Proof of the apple 'pulling' the earth?

plane said:
There can never be two masses that are precisely the same is the first point to make. But if they were precisely the same, neither would attract the other. That is on simple mathematical reasoning.
Not according to the textbook I used in 1st yr Physics.

Two bodies do attract each other with individual forces proportional to their individual masses.
It's called the Law of Universal Gravitation. It's known to act, for a given mass, with an attractive "pull", inversely proportional to the (square of the) distance of the other object. It takes two objects, or masses, for this to occur.

You can even write this in a mathematical formula. I can remember looking at this in high school...?
You're sure Kepler and Newton and everyone since (including me and the rest of "us"), all have the wrong idea with this?
 
Simple; the forces of gravity never becomes 0, only the net force, and therefore acceleration. However, there is no mathmatical rule which states that because
z=x+y
and z=0, that x and y=0.
indeed, all that can be derived is that x=-y, or in terms of this application (z=net force x is gravity on apple byearth, y is gravity on apple by moon,) that there is a force of gravity of equal magnitude but in opposite direction also acting upon the object. The magnitude of either force of gravity is never 0, just as Newton predicted.
Your assumption that: if z=0, and z=x+y, x MUST = y MUST=0, is the source of mathmatical error.

-Andrew


Your exactly right andbna. To a point anyway. X and Y are only theoretical values along the axis. One would exist if the other didn't

Here is a diagram of where they do exist.

6faba244d2dadc73fced465d6bba2f15.jpg


You get the picture. You have to think a bit and you will see it. Will reply to others later.
 
Plane,
It might have been pointed out, but if only the heavier mass attracts the lighter mass, how do you explain binary star systems and pulsars - where the stars rotate around each other?
 
plane:



This "direction of fall" you talk about is the direction a third object would fall, towards one or the other of the two gravitating objects. The assumption, of course, is that the third object is not massive enough to significantly perturb the system. .

Third object irrelevant. If zero objects are present direction of fall does not alter.


Where you go wrong is in jumping from the behaviour of a third body to conclusions about the original 2-body system.

Direction of fall is independent on falling body.



It doesn't. The Earth is always falling towards the Sun. .
Maybe having a misunderstanding about the issue at hand. Whatever, as the moon orbits the earth, the earths orbit of the sun is affected in such away that its distance from the sun increases. Look it up. If your result is different to this, post to that affect,
.


You're not being precise enough. There are actually three separate effects here. One is the intrinsic spin of the Earth around its axis; another is Earth's orbital motion about the centre of mass of the Earth-moon system; the third is the Earth's orbital motion around the Sun. These three motions are independent and have three different rotational axes. .

Your trouble is in explaining the second as being consistent with the first.



I explained carefully to you that "pull" is just one way to denote an attractive force. .

Not sure that your definition of carefully would match all others but what is an ‘attractive force’. A push is an exertion of matter upon matter. What is a pull in terms of matter?



Nobody can explain why gravity is an attractive force. It just is. All observation confirms it. It's just an observed feature of our universe. You can imagine a universe where things fall up instead of down, but that's not our universe, obviously. .

How do you know that nobody can explain it? Aren’t you saying you are god here?



I was trying to ascertain how much you understand about tides. .

Fair enough.



I don't understand. Newton's third law concerns equal and opposite forces on different bodies. How does it explain the second high tide?

Not really given to answering questions with questions, but how could Newton’s third law not explain equal and opposite high tides?




This is a basic error on your part.

Basic error on your part. What happens when opposite directions of ‘inverse square law’ meet. Indefinite extensions? Other than zero extensions are yours to explain.

All observational data supports the inference that gravity is an inverse-square force. It follows automatically that it has "indefinite extension".



My "proof" is:

1. Newton's third law states that for every force there is an equal and opposite force.
2. Therefore, when two bodies interact, if one exerts a force F on the other, the other exerts an equal force F on the first, but in the opposite direction.
3. Gravity is a force (in the Newtonian picture).
4. No known experiment with force has ever violated Newton's third law.
5. Therefore, if the Earth pulls on an apple, the apple must pull back on the Earth with an equal and opposite force.

That's really all the "proof" that is needed. .

Your problem is at three. Gravity is not a force. Gravity is known to cause an acceleration through space. This does not make gravity force. It makes it a cause of force. Incidentally, 3 to 5 is one hell of a jump.


Of course, there's also a lot of direct evidence, such as the kind of astronomical evidence cited previously.

