[Origin]

There are not many things in life that are a sure bet, but there is no doubt that after being shown lots of evidence showing Dave that he is wrong he will still double down on his WAG.

[Dave Lev (OP)]

Quote from: Dave Lev on Today at 06:27:15
Could it be that the total mass there is several times the Sun mass?

No, the Sun is the most massive object in the Solar System by a wide margin (99.8% of the Solar System's mass is in the Sun): https://solarsystem.nasa.gov/solar-system/sun/in-depth/#:~:text=Most%20of%20the%20nebula's%20material,of%20our%20solar%20system's%20mass.

The Sun and the whole solar system had been created from the same gas cloud.
Is it realistic to believe that 99.8% from the cloud had been used to create the sun itself?
How this kind of process could be so efficient?
How could it be that only 0.2% left over?
If it is so successful, why the whole 100% didn't fall inwards into the sun?

Do you have evidence that there are that many? Let's also not forget that the vast majority of them would be much too far away to help with your tidal energy problem.

It is stated that "All stars are born in pairs: Even the sun had a twin!"
https://www.indiatoday.in/education-today/gk-current-affairs/story/stars-born-pairs-983697-2017-06-20

Could it be that the sun has a nearby twin?

Quote from: Dave Lev on Today at 06:27:15
How do we know that there are no other invisible dark stars or even blackholes?
Because the effects of their gravity would be apparent.
That's how we know about dark matter.

Thanks for this great message.
What could force our Sun to oscillate around its mean Galactic orbit?
https://www.space.com/10532-earth-biodiversity-pattern-trace-bobbing-solar-system-path.html
"As the sun orbits around the center of the Milky Way, it bobs up and down relative to the plane of the galactic disk"
However, the Moon motion around the Sun is very similar to that Sun motion around the galaxy.
https://scienceblogs.com/files/startswithabang/files/2012/05/planetary_moon_comet_orbits.png

Therefore, why do we reject the idea that as the moon orbits around the earth (or actually around each other) while they both orbit around the sun, there is High possibility that the Sun orbits around its twin dark star or massive BH (/Bhs) and they all orbit around the galaxy?

It's important to remember that tidal forces drop of as an inverse cube, but attraction drops as an inverse square.
So, if the tidal forces were detectable, the attractive forces would be much bigger and we would notice them

So why do we ignore the real meaning of this sun wobbling motion?
Let's assume that we were not living on earth and it is invisible for us. How could we explain the wobbling motion of the Moon around the Sun? Why do we refuse to understand that the wombling motion of the sun is a clear indication that there must be some nearby invisible stars or BHs?

So if you want your idea to be taken seriously, you need to show us that the needed number of black holes at the needed distances are really out there. Otherwise, you are just speculating.

The science has proved that tidal heat process can generate EM energy.
We clearly know how the Geodynamo works based on tidal force.
So, instead of claiming that the visible matter is not good enough for the Sun tidal energy and look for other ideas as fusion, why don't we try to find the invisible Stars/Bhs that could do the job.

Fusion
I still think that there is a fatal problem with this process (I will cover the neutrino issue later on):
1. It is not realistic for a protostar to increase its internal heat from 1Kc to 10Mc just based on its size. However, as you have offer the math with this temp target, then lets assume that this idea is real.
2. However, 10Mc is not good enough for the Fusion. We need something to start that process. So, how this process could start while there are no neutrinos??
3. Let's assume that the fusion started somewhere in the core. So now the chain reaction would expand that activity anywhere is the core. However, any reaction would increase the nearby temp to 10Mc.
You have stated:

The Sun's core isn't made of metal anyway. It's made of hydrogen plasma (which is electrically conductive).

Hence, any nearby hydrogen could potentially be part of the Nuclear fusion process. so why that process would stop at the core? Why it can't continue all they way to the outer aria of the sun - Step by step and over time?
Is there any kind of envelop (or layer) in the sun that keeps the process only in the core?
4. Magnetic field -
Any Geodaynamo (even in the toy demo), there must be layers of different components.
In Earth it is a solid Iron core, liquid outer core and insolation layer.
Any basic battery is made out of different components.

The Sun's core isn't made of metal anyway. It's made of hydrogen plasma (which is electrically conductive).

So, how could it be that The Sun that is made out of hydrogen plasma (without any metal and isolation) can get its magnetic field.
4.There is also the problem of starting the Geodynamo.
It can't just work without electricity starter. So, even if we have a perfect Geodynamo in the Sun, how it could start working without nearby EM starter?
I assume that the Earth Dynamo got its first starter from the Sun EM power, but how the Sun itself got its first EM starter?
This could be one more indication that there might be a nearby BH that gave the Sun the requested EM starter.

