Gravitation on an Expanded Earth

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    Earth Gravitation
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Discussion Overview

The discussion revolves around the concept of weightlessness in the context of an imagined scenario where the Earth expands to the radius of a geostationary satellite while retaining its mass. Participants explore the implications of this scenario on gravitational force experienced by bodies on the equator of the expanded Earth.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants assert that bodies in orbit are weightless, interpreting weightlessness as the absence of a supporting force, while still acknowledging the presence of gravitational force.
  • Others clarify that bodies in orbit are not truly weightless in terms of gravitational force, as they are in free fall towards the Earth, but their orbital velocity causes them to fall around the Earth instead.
  • A participant questions whether a body on the equator of the expanded Earth would feel no gravitational force, suggesting that it would be weightless.
  • Another participant argues that a body lying on the equator would still register weight, contradicting the idea of weightlessness in that scenario.
  • Some participants discuss the implications of weightlessness as experienced by astronauts, noting that they register zero weight on scales while in orbit.
  • A later reply acknowledges the idealized nature of the scenario and agrees with the idea that a mass on the surface of a giant Earth would register zero weight on a scale.

Areas of Agreement / Disagreement

Participants express differing views on the definition of weightlessness and its implications in the context of the expanded Earth scenario. There is no consensus on whether a body on the equator would feel no gravitational force or be weightless.

Contextual Notes

The discussion includes assumptions about the nature of gravitational force and weightlessness, and the implications of an idealized scenario without resolving the underlying complexities.

Lazzini
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Bodies in orbit around the Earth are, as I understand it, weightless. Suppose, then, that by some unimaginable process the Earth expanded to a radius equivalent to the orbital radius of a geostationary satellite, but retained the same mass. Does that imply that a body lying on the equator of the Earth would feel no gravitational force - i.e. would be weightless?
 
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They are not weightless. In fact, they are falling towards earth. It just so happens that their orbit velocity is such that they fall "around" the Earth rather than straight towards the center. If they were stationary, they'd fall immediately into earth.
 
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Lazzini said:
Bodies in orbit around the Earth are, as I understand it, weightless.
"Weightless" just means that the supporting force on them is zero and thus they experience no stress from such a force. It does not mean that they experience zero gravitational force. After all, it's the gravitational force that holds them in orbit! Any projectile in free fall is "weightless".

Lazzini said:
Suppose, then, that by some unimaginable process the Earth expanded to a radius equivalent to the orbital radius of a geostationary satellite, but retained the same mass, does that imply that a body lying on the equator of the Earth would feel no gravitational force - i.e. would be weightless?
No.

Please read this wiki page on weightlessness.
 
They are not massless, certainly, but surely they are weightless in the sense that they would register zero weight on bathroom scales in the same orbit? This, after all, is a problem faced by astronauts in orbit, and why they have to drink from squeeze-bottles, being unable to contain their drinks in a normal drinking vessel.

PS - Sorry - this is a reply to Post #2.
 
Lazzini said:
a body lying on the equator of the Earth would feel no gravitational force - i.e. would be weightless?
Once it's lying on the equator, you can measure it's weight.
 
Doc Al said:
"Weightless" just means that the supporting force on them is zero and thus they experience no stress from such a force. It does not mean that they experience zero gravitational force. After all, it's the gravitational force that holds them in orbit! Any projectile in free fall is "weightless".
Yes - I appreciate that, and just as a geostationary satellite experiences no stress from such a force, why would that not also be true of a body lying on the equator of the expanded Earth?
 
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Lazzini said:
They are not massless, certainly, but surely they are weightless in the sense that they would register zero weight on bathroom scales in the same orbit? This, after all, is a problem faced by astronauts in orbit, and why they have to drink from squeeze-bottles, being unable to contain their drinks in a normal drinking vessel.
Actually, you are correct! If you rest a mass on the surface of a giant Earth the size of a geosynchronous orbit it would register zero weight on a bathroom scale.

(We are talking about an idealized example, of course.)

My bad for misinterpreting your question!
 
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Lazzini said:
Yes - I appreciate that, and just as a geostationary satellite experiences no stress from such a force, why would that not also be true of a body lying on the equator of the expanded Earth?
You are correct, sir! My mistake! :oops:
 

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