How does the earth moon crisscross (which you seem to reject) and so called binary star systems prove an apple attracts the earth.




Resultant zero gravity between adjacent objects pushes it aside.

Have a look at diagram in this thread.


temur said:
This picture is true only for smaller masses present nearby the two bodies, assuming that the two bodies are motionless. It does not show at all what forces the two bodies themselves experience.

Think about this: The Earth is made of many atoms, and any atom is smaller than an apple. So the apple pulls the Earth.


Temur, this does not make sense. The question is whether or not the smallest mass could attract any other mass.
 
plane said:
Not a matter of the smaller mass identifying its self
The mass that is smaller has to know that somehow - otherwise how would it know when to stop attracting the other masses ?

Any mass is going to be sometimes smaller, sometimes bigger. How does it know which times are which ?
 
No. The moon's orbit is exactly what we would expect given purely attractive gravity.

if there was only pure attraction, the moon the whole universe would be stuck at one point. but if there is repulsion, it's easy to explain why planets rotate, have motion and specific distance from the sun.

repulsion is an automatic consequence of attraction... when a river flows, i'm attracted to the way the river flows, and if i go upstream i'm repulsed. similarly, i think there is a magnetic river that flows through planets and everything.

Impossible. Two north magnetic poles always repel one another.

yes, but maybe it's because the strong magnet is smaller than the weak magnet, so the magnetic fields are a bit weird... or maybe they're bisexual? also, when i put together north and north the attraction is weaker than when i put together north and south.
 
if there was only pure attraction, the moon the whole universe would be stuck at one point. but if there is repulsion, it's easy to explain why planets rotate, have motion and specific distance from the sun.

Yorda, did you read the introductory paragraph of the Wiki page to which you linked?
wikipedia said:
The Titius-Bode law (sometimes termed just Bode's law) is a hypothesis that the semi-major axes of planets in the solar system follow a simple rule. It was discredited with the discovery of Neptune in 1846.

Your first statement is incorrect. In Newtonian mechanics, gravity is a purely attractive force, and this purely attractive force coupled with Newton's laws of motion perfectly explains why things do not gather into one point. Do the math; the solution of the two body problem has been known for a long time. Things get a bit more difficult with general relativity, in which gravity is not a true force (it is a pseudo-force, like the Coriolis effect). This pseudo-force remains purely attractive, however.
 
Your exactly right andbna. To a point anyway. X and Y are only theoretical values along the axis. One would exist if the other didn't

Here is a diagram of where they do exist.
That is exactly what I mean.
But this in no way prooves that X or Y are 0 at any point; rather your diagram demonstrates that they do indeed still have non-zero values, and abide by Newtons predictions.
It shows there are instances when the net gravitational field strength, z, is 0, but that's perfectly in accordance with Newtons laws.

Your logical argument is that:
A and G affect P,
therefore A must affect G.
This is fallacioiuse however:

Imagine a tabletop RPG which sais "Roll 1 6sided die and 1 8 sided die and add them to find skill X"
your argument is then:
D6 and D8 affect X
therefore D6 affect D8.
Obviously the outcome of the 6 sided die has absolutly no influence on that of the 8 sided die.

Thus the moons gravity has no effect on the earths gravity, and vice-versa.

-Andrew
 
Not according to the textbook I used in 1st yr Physics.

Two bodies do attract each other with individual forces proportional to their individual masses.
It's called the Law of Universal Gravitation. It's known to act, for a given mass, with an attractive "pull", inversely proportional to the (square of the) distance of the other object. It takes two objects, or masses, for this to occur.

You can even write this in a mathematical formula. I can remember looking at this in high school...?
You're sure Kepler and Newton and everyone since (including me and the rest of "us"), all have the wrong idea with this?


Kepler had ideas of a central ‘force’ holding the planets in place but he did not go on about every particle in the universe attracting every other particle in the universe.

Two bodies do attract each other with individual forces proportional to their individual masses.

Can’t you see the contradiction in what you and Isaac say. You are emphatic about individual forces and then you move to both exerting the same force on each other.

Just doesn’t make rational sense. Isaac tried but do you think he really wanted to brainwash the world with something that doesn’t make sense? If he had his time over agian, doubt that he would do it again. How do the two forces suddenly become one?

The mass that is smaller has to know that somehow - otherwise how would it know when to stop attracting the other masses ?

