From Newsgroup: sci.physics.research

In the frame https://ibb.co/PsG2JQXK taken from the video https://www.youtube.com/watch?v=bK8T-ZbcZZA
there are two bodies: body A (the satellite of mass m) and body B
(the Earth of mass M).

And there are two forces--gravitational ones, obviously: F1 (exerted by
the Earth on the satellite) and F2 (exerted by the satellite on the Earth).

The two forces F1 and F2 do not constitute a single force because they
act on different bodies and have opposite directions.

Therefore, they are two forces, not just one.

Just as obviously, there are two gravitational accelerations, as
required by Newton's second law: there is the acceleration +a1=F1/m of
body A to the right, and there is *also* the acceleration -a2=F2/M of
body B to the left.

Two different forces causing two different accelerations on the two
different bodies, within the inertial reference frame.

But what is this inertial reference frame?

To understand this, I have summarized the phenomenon in the figure https://www.geogebra.org/classic/wqhxgce8
showing two generic bodies, A and B, of equal mass "m" that are gravitationally attracting each other.

Since the bodies have the same mass, the common center of mass "CM" is
located halfway between them.

There is the inertial reference frame!

Both bodies accelerate within the reference frame of the center of mass
(CM), where only the CM remains stationary while everything else
accelerates.

In this reference frame, there are two distinct accelerations: that of
body A to the right (+a1=F1/m) and that of body B to the left (-a2=F2/m).

Conversely, in the reference frame of body A (just as in that of body
B), there is only one acceleration: that of the other body as it approaches.

Is the magnitude of this unique acceleration--measured in the reference
frame of A (or B, which amounts to the same thing)--equal to
2a=|a_1|+|a_2| or to something else?
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From Newsgroup: sci.physics.research

On 13/09/2026 20:47, Luigi Fortunati wrote:

In the frame https://ibb.co/PsG2JQXK taken from the video https://www.youtube.com/watch?v=bK8T-ZbcZZA
there are two bodies: body A (the satellite of mass m) and body B
(the Earth of mass M).

And there are two forces--gravitational ones, obviously: F1 (exerted by
the Earth on the satellite) and F2 (exerted by the satellite on the Earth).

Those two forces describe the same interaction.

The two forces F1 and F2 do not constitute a single force because they
act on different bodies and have opposite directions.

Therefore, they are two forces, not just one.

Just as obviously, there are two gravitational accelerations, as
required by Newton's second law: there is the acceleration +a1=F1/m of
body A to the right, and there is *also* the acceleration -a2=F2/M of
body B to the left.

Two different forces causing two different accelerations on the two
different bodies, within the inertial reference frame.

But what is this inertial reference frame?

To understand this, I have summarized the phenomenon in the figure https://www.geogebra.org/classic/wqhxgce8
showing two generic bodies, A and B, of equal mass "m" that are gravitationally attracting each other.

Since the bodies have the same mass, the common center of mass "CM" is located halfway between them.

There is the inertial reference frame!

Both bodies accelerate within the reference frame of the center of mass
(CM), where only the CM remains stationary while everything else
accelerates.

In this reference frame, there are two distinct accelerations: that of
body A to the right (+a1=F1/m) and that of body B to the left (-a2=F2/m).

Conversely, in the reference frame of body A (just as in that of body
B), there is only one acceleration: that of the other body as it approaches.

No, there is another one: the accleration of the center of mass, which
also is the acceleration of every inertial frame.

Is the magnitude of this unique acceleration--measured in the reference
frame of A (or B, which amounts to the same thing)--equal to
2a=|a_1|+|a_2| or to something else?

The asked acceleration is twice the acceleration of the other body
in the CM frame, so its magnitude is twice the magnitude of the
acceleration in the CM frame.

This "twice" only applies in the special case of equal magnitued.
Otherwise there is some other number instead.
--
Mikko
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From Newsgroup: sci.physics.research

On 09/15/2026 at 04:08, Mikko wrote:

On 09/13/2026 at 20:47, Luigi Fortunati wrote:

In the frame https://ibb.co/PsG2JQXK taken from the video
https://www.youtube.com/watch?v=3DbK8T-ZbcZZA
there are two bodies: body A (the satellite of mass m) and body B
(the Earth of mass M).

