free falling objects (and free orbiting Sun bullets) are truly free. Therefore, the needed inertial frame is small and local, it co-moves with bullets.

No that is not correct, Einstein's GR would give exactly the same result as Newton's Laws of Motion and Gravitation to a precision better than you could dream of measuring.
From

One condition the new equations must satisfy is that they must return Newtonian results for ordinary conditions. For Newton's theory works extraordinarily well for the weak, static gravitational fields of our solar system. The sentence highlighted in red says:
"However it turns out that this tensor does not reduce to the [Newtonian expression] Δφ in the case of infinitely weak, static gravitational fields."

From: Einstein's Pathway to General Relativity, Assembling the Pieces: The "Entwurf" Paper of 1913

Therefore, while the motion of these group A,B,C around the Sun, the segment AB (and W) changes its direction, it is not fixed on North Star. Hereby we are not talking about slow hypothetical precession of W axis (over 10 000 year period), but we are considering large changes of direction during one year period.

Note, that the axis of rotation of the Earth (the bullet C is the model of Earth) is not perpendicular to the plane of
the orbit around the Sun. If the Celestial Pole has 23 degree angle from the perpendicular to solar system, then the annual motion of Celestial Pole would have 23 degree radius unless the "Dark Force'' is present.

No, there is absolutely no need for any "Dark Force''.
Conservation of angular momentum (a vector, so it's in magnitude and direction) will keep the direction of the rotational axis of the earth always in a direction very close to that Polaris as in this very out-of-scale diagram:

Remember that Polaris has a declination of +89° 15′ 50.8″ so is about 0.74° from the North Celestial Pole.

It turns out, that in Newton's theory, in addition to Dark Matter, there is also a Dark Force turning the axis of the Earth towards the North Star.
However, the Dark Force might not be introduced, if the Flat Earth model is used. But even if it is necessary for FE, then it accounts for visible effects in FE model,
which otherwise would point to Globe Earth model.

As pointed out above, there is absolutely no need for any "Dark Matter" or "Dark Force" to turn "the axis of the Earth towards the North Star."

Alternative proof:
Imagine, that the angular velocity of bullet C is zero: w=0. Then segment ABC with axis of symmetry W is changing its direction in described way.
Then we let C rotate very very slowly: w=0.0000000000001 rad/sec. Then, because the system is physical, the ABC and W will continue the same action in described way. That means Newton's First law as conservation of direction of segment between two small free objects (not only the conservation of angular momentum we see in inertial laboratory!).

So your "Alternative proof" is quite unnecessary and meaningless.

The unshakable method of science sounds like "Science is refutable." Details:
https://en.wikipedia.org/wiki/Falsifiability
Same thing: "Science is possible to refute." Why then not to take opportunity? It is just like possibility of opening the can of fish. It is possible to open can, why then not?! "The theory is Scientific, if it can be shown, that theory is wrong."

The possibility that a can is able to be opened is quite diferent to someone being able to do it.

But no, "Science" is not what is 'falsifiable" because that statement is quite meaningless.
It is the individual theories of science that are falsifiable but sure If it is possible to open can, why then not? But real science is attempting to do that all the time.

Why nobody is laughing at this Popper's idea?
Perhaps theory is Science, if it can be rather proven or at least confirmed several times? The Popper's idea is not the same as saying "Possibly, the Science is refutable." Latter rejects the Popper as established, unshakable method of Science.

No a hypothesis might be taken as a theory when is has been confirmed by sufficient observations and is shown to have predictive value.
Newton's Laws Theories of Motion and Gravitation certainly had predictive value as they not only showed the reason for Kepler's hypothesised elliptical orbits but the oblateness of the earth.
Newton's value for that oblateness, approximate though it was, agreed quite closely with measurements taken soon after and to this day.

Popper's idea is that the theories of science have to be "falsifiable".
They will, however, remain "theories of science" until they are falsified and will then have their range of applicability limited and/or be replaced by a better theory.

[Astrophysics]

I don’t know what this “Dark Force” you refer to is. Can you link to anything describing it?

It is term in my own unpublished yet research. Noh, indeed: Wikipedia says, that there is Dark Matter. But with matter (tables, insects, flowers) comes force, which drives and changes it.

