How does a body escape its gravitational field?

[-Job-]

Might seem like a strange question, but why does the Earth move? Shouldn't it's gravitational field keep it in place? Wouldn't the space immediatly surrounding the Earth offer considerable resistance to its movement? Things on the surface of the planet have a hard time escaping the Earth's gravitational field, and yet the whole planet, as one, does it continuously. In the traditional model of gravity consisting of ball on top of a sheet, bending the sheet, the ball wouldn't be able to just get out of its hole without considerable energy, that movement then would expend some amount of energy, due to the "resistance of space", how much energy then wouldn't we need to have the Earth moving all this time? Is this a stupid question?

 

[Kurdt]

If you're using the rubber sheet analogy remember that the indentation caused by a mass is not fixed so a body cannot 'escape' its own gravity. If you roll a ball on a rubber sheet the indentation it makes does not impede its movement yet if something else were to roll close to it the indentation created by the ball would eefect that object.

 

[ZapperZ]

Might seem like a strange question, but why does the Earth move? Shouldn't it's gravitational field keep it in place? Wouldn't the space immediatly surrounding the Earth offer considerable resistance to its movement?

Whoa! Since when does "space" have "considerable resistance"?

Zz.

 

[Ich]

Whoa! Since when does "space" have "considerable resistance"?

Yes, You´re taking the rubber sheet analogy too seriously. Remember that even in GR the "speed of the Earth through space" is not defined, so contrary to a rubber sheet the indentation in spacetime does not move against spacetime. So space has no resistance against movement.

 

[-Job-]

I only meant "resistance" as the gravitational pull in that region in space. To any object at the surface of the planet the curvature of space prevents the object from leaving the planet easily, offering "resistance" to movement in the direction opposite to the gravitational pull.
What lead to this question was thinking about how movement of the Earth is processed. It can't be by: this portion moves, then this portion moves... etc, because each of the portions would be going against the gravitational pull of the rest of the planet. So the whole planet must move exactly at the same time, i suppose, otherwise it wouldn't be able to escape its own gravitational field, that was what i meant. But i don't know whether or not the whole planet moves at the same time, as in "after x seconds every 1/n of the planet has been displaced by exactly the same amount". I really have no idea how things move, or whether they do at all.

 

[Conal]

You seem to be picturing a flat plane of space-time with the Earth plonked in the middle, stuck in its own indentation. But the plane is not flat - its sloping down towards the sun, which has made a comparitively huge indentation. So the Earth would have to be moving, like a marble spinning round in a funnel.
I would think of the Earth moving as a single unit, not the individual particles that make it up because gravity is only really significant on a large scale.

 

[ZapperZ]

I only meant "resistance" as the gravitational pull in that region in space.

Then what is so special about gravitational pull if all you care about is "resistance" from being pulled away? Is it valid for me to argue that space has "resistance" since it is so difficult for me to pull an electron away from a positive charge? There's no gravity involved here.

These are nothing more than the force on an object. One requires no warping of spacetime to observe the IDENTICAL effect, i.e. the resistance of being pulled apart. So it is logically invalid to argue that "can't pull things apart" must be equal to "resistance of space".

Please note that you have a rather simplistic and naive view of GR in terms of the warping of Minkowski SPACE-TIME. It isn't just SPACE that is affected.

Zz.

 

[Hurkyl]

Might seem like a strange question, but why does the Earth move?

In some coordinate systems, it doesn't move.

And in an important sense, the Earth isn't moving: it's (more or less) blissfully following a geodesic through space-time without being accelereated.

Of course, you're not blissfully following a geodesic... you're being violently thrust away from an intertial path by that 9.8 m/s² force from the ground pushing you up.

 

[russ_watters]

I only meant "resistance" as the gravitational pull in that region in space. To any object at the surface of the planet the curvature of space prevents the object from leaving the planet easily, offering "resistance" to movement in the direction opposite to the gravitational pull.

Right, but Earth is not leaving itself, so it isn't traveling up in its own gravitational field.

Earth doesn't just reside in that curvature in the rubber sheet, it causes the curvature in that rubber sheet. So there is no reason why it would/could resist its own movement. To itself/its gravitational field, it is always stationary.