And there are two forces =E2=80=93 gravitational, of course: F1 (exer=

ted by the

Earth on the satellite) and F2 (exerted by the satellite on the Earth=

).

Those two forces describe the same interaction.

Yes, it is the gravitational interaction of the third law that provides=20
TWO forces, that of the Earth on the satellite and that of the satellite=20
on the Earth.

Two forces, not just one.

The two forces F1 and F2 do not constitute a single force because=20

they act

on different bodies and have opposite directions.

Therefore, these are two forces, not just one.

Equally obviously, there are two gravitational accelerations, as
required by Newton's second law: there is the acceleration +a1=3DF1/m=

of

body A to the right, and there is *also* the acceleration -a2=3DF2/M =

of

body B to the left.

Two different forces causing two different accelerations on the two
different bodies, within the inertial reference frame.

But what is this inertial reference frame?

To understand this, I summarized the phenomenon in the figure
https://www.geogebra.org/classic/wqhxgce8
showing two generic bodies, A and B, of equal mass "m" attracting=20

each other

gravitationally.

Since the bodies have the same mass, the common center of mass "CM" i=

s

located halfway between them.

Here is the inertial reference frame!

Both bodies accelerate in the center of mass (CM) reference frame,
where only the CM remains at rest while everything else
accelerates.

In this reference frame, there are two distinct accelerations: that
of body A to the right (+a1=3DF1/m) and that of body B to the left=20 (-a2=3DF2/m).

Conversely, in the reference frame of body A (as well as in that of b=

ody

B), there is only one acceleration: that of the other body as it=20 approaches.

No, there is another: the acceleration of the center of mass, which
is also the acceleration of any inertial frame.

This is not the acceleration of a body because the center of mass is not=20
a body.

Is the magnitude of this unique acceleration =E2=80=94 measured in th=

e frame of

reference of A (or B, which is the same) =E2=80=94 equal to
2a=3D|a_1|+|a_2| or something else?

The acceleration in question is double the acceleration of the other b=

ody

in the CM frame; therefore, its magnitude is double the magnitude of t=

he

acceleration in the CM frame.

This "double" is only true in the special case where the magnitudes=20

are equal.

Otherwise it has a different value.

Exactly, in this case it is double, in all other cases it is an=20
intermediate value, i.e. between F1 and |F1|+|F2|.

Luigi Fortunati
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From Newsgroup: sci.physics.research

On 17/09/2026 18:35, Luigi Fortunati wrote:

On 09/15/2026 at 04:08, Mikko wrote:
> On 09/13/2026 at 20:47, Luigi Fortunati wrote:
>> In the frame https://ibb.co/PsG2JQXK taken from the video
>> https://www.youtube.com/watch?v=bK8T-ZbcZZA
>> there are two bodies: body A (the satellite of mass m) and body B
>> (the Earth of mass M).
>>
>> And there are two forces =E2=80=93 gravitational, of course: F1 (exer> ted by the
>> Earth on the satellite) and F2 (exerted by the satellite on the Earth> ).
>
> Those two forces describe the same interaction.

Yes, it is the gravitational interaction of the third law that provides
TWO forces, that of the Earth on the satellite and that of the satellite
on the Earth.

Two forces, not just one.

Being two descriptions of the same interaction, if one is known then so
is the other. More specifically, F2 = -F1;

>> The two forces F1 and F2 do not constitute a single force because
they act
>> on different bodies and have opposite directions.
>>
>> Therefore, these are two forces, not just one.
>>
>> Equally obviously, there are two gravitational accelerations, as
>> required by Newton's second law: there is the acceleration +a1=F1/m> of
>> body A to the right, and there is *also* the acceleration -a2=F2/M > of
>> body B to the left.
>>
>> Two different forces causing two different accelerations on the two
>> different bodies, within the inertial reference frame.
>>
>> But what is this inertial reference frame?
>>
>> To understand this, I summarized the phenomenon in the figure
>> https://www.geogebra.org/classic/wqhxgce8
>> showing two generic bodies, A and B, of equal mass "m" attracting
each other
>> gravitationally.
>>
>> Since the bodies have the same mass, the common center of mass "CM" i> s
>> located halfway between them.
>>
>> Here is the inertial reference frame!
>>
>> Both bodies accelerate in the center of mass (CM) reference frame,
>> where only the CM remains at rest while everything else
>> accelerates.
>>
>> In this reference frame, there are two distinct accelerations: that
>> of body A to the right (+a1=F1/m) and that of body B to the left (-a2=F2/m).
>>
>> Conversely, in the reference frame of body A (as well as in that of b> ody
>> B), there is only one acceleration: that of the other body as it approaches.
>
> No, there is another: the acceleration of the center of mass, which
> is also the acceleration of any inertial frame.

