Does Gravity Between Two Equal Mass Objects Cancel Out?

[zarmewa]

Galileo was first to demonstrate that all objects fall at the same rate in the absence of an atmosphere. As it is said that the Earth and the Apple fall toward each other but apple looks a lot to falls to the Earth as compared to the falling of Earth toward the Apple which is so tiny to be detected.

Let's imagine Earth is a homogeneous sphere and two identical apples start falling simultaneously from same ANTIPODEAN altitude in the absence of all other gravitational attraction including atmosphere.

So what would be the direction of accelaration of earth?

If net accelaration of Earth is zero in aforementioned scenario then would gravity "g" of two equal spherical spheres/ planets cancel each other if placed on each other?

 

[Bobbywhy]

Galileo was first to demonstrate that all objects fall at the same rate in the absence of an atmosphere. As it is said that the Earth and the Apple fall toward each other but apple looks a lot to falls to the Earth as compared to the falling of Earth toward the Apple which is so tiny to be detected.

Let's imagine Earth is a homogeneous sphere and two identical apples start falling simultaneously from same ANTIPODEAN altitude in the absence of all other gravitational attraction including atmosphere.

So what would be the direction of accelaration of earth?

If net accelaration of Earth is zero in aforementioned scenario then would gravity "g" of two equal spherical spheres/ planets cancel each other if placed on each other?

Two points that are antipodal to one another are connected by a straight line running through the centre of the Earth. China and Argentina are one example of antipodal points. So, if you would please explain what "ANTIPODIAN altitude" means it would help me understand what you are asking. Thank you. By the way, it is spelled "acceleration"

 

[zarmewa]

Let A and B are anitipodal points.

Assume

An apple is dropped from a height of h = 100 feet above ground level [point A]

An apple is dropped from a height of h = 100 feet above ground level [point B]

 

[DaveC426913]

Galileo was first to demonstrate that all objects fall at the same rate in the absence of an atmosphere. As it is said that the Earth and the Apple fall toward each other but apple looks a lot to falls to the Earth as compared to the falling of Earth toward the Apple which is so tiny to be detected.

Galileo was not demonstrating that an apple falls toward the Earth at the same rate that the Earth falls toward an apple.

Galileo was demonstrating that two objects (both of insignificant mass compared to Earth), both falling toward Earth, fall at the same rate.

Let's imagine Earth is a homogeneous sphere and two identical apples start falling simultaneously from same ANTIPODEAN altitude in the absence of all other gravitational attraction including atmosphere.So what would be the direction of accelaration of earth?

Zero. What does this have to do with the first part of your post?

You are conflating two separate scenarios.

If net accelaration of Earth is zero in aforementioned scenario then would gravity "g" of two equal spherical spheres/ planets cancel each other if placed on each other?

What do you mean by "cancel each other out"? They are still pulled toward each other with a significant force.

Regardless of the mass of the two (or even three) objects, the centre of mass of the two (or three) body system will have an acceleration of zero (i.e. the CoM will not move). What does this have to do with Galileo's discovery?