[Astrophysics]

Popper's idea is that the theories of science have to be "falsifiable".
They will, however, remain "theories of science" until they are falsified and will then have their range of applicability limited and/or be replaced by a better theory.

One hundred percent sure, comrade. :-) Officials cirtainly clean the mess they are creating. LOL:
John P.A. Ioannidis, ``Why Most Published Research Findings Are False''. PLoS Medicine.  2: e124, 2005.

[rabinoz]

Popper's idea is that the theories of science have to be "falsifiable".
They will, however, remain "theories of science" until they are falsified and will then have their range of applicability limited and/or be replaced by a better theory.

One hundred percent sure, comrade. :-) Officials cirtainly clean the mess they are creating. LOL:
John P.A. Ioannidis, ``Why Most Published Research Findings Are False''. PLoS Medicine.  2: e124, 2005.

There is nothing in that video about any "theories" in the strict scientific sense being debunked though it does show a recognized defect in the "publish or perish" philosophy.
But I hope you noted that steps are being taken rectify that situation.

But one thing you have done is helped demonstrate that "science" does not censor publications that disagree with "mainstream science" in the way many claim.

But laugh all you like but that video is quite irrelevant to your attempt to disprove the heliocentric solar system.
Now would you please answer the points that I raised in my reply to your OP.  Remember these points that you have totally ignored?

According to Newton the inertial frame is such reference system, where free objects (our bullets A and B, and even C) hold the constant position (or velocity vectors, and angular momentum vector (of C)).

No, there is nothing to say that "according to Newton" "free objects (our bullets A and B, and even C) hold the constant position" because they are subject to very slightly different forces.

Note, that the axis of rotation of the Earth (the bullet C is the model of Earth) is not perpendicular to the plane of the orbit around the Sun.
If the Celestial Pole has 23 degree angle from the perpendicular to solar system, then the annual motion of Celestial Pole would have 23 degree radius unless the "Dark Force'' is present.

<< addition: What do you even mean by "would have 23 degree radius"? >>
No, there is absolutely no need for any "Dark Force''.
Conservation of angular momentum (a vector, so it's in magnitude and direction) will keep the direction of the rotational axis of the earth always in a direction very close to that Polaris as in this very out-of-scale diagram:

Remember that Polaris has a declination of +89° 15′ 50.8″ so is about 0.74° from the North Celestial Pole.

It turns out, that in Newton's theory, in addition to Dark Matter, there is also a Dark Force turning the axis of the Earth towards the North Star.

As pointed out above, there is absolutely no need for any "Dark Matter" or "Dark Force" to turn "the axis of the Earth towards the North Star."

All that is needed to keep the axis of the earth's pointing in the same direction is conservation of angular momentum.
Any applied torque will cause a precession of that direction and that slow precession is the cause of the "precession of the equinoxes".
"Hipparchus is credited with discovering precession of the equinoxes".

[Astrophysics]

As pointed out above, there is absolutely no need for any "Dark Matter" or "Dark Force" to turn "the axis of the Earth towards the North Star."

All that is needed to keep the axis of the earth's pointing in the same direction is conservation of angular momentum.
Any applied torque will cause a precession of that direction and that slow precession is the cause of the "precession of the equinoxes".
"Hipparchus is credited with discovering precession of the equinoxes".

I can not add to mine arguments. You have your opinion, and I - mine. Mine opinion is sent to EPJC for peer-review. We will see the result.

[rabinoz]

As pointed out above, there is absolutely no need for any "Dark Matter" or "Dark Force" to turn "the axis of the Earth towards the North Star."

All that is needed to keep the axis of the earth's pointing in the same direction is conservation of angular momentum.
Any applied torque will cause a precession of that direction and that slow precession is the cause of the "precession of the equinoxes".
"Hipparchus is credited with discovering precession of the equinoxes".

I can not add to mine arguments. You have your opinion, and I - mine. Mine opinion is sent to EPJC for peer-review. We will see the result.

You really have made no arguments.
All you have done is to make baseless claims that to me seemed quite incorrect then refused to answer my requests for elucidation.
So either you back up your claims or we're done.

[Astrophysics]

All you have done is to make baseless claims that to me seemed quite incorrect then refused to answer my requests for elucidation.
So either you back up your claims or we're done.

Is gravity a force? Newton - yes, Einstein - no.

[rabinoz]

All you have done is to make baseless claims that to me seemed quite incorrect then refused to answer my requests for elucidation.
So either you back up your claims or we're done.