This is not the acceleration of a body because the center of mass is not
a body.

>> Is the magnitude of this unique acceleration -- measured in th> e frame of
>> reference of A (or B, which is the same) -- equal to
>> 2a=|a_1|+|a_2| or something else?
>
> The acceleration in question is double the acceleration of the other b> ody
> in the CM frame; therefore, its magnitude is double the magnitude of t> he
> acceleration in the CM frame.
>
> This "double" is only true in the special case where the magnitudes
are equal.

> Otherwise it has a different value.

Exactly, in this case it is double, in all other cases it is an
intermediate value, i.e. between F1 and |F1|+|F2|.

Tht "it" means the acceleration. Whith unequal masses it can be more
or less than twice, depending on which body is more massive.
--
Mikko
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From Newsgroup: sci.physics.research

Il 19/09/2026 23:10, Mikko ha scritto:

On 17/09/2026 18:35, Luigi Fortunati wrote:

>> In the frame https://ibb.co/PsG2JQXK taken from the video
>> https://www.youtube.com/watch?v=bK8T-ZbcZZA
>> there are two bodies: body A (the satellite of mass m) and body B
>> (the Earth of mass M).
>>
>> And there are two forces =E2=80=93 gravitational, of course:

F1 (exer> ted by the

>> Earth on the satellite) and F2 (exerted by the satellite on

the Earth> ).

>
> Those two forces describe the same interaction.

Yes, it is the gravitational interaction of the third law that provides
TWO forces, that of the Earth on the satellite and that of the satellite
on the Earth.

Two forces, not just one.

Being two descriptions of the same interaction...

How can it be the same interaction if *two* entities are acting?

One body pulls in one direction and the other in the opposite direction, exactly like in a tug-of-war.

The rope pulls and is pulled at one end (interaction 1) and pulls and is pulled at the other (interaction 2).

It is as if, rather than a rope, a spring were acting between bodies A
and B, pulling them and exerting *two* interactions rather than just one.

Luigi Fortunati
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From Newsgroup: sci.physics.research

On 23/09/2026 20:49, Luigi Fortunati wrote:

Il 19/09/2026 23:10, Mikko ha scritto:
> On 17/09/2026 18:35, Luigi Fortunati wrote:
>> >> In the frame https://ibb.co/PsG2JQXK taken from the video
>> >> https://www.youtube.com/watch?v=bK8T-ZbcZZA
>> >> there are two bodies: body A (the satellite of mass m) and body B
>> >> (the Earth of mass M).
>> >>
>> >> And there are two forces =E2=80=93 gravitational, of course:
F1 (exer> ted by the
>> >> Earth on the satellite) and F2 (exerted by the satellite on
the Earth> ).
>> >
>> > Those two forces describe the same interaction.
>>
>> Yes, it is the gravitational interaction of the third law that provides
>> TWO forces, that of the Earth on the satellite and that of the satellite
>> on the Earth.
>>
>> Two forces, not just one.
>
> Being two descriptions of the same interaction...

How can it be the same interaction if *two* entities are acting?

How many doublet sets can you make of those two entities? All known interactions involve a pair. In principle there could be interactions
that require bigger sets but none is known.

One body pulls in one direction and the other in the opposite direction, exactly like in a tug-of-war.

That is, the interaction is attractive.

The rope pulls and is pulled at one end (interaction 1) and pulls and is pulled at the other (interaction 2).

That is, there are three bodies and two interactions.

It is as if, rather than a rope, a spring were acting between bodies A
and B, pulling them and exerting *two* interactions rather than just one.

Very much except that there is not spring there. Newton's gravity is a non-local interaction between two bodies.
--
Mikko

[[Mod. note -- According to https://physics.stackexchange.com/questions/386627/why-there-is-no-3-body-or-more-generally-n-body-fundamental-force
there are a few 3-body interactions in physics (though not in
Newtonian mechanics).
-- jt]]
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