[Bored chemist]

There are not many things in life that are a sure bet, but there is no doubt that after being shown lots of evidence showing Dave that he is wrong he will still double down on his WAG.

Got it in one.
He's really not good at reading and understanding.
But, just in case some lost soul thinks that his idea is science, rather than nonsense, I will point out some of the most glaring errors.

[alancalverd]

Having skimmed through Dave's questions, I can safely say that the answer to every one is in the textbooks, so I see little point in anyone contributing further to this thread.

[Bored chemist]

As usual Dave, everything you have said is clearly wrong.

Is it realistic to believe that 99.8% from the cloud had been used to create the sun itself?

Yes

How this kind of process could be so efficient?

Gravity is a positive feedback system.
Once something is heavy, it attracts the other heavy things and they all stick together.

If it is so successful, why the whole 100% didn't fall inwards into the sun?

Mainly the conservation of linear and angular momentum.

Were you actually asking those as serious questions or did you somehow imagine they would be "difficult"?

Could it be that the sun has a nearby twin?

No.
the thing about stars is that they are bright.
If there was one nearby we would see it.

What could force our Sun to oscillate around its mean Galactic orbit?

Gravitational (but not tidal) forces of other objects.

Try to remember that tidal effects are much much smaller than gravitational ones unless you are very close to a mass.

Therefore, why do we reject the idea that as the moon orbits around the earth (or actually around each other) while they both orbit around the sun

I wasn't aware that we did reject that.

there is High possibility that the Sun orbits around its twin dark star

Nope, we would notice if we were going round in circles.

So why do we ignore the real meaning of this sun wobbling motion?

Why have you put the word "so" at the start of that sentence?

We don't ignore it; we even measured it and it's tiny.

Why do we refuse to understand that the wombling motion of the sun is a clear indication that there must be some nearby invisible stars or BHs?

Because it's actually an indication of the presence of planets (especially Jupiter- which is big).

We clearly know how the Geodynamo works based on tidal force.

It does not.

You really really need to learn that gravity and tides are not the same thing.
But it's beside the point; the earth's magnetic field is driven by the production of heat deep in the earth.

So, instead of claiming that the visible matter is not good enough for the Sun tidal energy and look for other ideas as fusion, why don't we try to find the invisible Stars/Bhs that could do the job.

For the third time.
If the tides were driving teh heating of the Sun then we would see the sun change size and shape the same way that we see the oceans change.

But the Sun is almost perfectly spherical.
So we know that any tides are tiny.
So we know that can not explain the huge amount of energy the sun puts out.

I still think that there is a fatal problem with this process

People who understand science and evidence do not think there is a problem.

Who should we believe?

[Bored chemist]

It is not realistic for a protostar to increase its internal heat from 1Kc to 10Mc just based on its size.

Yes it is.
Do the maths.

. However, 10Mc is not good enough for the Fusion.

Yes it is.
Do you know that people do fusion in their garages?
https://en.wikipedia.org/wiki/Fusor

We need something to start that process. So, how this process could start while there are no neutrinos??

Again, you keep posting your mistakes as if they are facts.
It just makes you look arrogant as well as ill-informed.

Hence, any nearby hydrogen could potentially be part of the Nuclear fusion process. so why that process would stop at the core? Why it can't continue all they way to the outer aria of the sun

Density and temperature.
The outer areas of the sun cool by radiation into space and so hey are too cold for much fusion to take place.

Is there any kind of envelop (or layer) in the sun that keeps the process only in the core?

Yes.
Gravity.

That's what keeps the centre dense enough for the reaction to happen "quickly".

Any Geodaynamo (even in the toy demo), there must be layers of different components.
In Earth it is a solid Iron core, liquid outer core and insolation layer.

No; we already explained this.
As we have demonstrated with the molten sodium experiment.
You do not need a solid core.

So, how could it be that The Sun that is made out of hydrogen plasma (without any metal and isolation) can get its magnetic field.

Because ionised gases conduct electricity.

There is also the problem of starting the Geodynamo.

No, there isn't, as they said in the video about the molten sodium sphere.
Why do you not listen when people explain things to you?

I assume...

Wrongly, as usual.

This could be one more indication that there might be a nearby BH that gave the Sun the requested EM starter.

No.

