If one thinks both A and B fall towards each other with just an acceleration of GM/d2=Gm/d2 then s/he is wrong. It is very clear that higher types of motion are involved in their falling just because on-center decreases on either (both) sides not just on one side. (Am I wrong to say that?). Isn’t it justified?
Yes, you are wrong. No, it is not justified.
No, they aren't.
They each accelerate towards each other.
That doesn't mean the distance between them will shrink at that rate.
The acceleration of each object is not necessarily the same as the time rate of change of the time rate of change of the distance between the centres.
Instead, that time rate of change is the sum of the 2 individual rates.
i.e. if you have 2 objects of equal mass M, that are separated by a distance d, then the acceleration of each mass will be equal to GM/d^2, and thus the time rate of change of the time rate of change of the distance between the centres will be 2*GM/d^2.
That means at some time t, the distance between them will be 0.
If you assume they are spherical masses of radius r, you have 0 at the centre, object 1 starting at d/2 and object 2 starting at -d/2, such that the initial separation is d.
Then at some time t, the 2 objects collide such that object 1 is now at r and has travelled a distance of d/2-r, object 2 is at -r and has travelled a distance of d/2-r, and the separation between them has shrunk to 2r, or by d-2*r.
It is a simple scaling factor.
There is no problem here, just annoying math.
If you want to do the math to show there is a problem, go ahead.
I might later, but as you need to solve d
2x/dt
2 = -k/x^2, which is not trivial to solve, I can't be bothered at the moment, especially when you show absolutely no willingness to deal with the refutation/rebuttal of your claims and instead you just move on to something else.
Now like I said, if you have a point, make it. Don't expect others to do your work for you.
So if we don’t know the “g” of the moon then why astronauts pretended their moonwalks similar to the celestial body which has 1/6th gravity of earth.
But we do know. And there you go again, just assuming it is all faked with no justification at all.
Both axial rotation and orbital rotation of earth are independent of each other. We know that both noon and anti-noon are happening together at once instantly. Neither one can be delayed. At any instance, multiple midnights are not possible for single noon.
And there isn't multiple midnights for any noon.
An "instant" represents a single point in time, which corresponds to a single angle, not an arc or any length. At any angle in your image there is a single noon and a single midnight. Thus there is no issue.
If you want to focus on a length, then you still need to consider the rotational motion of Earth and consider just how far it moves in a given time.
In the sun centred inertial frame, the point on the surface of Earth at midnight is travelling faster than the point on the surface at noon. Thus it will sweep out a longer path.
Again, THERE IS NO PROBLEM!
The nonsense you are spouting now is like claiming that rotational motion is impossible because the outside needs to travel further than the inside.
Is Galileo's statement correct, theoretically?
Yes.
Three masses are involved in the Galileo statement. Mass of earth, mass object A and B. it's not necessary A and B have to be small masses like feather and hammer. You will notice what I said earlier once you play with masses of A and B including earth.
Deal with what has been said rather than just ignoring it.
Play with the masses all you like, it won't magically make Earth accelerate differently at the same time.
You cannot physically have Earth accelerate more towards the heavier object while at the same time have it accelerate less towards the lighter object when both objects are in the same direction.
Like I said, and clearly demonstrated, on Earth, the acceleration of Earth is insignificant.
And again, Earth accelerating towards the object doesn't magically mean the objects accelerate more.
As both ge and gie are equal in magnitude but opposite in direction therefore both will cancel each other. This means both earths are weightless
No.
The 2 forces are acting on different objects.
That means each object has a weight.
What it means is that if you were to place an object in the middle of them, there would be no net force. Or alternatively if you consider the system of both "Earths" there would be no net force and thus the centre of mass of the system would not move.