Gravitation on an Expanded Earth

[Lazzini]

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?

 

[jasonleroy]

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.

 

[Doc Al]

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".

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.

 

[Lazzini]

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.

 

[jasonleroy]

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.

 

[Lazzini]

"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?

 

[Doc Al]

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!

 

[Doc Al]

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!