Any mass is going to be sometimes smaller, sometimes bigger. How does it know which times are which ?

iceaura please look at the first diagram I posted. If your question is not answered there, let us know.

Plane,
It might have been pointed out, but if only the heavier mass attracts the lighter mass, how do you explain binary star systems and pulsars - where the stars rotate around each other?

Binary stars have been mentioned. If you looked at the earth moon system from said binary system, the earth moon system would appear to be the earth and moon rotate around each other.

That is exactly what I mean.
But this in no way prooves that X or Y are 0 at any point; rather your diagram demonstrates that they do indeed still have non-zero values, and abide by Newtons predictions.
It shows there are instances when the net gravitational field strength, z, is 0, but that's perfectly in accordance with Newtons laws.

Your logical argument is that:
A and G affect P,
therefore A must affect G.
This is fallacioiuse however:

Imagine a tabletop RPG which sais "Roll 1 6sided die and 1 8 sided die and add them to find skill X"
your argument is then:
D6 and D8 affect X
therefore D6 affect D8.
Obviously the outcome of the 6 sided die has absolutly no influence on that of the 8 sided die.

Thus the moons gravity has no effect on the earths gravity, and vice-versa.

-Andrew

Andrew Newton’s prediction is that A affects G. It is how he explains the high tide under the moon. Not sure how you can type your last line and acknowledge that the earth experiences a tidal system that is in a rhythm with the moon’s orbit of the earth. You are making up an argument to defeat your own argument as, incidentally, Newton did with himself.

I am only really after why people believe an apple attracts the earth but could you possible explain which of Newton’s laws predicts Z = zero as you state above?

Anyway we have the crisscross of the earth across its solar obit being in tune with the moon’s orbit of the earth, binary star systems and Newton’s third law as reasons that people believe an apple attracts the earth. And a few thought experiments. At first glance the most credible would be the crisscross but it has the problem of the sun’s gravity strength being stronger at the earth than the moon’s. Was initially disappointed in ben the man saying he had laboratory proof of the apple and then not being able to supply it but he did then acknowledge that I was right. Thanks. Will keep an eye out to see if any other reasons of belief turn up.
 
plane said:
iceaura please look at the first diagram I posted. If your question is not answered there, let us know.
No, it's not.

You are claiming that when two bodies are attracted to each other, only the larger is "pulling". The question is: how does either body know which one is larger ?
 
but he did then acknowledge that I was right. Thanks.

You're welcome.

I will also acknowledge that nothing you have said bears any resemblance to science, and that I made a mistake by not moving this thread in the first place.
 
plane said:
me said:
Two bodies do attract each other with individual forces proportional to their individual masses.
Can’t you see the contradiction in what you and Isaac say.
What contradiction? Where is there a contradiction?:confused:
plane said:
You are emphatic about individual forces and then you move to both exerting the same force on each other.
What do you mean "I move to both exerting the same force on each other"? What is this supposed to mean?? Each mass always exerts a force on another mass. The force is constant if the mass is constant.
They individually "exert" a force which is proportional to their individual mass.

For a two-body system. there is a centre/center of mass which lies outside of the CoM of either individual body. The Solar system has such a center, which is always outside the actual center of mass of the Sun.
With the planets, the center of mass changes, the Sun wobbles around this CoM constantly, because of the gravitational attraction (an individual attractive force from each individual mass).
 
Last edited:
Andrew Newton’s prediction is that A affects G.
Really? Please, site your source.
The high tide under the moon is caused because the net force acting upon the water has changed, not because the gravitational field strength of the earth has changed. That said, the tides are a complex process, and are thus a fairly poor example.

Not sure how you can type your last line and acknowledge that the earth experiences a tidal system that is in a rhythm with the moon’s orbit of the earth.
Simple: I acknowlege Netwons second law of motion as well, and all works out.

could you possible explain which of Newton’s laws predicts Z = zero as you state above?
Certainly, though he doesnt have a single law, it is more of applying his laws to the scenario you created.

The net force is defined as the sum of all forces acting upon an object, which is how we get z=x+y, assuming we keep our system simple (only taking the gravitation of the two bodies into account.) From here, it is all mathmatics (using Newtons law of universal gravitation to find out values for x and y)
Z=0 if the location of our particle happens to resault in an x value of equal magnitude as the y value, but in an opposite direction.

