Gravity at Earth's Center: Does Weightlessness Follow?

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Discussion Overview

The discussion centers around the concept of weightlessness at the center of the Earth and the implications of being in a void within a spherical shell of uniform density. Participants explore the nature of gravitational forces and sensations experienced in such environments, comparing them to deep space.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that at the center of the Earth, one would feel weightless due to the lack of net gravitational force acting from below.
  • Others clarify that this weightlessness is contingent on the assumption of perfect spherical symmetry of the Earth.
  • A hypothetical scenario is introduced where a person floats in a vacuum void at the Earth's center, prompting questions about the sensations experienced compared to deep space.
  • It is proposed that all locations inside a hollow symmetric spherical shell provide a net gravitational acceleration of zero, regardless of the shell's size or thickness.
  • Some participants debate the distinction between gravity as a force and gravitational acceleration, with differing views on how these concepts relate in Newtonian physics.
  • Concerns are raised about whether the uniform gravitational pull in a void would create tensile stress on an astronaut's body, with some arguing that no stress would be present due to the absence of a gravitational gradient.

Areas of Agreement / Disagreement

Participants express differing views on the nature of gravitational forces and the implications of being in a void versus deep space. There is no consensus on whether the sensations experienced would be identical or if there would be any physical stress involved.

Contextual Notes

Assumptions about the Earth's symmetry and the nature of gravitational forces are critical to the discussion. The mathematical principles underlying gravitational effects within a hollow shell are referenced but not fully resolved.

enokwei perez
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gravitational force act in pairs, and they act toward the center of the earth. does it mean that if u find yourself at the Earth center will your fill weightless?
 
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Welcome to PF;
I'm not sure what you mean by "gravitational force act in pairs" so I'll go right to your question ...
In the center of the Earth, there is no mass "below" you - so no net gravitational force acts on you from the Earth - though you will have your own gravity - so you could describe this as "weightless".
 
"does it mean that if u find yourself at the Earth center will your fill weightless?"
Yes, of course. (Assuming the Earth had perfectly spherical simmetry, otherwise its geometrical centre doesn't correspond to its centre of mass)
 
Continuing on with this question on weightlessness ...
Suppose there was a spherical Void in the center of a Earth (assume equal density throughout) and the void was a vacuum similar to deep space. If a person with an astronaut suit was "floating" in this void, would the sensation be the same as that in deep space?
 
Yes, all locations inside a hollow symmetric spherical shell of constant thickness and density provide a net gravitational acceleration of zero.
This is true for a sphere of any size, a symmetric shell of any thickness of constant density, any size hollow symmetric centered space within the shell, for any location within the hollow space within the shell, not just the center.

The inverse square relation and the distance to the way the mass is distributed in the shell makes this so for all locations inside the shell.

Also, gravitation is an acceleration, not a force...
 
bahamagreen said:
Also, gravitation is an acceleration, not a force...
What do you mean by this? Gravity is most certainly a force in the Newtonian framework. Don't confuse the force of gravity with the strength of the gravitational field, the latter of which is an acceleration.
 
@iluvtek: welcome to PF;
You can quickly understand the answer to your question by figuring out where the sensation of "being in deep space" comes from.
 
Although I understand zero gravity does not exist, let's assume deep space is located in area virtually free of any gravitational pull. Wouldn't this be different than having a uniform gravitation force applied from all directions (as is the case with the void in the earth)? If the gravitation pull was strong enough wouldn't this create a type of tensile stress on the astronaut's body?
 
The void (in the Earth or shell) has no gravitational gradient (no tidal effects), the space there is flat at all interior locations... same as "zero gravity" deep space.
 
  • #10
iluvtek said:
Although I understand zero gravity does not exist, let's assume deep space is located in area virtually free of any gravitational pull. Wouldn't this be different than having a uniform gravitation force applied from all directions (as is the case with the void in the earth)? If the gravitation pull was strong enough wouldn't this create a type of tensile stress on the astronaut's body?

No stress would be present, as there is no gravity gradient inside a hollow shell. It is 0 at all points. It's counterintuitive, but it is how the math works out!
 

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