Is gravity a force? Newton - yes, Einstein - no.

I'm waiting for your answers to my questions!

But as to: "Is gravity a force? Newton - yes, Einstein - no."
Not quite there is no real difference in the end result under low velocity (<< c) and low mass (even near the sun the deviation is almost immeasurably small).
And the reason for that is because Einstein, having noted that "Newton's theory works extraordinarily well for the weak, static gravitational fields of our solar system", designed GR that way.

In Einstein's GR, mass (and energy) cause spacetime to curve. Objects in "free fall" (subject to no forces) follow what are known as geodesics in spacetime.
Objects prevented from following a geodesic in spacetime, such as resting on a table or supported by a rope, experience an inertial force comparable to, say, centripetal force.

So in Einstein's GR gravitation can still be looked on as "being a force".
But instead of simply being mass attracts mass, GR asserts that mass causes spacetime to curve and the force results from preventing an object from following this curvature.

There's a lot more that could be said but it should be pointed out that spacetime can be broken up into spacelike and timelike components.
The curvature in our region of space is extremely small (parts in 10⁹) but that is enough to explain gravity.

Forces that result from being in a non-inertial frame of reference, such as centrifugal force or the force felt when in an accelerating vehicle, are commonly known as pseudo-forces because they are due to the FOR we are in. But they are certainly real forces to the object or person experiencing them.

But there is no reason to use GR in any calculations you or I are likely to do - within the Solar System it is only needed when extreme accuracy is needed.

<< Add explanation re non-inertial frame of reference. >>

[Astrophysics]

All you have done is to make baseless claims that to me seemed quite incorrect then refused to answer my requests for elucidation.
So either you back up your claims or we're done.

Is gravity a force? Newton - yes, Einstein - no.

I'm waiting for your answers to my questions!

But as to: "Is gravity a force? Newton - yes, Einstein - no."
Not quite there is no real difference in the end result under low velocity (<< c) and low mass (even near the sun the deviation is almost immeasurably small).
And the reason for that is because Einstein, having noted that "Newton's theory works extraordinarily well for the weak, static gravitational fields of our solar system", designed GR that way.

You know the subjects very well. What are your questions? If gravity is a force, then bullets are not free. Therefore, they are not subject to Newton first law. Do you follow?

[rabinoz]

I'm waiting for your answers to my questions!

But as to: "Is gravity a force? Newton - yes, Einstein - no."
Not quite there is no real difference in the end result under low velocity (<< c) and low mass (even near the sun the deviation is almost immeasurably small).
And the reason for that is because Einstein, having noted that "Newton's theory works extraordinarily well for the weak, static gravitational fields of our solar system", designed GR that way.

You know the subjects very well. What are your questions? If gravity is a force, then bullets are not free. Therefore, they are not subject to Newton first law. Do you follow?

Your OP stated:

Consider in your imagination three bullets, which fly on a ring orbit around the Sun.

That depends on how you want to view these bullets.
If the observer is in a "local sun-centred inertial reference frame" the bullets could be considered subject to the "force of gravitation" which is balanced by the "centripetal acceleration" from the curve of the orbit.

Newton's First Law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. It may be seen as a statement about inertia, that objects will remain in their state of motion unless a force acts to change the motion.

So the observer in this Inertial Reference Frame sees the bullets follow a curved (accelerating) path because they are subject to a force.

But if you travel with a bullet you will simply be in "free-fall" (as Newtonian Mechanics would describe it) or "following a geodesic in spacetime" (as general Relativity would describe it).
The end result is exactly the same and in most cases, Newtonian Mechanics is by far the simpler way to analyse the problem.
Newtonian Mechanics can be used for most orbital calculations, though NASA's spacecraft trajectory calculation programs have the option is using GR if requested.
But all earlier spacecraft trajectory calculations were done using Newtonian Mechanics and initially with no more assistance than a mechanical calculator.
Take a look at: She Was a Computer When Computers Wore Skirts - no GR for any of those early missions.

If you want to try your hand a GR for the "simple case" of a small body (planet, bullet or artificial satellite) moving in the vicinity of a large spherical body (sun or earth) read up on it in:
         Spherically-symmetric solutions in general relativity, Do Young Kim, Anthony N. Lasenb and Michael P. Hobson
or     Determination Of Newtonian Gravitation From The Schwarzschild Spacetime Within The Region Of Spherical Geometry by Okpara, P. A., et al.
But please don't ask me to explain any of it - it's way out of my league.