Why do you post on science pages?
You are clearly not interested in science.

[Bored chemist]

(I will cover the neutrino issue later on):

You have yet to cover anything else.
You just post rambling misunderstandings.

[Origin]

. We need something to start that process. So, how this process could start while there are no neutrinos??

The process can start without neutrinos because neutrinos are not needed for fusion to occur.
Edit:
I see Board chemist already addressed this.  Dave has presented so many errors I lost track.

[Bored chemist]

Dave has presented so many errors...

Has he posted anything else?


Scientists.png (301.67 kB . 526x592 - viewed 1557 times)

[Kryptid]

Is it realistic to believe that 99.8% from the cloud had been used to create the sun itself?

Yes, because that is what happened.

How this kind of process could be so efficient?
How could it be that only 0.2% left over?
If it is so successful, why the whole 100% didn't fall inwards into the sun?

I don't know the answer to that question, but it's irrelevant. We can measure the mass of the objects in the Solar System. The Sun has 99.8% of the Solar System's total mass. If your model can't work with that, then it can't work.

It is stated that "All stars are born in pairs: Even the sun had a twin!"
https://www.indiatoday.in/education-today/gk-current-affairs/story/stars-born-pairs-983697-2017-06-20

Could it be that the sun has a nearby twin?

Possibly. That would be the Nemesis hypothesis: https://en.wikipedia.org/wiki/Nemesis_(hypothetical_star) If Nemesis does exist, it would have to be very cool, very low mass star. Otherwise, it would be bright enough to easily detect and we would have found it by now. So the existence of Nemesis wouldn't be good enough to make your model work.

So why do we ignore the real meaning of this sun wobbling motion?
Let's assume that we were not living on earth and it is invisible for us. How could we explain the wobbling motion of the Moon around the Sun? Why do we refuse to understand that the wombling motion of the sun is a clear indication that there must be some nearby invisible stars or BHs?

There can't possibly be enough of them. Remember,  there would need to be the equivalent of a black hole 2,000 times heavier than the entire Milky Way galaxy parked a mere 4.3 light-years away from us in order to get the needed tidal energy transfer.

The science has proved that tidal heat process can generate EM energy.

In the sense that all hot objects emit electromagnetic radiation, yes.

We clearly know how the Geodynamo works based on tidal force.

Tidal forces aren't needed for a geodynamo to work. We've explained this.

So, instead of claiming that the visible matter is not good enough for the Sun tidal energy and look for other ideas as fusion, why don't we try to find the invisible Stars/Bhs that could do the job.

There can't possibly be enough of them. Did you not read what I said about that multi-quadrillion solar mass black hole?

2. However, 10Mc is not good enough for the Fusion. We need something to start that process. So, how this process could start while there are no neutrinos??

Please learn how fusion works before criticizing it. Neutrinos are a byproduct of fusion, not a trigger for it. We can create fusion in the laboratory without using neutrinos to get it started (whatever that would even mean).

Hence, any nearby hydrogen could potentially be part of the Nuclear fusion process. so why that process would stop at the core? Why it can't continue all they way to the outer aria of the sun - Step by step and over time?
Is there any kind of envelop (or layer) in the sun that keeps the process only in the core?

The pressure and temperature isn't high enough outside the core for fusion to occur there.

Any Geodaynamo (even in the toy demo), there must be layers of different components.

Support this assertion with a reputable source.

So, how could it be that The Sun that is made out of hydrogen plasma (without any metal and isolation) can get its magnetic field.

Because plasma is a conductive fluid.

It can't just work without electricity starter.

Prove that you aren't just making stuff up by providing a citation for this.

[Dave Lev (OP)]

Neutrinos

Some basic data about Neutrinos
https://en.wikipedia.org/wiki/Neutrino

"Flavor, mass, and their mixing - Weak interactions create neutrinos in one of three leptonic flavors: electron neutrinos (νe), muon neutrinos (νμ), or tau neutrinos (ντ), associated with the corresponding charged leptons, the electron (e−), muon (μ−), and tau (τ−), respectively.[35]
Although neutrinos were long believed to be massless, it is now known that there are three discrete neutrino masses;
For each neutrino, there also exists a corresponding antiparticle, called an antineutrino, which also has no electric charge and half-integer spin.
Nuclear reactions- Neutrinos can interact with a nucleus, changing it to another nucleus. This process is used in radiochemical neutrino detectors
It is very hard to uniquely identify neutrino interactions among the natural background of radioactivity.
Within a cubic meter of water placed right outside a nuclear reactor, only relatively few such interactions can be recorded, but the setup is now used for measuring the reactor's plutonium production rate.
The three known neutrino flavors are the only candidates for dark matter that are experimentally established elementary particles ? specifically, they would be hot dark matter. However, the currently known neutrino types seem to be essentially ruled out as a substantial proportion of dark matter, based on observations of the cosmic microwave background.
Cosmic neutrinos
Main articles: cosmic neutrino background and diffuse supernova neutrino background