So, let's model the apple between the earth and moon, using newtons equations.
The scenario to be modeled: earth and moon and apple are in a line, apple is some distance d, from earth and moon, determin acceleration, y, on apple at given distance d.
Assume the moon has distance 5 from earth.
Let d be the distance of the apple to earth, where 5<d<0.
Let y be the net acceleration of the apple towards earth. (Negative meaning towards moon, force is a vector, so a negativ simply denotes opposite direction.)

Using Newtons law of universal gravitation:
If we say Fearth=G*Earth*Apple/d^2
Let G*earth*apple=4
Fearth=4/d^2

Fmoon=G*moon*apple/(5-d)^2
where G*moon*apple=1 (moon's mass is roughly 1/4 of the earth's)
Fmoon=-1/(5-d)^2
(5-d) meaning, the distance of the moon to earth minus the distance of the apple to earth give us the distance of the apple to the moon, -1 because the moon is pulling the apple away from the earth.

Now, we know that Fnet equals the sum of all forces, so assume the two above are the only forces in the system:

Fnet=Fearth+Fmoon

Newtons second law states that Fnet=ma, where y=a, and the mass of apple is 1:
ma=Fearth+Fmoon
my=Fearth+Fmoon
y=(Fearth+Fmoon)/m
y=(Fearth+Fmoon)/1
y=Fearth+Fmoon
y=4/d^2 + -1/(5-d)^2

So we have 3 functions, the acceleration on the apple due to the earth, Fearth (okay thats the force but deviding by the 1 mass of apple keeps the function the same)
the acceleration on the apple due to the moon Fmoon, and the aceleration on the apple due to both, y.

Now punch those into a graphing calculator such as this one:
http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
And we see that, according to newton, the acceleration of the apple is indeed 0 at one point, because the function y intersects the d-axis (near 3.3)
We can also note that at that value of d, the forces due to the gravity of the earth and the moon have non-zero magnitudes, furthurmore they have equal magnitudes, and are opposite, fullfilling newtons first law; as they are balanced, and causing there to be no acceleration on the apple.

-Andrew
 
plane:

With that said, I can understand that no-one wants to debate a diagram that expressly says the third element of Newton’s law of gravity (every mass attracting every other mass) is wrong.

What are we doing now, if not debating?

Take the two masses two represent to adjacent celestial bodies. The earth and the moon if like but not necessarily. At all times and at all earth moon separations there is point along the axis between the earth and moon centres where the resultant rate of acceleration due gravity is zero.

Once you have found any resultant zero rate of acceleration you have disproved the universal aspect of Newton’s law of gravity. That’s the key point that no-one likes much.

You go wrong in the bolded sentence.

Gravitational forces obey what in mathematics is called the Principle of Superposition. This means that at a given point in space, the gravitational forces on any object are a simple vector sum of the individual gravitational forces from the surrounding objects.

Take two equally-massive objects, and place a test mass exactly half way between them. The test mass experiences no net gravitational force. Why? Not because gravity is not "universal", but simply because the two gravitational forces from the surrounding masses are equal in magnitude and opposite in direction at the position of the test mass.

Newton presumed that each gravity is an indefinite extension that is uninterrupted by any other gravity.

Not exactly. He presumed (and all the evidence says he was right) that individual gravitational forces add vectorially.

As soon as you recognize that adjacent gravities must have a zero rate of acceleration between them, you are doing a mathematical analysis that undoes Newton’s premise of all gravities being infinite extensions. You then know he was wrong about an apple attracting the earth.

You're laboring under a simple misapprehension.

I suggest you grab any introductory textbook on physics and read up on Newton's laws of motion. You'll probably only need to go as far as the first three chapters or so to understand your error.

------

In response to your comments on my previous post...

Maybe having a misunderstanding about the issue at hand. Whatever, as the moon orbits the earth, the earths orbit of the sun is affected in such away that its distance from the sun increases. Look it up. If your result is different to this, post to that affect.

No need. I agree with you. So what?

You're not being precise enough. There are actually three separate effects here. One is the intrinsic spin of the Earth around its axis; another is Earth's orbital motion about the centre of mass of the Earth-moon system; the third is the Earth's orbital motion around the Sun. These three motions are independent and have three different rotational axes.

Your trouble is in explaining the second as being consistent with the first.

The motions are independent. There's no inconsistency to explain.

I explained carefully to you that "pull" is just one way to denote an attractive force.

Not sure that your definition of carefully would match all others but what is an ‘attractive force’. A push is an exertion of matter upon matter. What is a pull in terms of matter?

