Hope you may convince in my last try

NEWTON LAW OF GRAVITATION: The gravitational force

**BETWEEN** two masses = F GMm/d^

^{2 }SPLIT ANALYSIS of Earth and Apple:

**When an Earth is a gravitating mass and an Apple is a falling mass**

Acceleration due to gravity of earth; g

_{e} = GM/R^

^{2} (on the the surface of earth); where R = radius of earth.

So an apple fall on earth at the rate of g

_{e}**When an Apple is a gravitating mass and an Earth is a falling mass**

Acceleration due to gravity of apple; g

_{a} = Gm/r^

_{2} (on the surface of apple); where r = radius of apple

So an earth falls on an apple at the rate of g

_{a}Force of Earth on Apple = Force of Apple on Earth

An apple falls due to g

_{e} on Earth. The earth also moves upwards towards apple due to g

_{a} of apple but by such a minuscule amount to be noticed or measured.

**Shell Theorem **

The presence of any mass M inside homogeneous Hallow Sphere HS. Two gravitational accelerations “g” are involved in this problem

1- Acceleration due to gravity “g” of HS

2- Acceleration due to gravity “g” of M

Three possible conditions

The “g” of HS < The “g” of M, The “g” of HS = The “g” of M, The “g” of HS > The “g” of M

Also, the size, mass, and shape of M can be varied and its location inside HS as well

According to shell theorem: The entire spherical shell exerts zero net force on M

This may be true as I said earlier but this is not the end of story. There is mammoth difference between

“Gravitational Force

**ON** a mass and Gravitational Force

**BETWEEN** two masses”

Newton’s gravitational force is between two masses. Gravitational force on a mass is only considered during split analyses like “Earth on apple” and “Apple on earth”. Their combined effect appears in F = GMm/d^

^{2}. As gravitational force is a force that attracts any objects with mass therefore HS attracts M but M also attracts HS.

**The miscalculation in shell theorem is that HS attracts M but M doesn’t attract HS. **

SPLIT ANALYSIS of HS amd M

**When HS is a gravitating mass and M is a falling mass**

Mass on one side is closer, but there is more mass on another side.

There are three masses and three centers of gravities “cg”

A represents the “cg” of Closer mass

B represents the “cg” More mass

C represents the “cg” of M

The distance between A and C is h

The distance between B and C is h1

Obviously, h1 > h. The entire spherical shell exerts zero net force on M – OK for the sake of arguments BUT the entire M also exerts a force on Closer mass as well as More mass of the HS. Here

**When M is a gravitating mass and HS is a falling mass**

Closer mass of HS falls on M with “g” of M

More mass of HS also falls on M with “g” of M

As h < h1 therefore the value of "g" of M at A > the value of "g" of M at B. Since net pull of M on two different parts of HS is not zero, therefore, Closer mass falls on M with little bit resistance from more mass of HS

**Conclusion**:

**Accelerations due to gravities of Closer mass and More mass of HS may be cancelled at the center of M BUT the value of “g” of M at A is greater than the value of “g” of M at B due to the difference in heights therefore movement happens because of unbalance pull of M on two parts of the HS**