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7298169/
The Sun produces abundant neutrinos due to nuclear fusion reactions. A pioneering experiment in the early '70s detected neutrinos from the Sun, but found that the observed flux was smaller than expected, which was then called the missing solar neutrino problem.
all of the experiments indicated deficits of the observed solar neutrinos. It was something like to solve a jigsaw puzzle to draw a consistent view among the experiments.
Neutrino oscillation may violate CP invariance.
Neutrinos, on the contrary, taking only 3% of the total energy released, reach the surface of the Sun in 2 seconds and arrive at Earth 8 minutes after emanation. Therefore, neutrinos can monitor the current status of the solar core.
Large numbers of incoming neutrinos and huge detectors are needed to detect and study neutrinos. But this is not a trivial matter. Therefore, even the basic properties of neutrinos, like masses, were not addressed until recently.
the electron neutrinos created in the core as ν2m = νe, finally exit the Sun as νμ. The solar neutrinos convert to another type of neutrinos. This process is called an adiabatic resonance conversion (MSW effect87)). The survival probability is sin2 θ.84)
Although we have a variety of handles on the solar neutrino measurements, the common problems of solar neutrino experiments are that they have small cross sections (10−44∼−42 cm2) and large backgrounds (see section 3 in details). The detectors thus need to be big, more than several tens of tons to ∼kilo tons. The small event rates of about one in a few days in the early experiments increased to 10?20 events per day in recent experiments. The radioactive impurities that influence signal detection must be removed.
The deficit of solar neutrinos that the solar neutrino event rate observed was significantly smaller than the prediction of the solar model calculation, was first indicated in the '70s by the Homestake experiment. This solar neutrino problem, which has been persistent, never diminished and became stronger when adding new results available from new experiments.
The solar neutrinos in the daytime reach the detector directly, but in the nighttime they need to traverse Earth before arriving. Those neutrinos passing through Earth may be affected by Earth?s matter effect. There may be a difference between the daytime and nighttime fluxes.
As described above, the Super-K results from 1,258 days of data showed no energy spectrum distortion, no seasonal variations and a small day/night flux difference.
Therefore, further study of the day/night flux difference is necessary. The results are still statistics dominant, and the size of the Super-K detector is a limiting factor.

Hence:
1. It is stated: "the electron neutrinos created in the core as ν2m = νe, finally exit the Sun as νμ. The solar neutrinos convert to another type of neutrinos. This process is called an adiabatic resonance conversion (MSW effect87)). The survival probability is sin2 θ.84)"
If the electron neutrinos from the core of the Sun is converted to another type of neutrinos, how do we know for sure that this detected type is clearly from the fusion activity in the sun core and not due to some other activity?

2. Ionized hydrogen is a hydrogen atom that has lost its electron and is now positively charged.  So, could it be that we actually measure the electron neutrinos which had been ejected from the hot plasma at the surface of the Sun and not from its core?

3. It is stated: " As described above, the Super-K results from 1,258 days of data showed no energy spectrum distortion, no seasonal variations and a small day/night flux difference"
So, as there is no seasonal variations and a small day/night flux difference, why can't we assume that we just get Cosmic neutrinos?

4. The Sun is not the only star in the Universe. There are billions of Sun like stars just in our galaxy. So, if it ejects Notorious, why the other stars in the universe can't do the same? So, why can't we claim that the Notorious that we detect are due to other Stars, cosmic neutrino background or diffuse supernova neutrino background? Actually the accretion disc around the SMBH could be an excellent source. The temp there is about 10^9c it has plenty of particles/atoms including Hydrogens. So why the Notorious that are ejected from the Billions accretion discs can't fill the Universe with a constant Notorious stream that is equal from all directions. Therefore, we get the same Notorious flux from all directions in daytime and nighttime?

5. It is stated: " Neutrinos, on the contrary, taking only 3% of the total energy released, reach the surface of the Sun".
Do we really get all of those 3% Neutrinos from the total energy? Can you please show the article to support that indication?
Even if we detect this quantity, how do we know that all of them are due to our sun fusion activity?