A pull is an exertion of matter on matter too. There's no difference at the atomic level.

Nobody can explain why gravity is an attractive force. It just is. All observation confirms it. It's just an observed feature of our universe. You can imagine a universe where things fall up instead of down, but that's not our universe, obviously.

How do you know that nobody can explain it? Aren’t you saying you are god here?

Ok, let me carefully qualify my statement. I personally know of nobody who can explain why gravity is an attractive force.

Do you?

Not really given to answering questions with questions, but how could Newton’s third law not explain equal and opposite high tides?

Merely stating Newton's third law is not an explanation. You'll have to do better than that.

My "proof" is:

1. Newton's third law states that for every force there is an equal and opposite force.
2. Therefore, when two bodies interact, if one exerts a force F on the other, the other exerts an equal force F on the first, but in the opposite direction.
3. Gravity is a force (in the Newtonian picture).
4. No known experiment with force has ever violated Newton's third law.
5. Therefore, if the Earth pulls on an apple, the apple must pull back on the Earth with an equal and opposite force.

That's really all the "proof" that is needed.

Your problem is at three. Gravity is not a force. Gravity is known to cause an acceleration through space. This does not make gravity force. It makes it a cause of force. Incidentally, 3 to 5 is one hell of a jump.

Pick up any textbook and you will see that all physicists agree that gravity is a force. (Caveat: we're not dealing with the general relativistic description of gravity here. Walk before you run.)

Do you think all physicists are wrong?
 
pardon
what is the gr des of grav?

this boggles
how can something so basic be such a mystery?

pardon
is it a mystery?
 
You're welcome.

I will also acknowledge that nothing you have said bears any resemblance to science, and that I made a mistake by not moving this thread in the first place.


Ben thanks for moving into what is known as pseudoscience. Only complaint is it didn't have moved status on the other forum. Had a bit of trouble finding it. Thought it must have been censored for a start.

Anyway all replies received definitely have a pseudo element to them so this is a fitting spot.

I should state though, that there is nothing false about pursuing what others consider to be proof of an apple attracting the earth. That is a genuine thing to do.

On going though just what everybody seems to have in their heads, there is mildly reoccurring theme. A beleaguered cry of how would the smaller mass know it was the smaller mass and thus know not to not use its gravity.


iceaura said:
You are claiming that when two bodies are attracted to each other, only the larger is "pulling". The question is: how does either body know which one is larger ?

For a start I don't use the term pulling. In between adjactent bodies, the direction of acceleration of gravity of each is always opposite.


0654fc95afac72948b816042231bc471.jpg


Mathematically there must always be a termination of gravity at some point between the adjacent bodies. It is not a matter of the smaller body somehow knowing it is smaller, beyond the termination point there is no direction of fall towards it. Pretty straight forward really. Surprised that you are having trouble seeing it. Possibly you are missing seeing that the direction of fall between adjacent bodies is always in opposite directions.



Really? Please, site your source.
The high tide under the moon is caused because the net force acting upon the water has changed, not because the gravitational field strength of the earth has changed. That said, the tides are a complex process, and are thus a fairly poor example.

You are like JR and have to explain how you know that gravity is a force. Not sure why you would say the gravitational field strength of the earth has not changed. Drop something under the moon. It falls at a slower rate to something dropped 6 hours further around the earth. The change is measurable. You are trying to say black isn't black for some reason or other.

Simple: I acknowlege Netwons second law of motion as well, and all works out.


Certainly, though he doesnt have a single law, it is more of applying his laws to the scenario you created.

The net force is defined as the sum of all forces acting upon an object, which is how we get z=x+y, assuming we keep our system simple (only taking the gravitation of the two bodies into account.) From here, it is all mathmatics (using Newtons law of universal gravitation to find out values for x and y)
Z=0 if the location of our particle happens to resault in an x value of equal magnitude as the y value, but in an opposite direction.

So, let's model the apple between the earth and moon, using newtons equations.
The scenario to be modeled: earth and moon and apple are in a line, apple is some distance d, from earth and moon, determin acceleration, y, on apple at given distance d.
Assume the moon has distance 5 from earth.
Let d be the distance of the apple to earth, where 5<d<0.
Let y be the net acceleration of the apple towards earth. (Negative meaning towards moon, force is a vector, so a negativ simply denotes opposite direction.)

