Gravitation Inside a Uniform Hollow Sphere

Over the heads of the living creatures there was the likeness of an expanse, shining like awe-inspiring crystal, spread out above their heads.

(Ezekiel 1:22) Good News Translation

We (that’s me and the Holy spirit) have an example of scientific sleight-of-hand. Scientists who understand it think that it’s a simple rationalization of a phenomenon. The problem is that the phenomenon doesn’t exist.

It’s based on the assumption that gravity is a property of space-time (Newton/Einstein gravitation). That’s the real issue. The situation that the algebra below is designed to address doesn’t exist. Take a look and see what you think. Can you find the flaw in the logic?

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We all have the same evidence. Our choice of paradigm determines what we think it’s evidence of.

– Matty’s Razor

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The gravitational force inside a hollow sphere shell of uniform areal mass density is everywhere equal to zero, and may be proved by the following argument:

Let the sphere have a radius a. Place a point P inside the sphere at a distance r from the center where r < a; i.e., r is strictly less than a. Draw a line through P to intersect the sphere at two opposite points. Call these points ά and β. Let the distance from P to ά be r₁, and the distance from P to β be r₂ .

Now place a differential area dA ά at ά , and project straight lines through P to acquire its image dA β at β. These two areas subtend a solid angle d ϕ at P. Let the sphere have areal mass density ρ (kg/m²). Then the net differential attraction dF of dA ά and dA β at P directed toward ά is just

dF = ρ( dA ά /r₁² – dA β /r₂²).

But dA ά = r₁² d ϕ , and dA β = r₂² d ϕ by definition of the solid angle. Thus,

dF = ρ ((r₁² d ϕ )/r₁² – (r₂² d ϕ )/r₂²) = 0.

This result is true for all choices of dA ά and dA β . The gravitational force within the sphere is everywhere equal to zero.

– Gravitation Inside A Uniform Hollow Sphere

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Faith is believing in something that you can’t see, because of evidence.

– Faith, definition

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If, however, gravity is a field emitted from the center of the Earth then the argument is irrelevant, because the “hollow sphere shell” doesn’t have uniform areal mass density. The density is highest at the center, and diminishes as you get further away. It’s a conundrum wrapped up in a paradox for you.

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