6. It is stated: "The three known neutrino flavors are the only candidates for dark matter that are experimentally established elementary particles"
If the neutrino had been changed its flavors when it had been ejected from the Sun core, why other neutrino that had been ejected from the dark matter can't change its flavors?
In other words, could it be that the detected neutrinos are also due to dark matter?

[Bored chemist]

Why did you start that with about 60 lines of stuff from wiki that we already know, and you don't understand?

, how do we know for sure that this detected type is clearly from the fusion activity in the sun core and not due to some other activity?

Because there's no other pathway, they are produced in the right numbers and they come from the sun.

So, could it be that we actually measure the electron neutrinos which had been ejected from the hot plasma at the surface of the Sun and not from its core?

No.
That plasma isn't hot enough to get nuclei close enough together to fuse efficiently.

So, as there is no seasonal variations and a small day/night flux difference, why can't we assume that we just get Cosmic neutrinos?

Because their direction shows them to come from the sun.

Isn't that obvious?

why the other stars in the universe can't do the same?

They do.
Have you noticed that starlight is not as bright as sunlight?
That's because the other stars are far away.

Actually the accretion disc around the SMBH could be an excellent source.

It is a source, but not necessarily a good one.
The density is low.

Do we really get all of those 3% Neutrinos from the total energy?

No, but the article didn't say we did.

Can you please show the article to support that indication?

You made up that assertion; it's your job to find evidence for it.

n other words, could it be that the detected neutrinos are also due to dark matter?

As usual, you have not understood it.

the neutrinos are not the source of the dark matter they are dark matter.

[Kryptid]

In other words, could it be that the detected neutrinos are also due to dark matter?

I thought you didn't believe in dark matter.

[Bored chemist]

In other words, could it be that the detected neutrinos are also due to dark matter?

I thought you didn't believe in dark matter.

Glory Be!
Someone contact the Vatican.
It's a miracle.
A fact has made it into Dave's head (at least for the moment).

(I hope it's not too lonely).

[Dave Lev (OP)]

In other words, could it be that the detected neutrinos are also due to dark matter?

I thought you didn't believe in dark matter.

You are correct.
However, I hope that you don't ask this question inorder to band the thread after getting my reply.

Therefore, I will only focus on the following clear observations:

1. There are only two linear Bar arms in the spiral galaxy.
2. The velocity of the stars in the Bar is increase linearity and dramatically as we move from the Bulge to the ring.
3. The spiral arms are always symmetrical
4. The spiral arms always connected to a ring at the base (In the milky way the ring is located at 3KPC).
5. The thickness of the spiral arm at the base is 3000LY.
    The thickness of the arm at our location (8KPC) is 1000LY.
    The thickness of the arm at the edge (12-15 Kpc) is 400LY.
6. The orbital velocity of stars in the spiral arms is constant (about 220K/s in our galaxy).
7. The density of G stars in our location (in the spiral arm) is 64 per 50LY. For every G star there is about 20 M stars
8. The Sun is wobbling while orbiting around the galaxy.

The science community think that the observable ordinary matter is not good enough to perform all the above and I fully agree with this understanding.
However, while they claim for dark matter, I claim for dark invisible ordinary matter.

Nemesis is a perfect example:

Quote from: Dave Lev on 04/07/2023 21:18:07
It is stated that "All stars are born in pairs: Even the sun had a twin!"
https://www.indiatoday.in/education-today/gk-current-affairs/story/stars-born-pairs-983697-2017-06-20
Could it be that the sun has a nearby twin?

Possibly. That would be the Nemesis hypothesis: https://en.wikipedia.org/wiki/Nemesis_(hypothetical_star) If Nemesis does exist, it would have to be very cool, very low mass star. Otherwise, it would be bright enough to easily detect and we would have found it by now. So the existence of Nemesis wouldn't be good enough to make your model work.

Nemesis is a dark invisible ordinary matter.
If it is a dark star at a low mass & temp, then it can't do the job by itself.
There might be several others nearby dark stars.
On the other hand, it could be a BH or even a MBH (assuming that we consider the BH as ordinary matter).
It is just invisible (and looks cold) as it has no accretion disc yet.

We clearly know that there are 20 M stars for each G star.
Therefore, there is a possibility for 500 (or more) Dark stars (including BHs/MBHs) for each M star.