Using Newtons law of universal gravitation:
If we say Fearth=G*Earth*Apple/d^2
Let G*earth*apple=4
Fearth=4/d^2

Fmoon=G*moon*apple/(5-d)^2
where G*moon*apple=1 (moon's mass is roughly 1/4 of the earth's)
Fmoon=-1/(5-d)^2
(5-d) meaning, the distance of the moon to earth minus the distance of the apple to earth give us the distance of the apple to the moon, -1 because the moon is pulling the apple away from the earth.

Now, we know that Fnet equals the sum of all forces, so assume the two above are the only forces in the system:

Fnet=Fearth+Fmoon

Newtons second law states that Fnet=ma, where y=a, and the mass of apple is 1:
ma=Fearth+Fmoon
my=Fearth+Fmoon
y=(Fearth+Fmoon)/m
y=(Fearth+Fmoon)/1
y=Fearth+Fmoon
y=4/d^2 + -1/(5-d)^2

So we have 3 functions, the acceleration on the apple due to the earth, Fearth (okay thats the force but deviding by the 1 mass of apple keeps the function the same)
the acceleration on the apple due to the moon Fmoon, and the aceleration on the apple due to both, y.

Now punch those into a graphing calculator such as this one:
http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
And we see that, according to newton, the acceleration of the apple is indeed 0 at one point, because the function y intersects the d-axis (near 3.3)
We can also note that at that value of d, the forces due to the gravity of the earth and the moon have non-zero magnitudes, furthurmore they have equal magnitudes, and are opposite, fullfilling newtons first law; as they are balanced, and causing there to be no acceleration on the apple.

-Andrew

That’s rubbish Andrew. You are presuming that the apple attracts the earth, rather like in Cavendish experiments where a universal constant is worked out when the large mass has not been observed to move and the small mass has taken no part in the calculation. Your trouble is you are seeing Z as a net force of zero. It is a resultant rate of acceleration of zero.




Pick up any textbook and you will see that all physicists agree that gravity is a force ?

Sorry JR but this does not make gravity a force. You seem to be saying gravity is a force because everyone says it’s a force. That is very much a psuedoscience answer.

We know

1/that gravity causes mass to accelerate

or that 2/ gravity causes mass to become weight when such acceleration is restricted by the presence of other mass

How and why do you jump to gravity is a force from there beyond doing it because everyone else does is yours to answer. Not mine.

plane:Do you think all physicists are wrong??

Anybody who believes that a small mass attracts a large mass has their case to prove.

0654fc95afac72948b816042231bc471.jpg


Can you really explain how there is an acceleration towards the smaller mass from the point indicated.

Please don’t waste your time replying if you don’t want to.

Only really after why everybody believes a small mass attracts a large mass. The asking of "how would the small mass know its the small mass" has been of some help.

Cheers.
 
plane:

You seem to be saying gravity is a force because everyone says it’s a force. That is very much a psuedoscience answer.

We know

1/that gravity causes mass to accelerate

or that 2/ gravity causes mass to become weight when such acceleration is restricted by the presence of other mass

You're arguing against yourself.

Take your point (1): gravity causes mass to accelerate. Newton's second law says what? Hmm... that's right. Here it is:

F = ma

On the right we have mass and acceleration. On the left, we have what causes that acceleration. What causes acceleration? Oh look! Force. And you know what? Nothing other than a force can cause a mass to accelerate. That's what we mean by "force". A force is something that causes an acceleration.

Therefore, we see by your own statement that gravity is a force.

I don't understand statement (2); it's not clear.

Please don’t waste your time replying if you don’t want to.

I'll be selective - just as you are selective in responding to my points. I notice that you won't engage with points you find inconvenient for your argument.

Do you have an open or closed mind about this?
 
What do you mean "I move to both exerting the same force on each other"? What is this supposed to mean??

A mass always exerts a force on another mass. The force is constant if the mass is constant.
They individually "exert" a force which is proportional to their individual mass.

What is the big problem with this, that 2 bodies will attract each other with force proportional to mass?
Why would this become zero at some point? There is a point between two bodies, that will see no net attraction because the forces are equal, or whatever third object is at such a point will not accelerate, or will have no weight in either gravitational field, it's said to be at an equilibrium point.
This isn't because the attraction from either mass on the third body between them is zero, it's just balanced, or algebraically zero--like when two cars collide head-on, their velocity becomes zero, but momentum doesn't.
 
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