Gravitation on an Expanded Earth

In summary, objects in orbit around the Earth are not truly weightless, as they still experience gravitational force. However, they do not experience any supporting force, resulting in a sensation of weightlessness. If the Earth were to expand to the size of a geostationary satellite, a body lying on the equator would also experience weightlessness, as there would be no supporting force. This is a problem faced by astronauts in orbit, as they are unable to use normal drinking vessels and must resort to squeeze-bottles.
  • #1
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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  • #2
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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  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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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  • #7
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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  • #8
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:
 

Related to Gravitation on an Expanded Earth

1. What is "Gravitation on an Expanded Earth"?

"Gravitation on an Expanded Earth" is a theory that suggests that the Earth's diameter has increased over time, resulting in a decrease in its gravitational pull.

2. How does the expansion of the Earth affect its gravitational pull?

The theory proposes that as the Earth expands, the distance between its center and its surface increases, causing a decrease in the Earth's gravitational pull.

3. What evidence supports the theory of "Gravitation on an Expanded Earth"?

One piece of evidence is the observation that the Earth's surface features, such as mountains and valleys, seem to fit together like puzzle pieces, suggesting that the Earth was once smaller and has since expanded. Additionally, the decreasing strength of the Earth's magnetic field over time supports the idea of a changing Earth.

4. How does the theory of "Gravitation on an Expanded Earth" impact our understanding of the Earth's history?

If the theory is proven to be true, it would change our understanding of the Earth's history and geological processes. It would suggest that the Earth has undergone significant changes over time, including an expansion in size.

5. What are the potential implications of the theory of "Gravitation on an Expanded Earth"?

If the theory is correct, it could have implications for various fields such as geology, paleontology, and even astronomy. It could also lead to new discoveries and advancements in our understanding of the Earth and its history.

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