Please excuse any imperfection in my explanations as I'm certainly no physicist or mathematician.

But, I have a question for you: Do you accept Newton Laws and/or Einstein's General Relativity as being at least locally correct?

[Astrophysics]

the bullets could be considered subject to the "force of gravitation" which is balanced by the "centripetal acceleration" from the curve of the orbit.

But, I have a question for you: Do you accept Newton Laws and/or Einstein's General Relativity as being at least locally correct?

It is indifferent what I am and what I think: I am facing the Absolute Truth (He is beutiful!). But I have papers in European P J B and Physical Review.

The Newton First Law speakes about forces, not about (fictional) inertial forces. Thus, for Newton free falling cabin of spaceship has no inertial frame in it. But reread my post, I have changed it drastically.

[rabinoz]

the bullets could be considered subject to the "force of gravitation" which is balanced by the "centripetal acceleration" from the curve of the orbit.

But, I have a question for you: Do you accept Newton Laws and/or Einstein's General Relativity as being at least locally correct?

It is indifferent what I am and what I think:

It's you I'm asking and if you can't answer such a direct question I'm not going to take the time to bother with your claims.

I am facing the Absolute Truth (He is beutiful!).

Well, what is this "Absolute Truth"?
If you have the "Absolute Truth" what is the point if all these questions and claims? Just present this "Absolute Truth" and stop all this time wasting.

But I have papers in European P J B and Physical Review.

So what? You were the one that posted the video "Is Most Published Research Wrong?" so unless I see your papers why should I believe that they are not wrong too.

The Newton First Law speakes about forces, not about (fictional) inertial forces. Thus, for Newton free falling cabin of spaceship has no inertial frame in it.

Pseudo-forces are still forces that can be measured and cause acceleration.

But reread my post, I have changed it drastically.

I spent a lot of time answering it the first time.
You refuse to answer my direct questions so I fail to see why I should spend more time especially with one who claims "Absolute Truth".

[rabinoz]

I will relent a make some comments on the hypothesised dark matter and dark energy. Neither has the the slightest significance within the Solar system.

Noh, indeed: Wikipedia says, that there is Dark Matter. But with matter (tables, insects, flowers) comes force, which drives and changes it.

Wikipedia does NOT say, "that there is Dark Matter". What Wikipedia does say is:

Dark matter
Dark matter is a hypothetical form of matter that is thought to account for approximately 85% of the matter in the universe, and about a quarter of its total energy density.

Dark Matter is hypothesised to cause "gravitational force" but it has such a low density (approximately 1 proton-mass for every 3 ccs), that it has no effect on the earth's rotation!

DARK MATTER IN THE SOLAR SYSTEM
Dark matter should have gravitational effects on the planets orbits and on space probes, but we are so far unable to detect them.
This is not surprising, however, because they are hidden by bigger effects: the gravitational pulls of the sun and planets are much, much larger.
The average density of dark matter near the solar system is approximately 1 proton-mass for every 3 cubic centimeters, which is roughly 6x10^-28 kg/cm³. The actual density might be a little lower or higher, but this is the right order of magnitude.
Based on this number, we can work out the total mass of dark matter within the radius of Earth's orbit around the sun: for an orbital radius of 100 million km, we get a total of 2.3x10¹² kg of dark matter within the Earth's orbit.
This sounds like a lot, but the sun's mass is 2x10³⁰ kg. All of that dark matter only weighs 10^-18 as much as the sun does, so we cannot detect the tiny pull of dark matter upon the Earth's orbit.
The same story is true all over the solar system: the gravitational pulls of the sun and planets are always much larger than that of the dark matter.
Jeffrey Filippini
Particle Cosmology Group
University of California - Berkeley

However, the Dark Force might not be introduced, if the Flat Earth model is used.

The is no Dark Force even postulated. I do wish that you would read what is written in your sources and not what you wished was in there.
Dark Energy is a name given to whatever drives the apparently accelerated expanding Universe but that is totally insignificant within thousands of light years of here.

All these things are well known to anyone claiming any connection with Astronomy or Astrophysics so why are you not familiar with these matters?