The dark matter might give an answer to the orbital motion of the star in the spiral arm:
"6. The orbital velocity of stars in the spiral arms is constant (about 220K/s in our galaxy)."
However, it can't answer all the other observations.

So why the science community ignore all of those observations?
Why they only give an answer to no. 6. (and some limited explanation for 8.)
What about all the others?
As they believe that the dark matter is real and it has the requested mass that is needed to hold the sun in its orbital motion by mighty gravity force, then why this force (from the dark matter) can't be used for the sun requested tidal force.

Don't you agree that tidal heat is also due to gravity?
So why the dark matter can hold the Sun by its mighty gravity force but it can't contribute any tidal gravity force?

[Bored chemist]

I claim for dark invisible ordinary matter.

You don't know what "dark" means, do you?

[Kryptid]

To be fair, black holes are a dark matter candidate.

As they believe that the dark matter is real and it has the requested mass that is needed to hold the sun in its orbital motion by mighty gravity force, then why this force (from the dark matter) can't be used for the sun requested tidal force.

The dark matter does help. Some. My previous calculation only considered the stars in the galaxy. Adding in the dark matter increases the tidal force by 2.875 times. That's still nowhere near enough, though. The required tidal force is equal to that produced by a 2.489 quadrillion solar mass black hole at 4.3 light-years from the Sun. The Milky Way galaxy (dark matter included) can only provide 1.15 trillion solar masses.

[Dave Lev (OP)]

Lets focus on the tidal force formula:

Doubling posting, I know, but I did some math. Here's a webpage describing the equation to calculate tidal forces: https://www.astro.uvic.ca/~jwillis/teaching/astr201/maths.7.tidal_heating.pdf

The tidal force is described by: (2GM1M2)/r3, where

G is the gravitational constant
M1 is the mass of one body
M2 is the mass of the other body, and
r is the distance between the masses.

Are you sure that this formula is correct?
In the article it is stated that:
"The tidal force refers to the difference in gravitational force experienced by the near and far sides
of a satellite orbiting a parent body.
 the tidal force is just to compute the difference between the near and far side gravitational force, e.g.
Ftidal = F(r − RIo) − F(r + RIo)."

In order to verify this issue, let's try to understand how tidal force really works:
Please see the following diagram:
https://www.wolframcloud.com/objects/demonstrations/TidalForces-source.nb
We see that the tidal force works on every atom in the Object.
In the left side of the object, every atom is pulled to the left, while in the right side of the object every atom is pushed to the right.
The side effect is the any atom that is located directly upwards and downwards from the central mass is pulled to the center.
In other words, we can claim that tidal force represents a Push / Pull mechanism.
Hence, each atom in the object "feels" the impact of that tidal force.
Please remember
When tidal works on the sea, the water is rising up quite dramatically, however, even the ground below the sea is rising up.

As electronic Eng., I would compare this tidal push pull mechanism to a push/pull amplifier:
https://www.watelectronics.com/push-pull-amplifiers-circuit-diagram-working-and-applications/
"Push-pull amplifiers  are the combinations of two bipolar junction transistors that is one of P-N-P type and the other is of N-P-N type. In this combination one act as push type and the other acts as pull type."
The total power is the sum of the Push power to the Pull power.

Therefore, the total tidal force must be the sum of all the tidal forces on each atom in the object.
As tidal works on every atom in a push /pull mechanism, why can't we claim that:
Ftidal(total) = ∑(all push forces) + ∑(all pull forces) = F(r − RIo) + F(r + RIo) + + +....

So, why the science community have decided to ignore all the internal tidal forces, including the tidal push /pull mechanism, and used the following formula:
Ftidal = F(r − RIo) − F(r + RIo).

[Bored chemist]

As electronic Eng., I would compare this tidal push pull mechanism to a push/pull amplifier:
https://www.watelectronics.com/push-pull-amplifiers-circuit-diagram-working-and-applications/
"Push-pull amplifiers  are the combinations of two bipolar junction transistors that is one of P-N-P type and the other is of N-P-N type. In this combination one act as push type and the other acts as pull type."
The total power is the sum of the Push power to the Pull power.

You have got that wrong too.

With a  single ended amp the best power I can get to the load has a peak to peak voltage equal to value of the supply voltage.

With a push-pull amp, I can get twice the peak voltage.

So the power available is four times greater.
1+1 is not 4.

[Bored chemist]

So, why the science community have decided to ignore all the internal tidal forces, including the tidal push /pull mechanism, and used the following formula:

Because tides are not the same as gravity.

Why do you not realise that?
You have been told several times.