Inside a Spherical Chamber

[Just thinking]

You would go immediately to Zero G.

 

[Ziggurat]

So if you had a bubble with a large mass the gravitational fields on the outside of the bubble would be affected by that mass but the gravitational fields inside the bubble would be as if there was no bubble at all?
Would there be some sort of step as you cross the boundary?

If the shell is infinitely thin, the transition would be like a step function. If the shell has thickness, then the gravitational field will vary linearly within the shell (assuming uniform density), going from zero on the inner surface to whatever value it takes on the outer surface. In this context, "within the shell" is different from "inside the shell", and means inside the material of the shell itself, if you catch my meaning.

 

[jasonpatterson]

What often winds up confusing students when they try to apply the shell theorem is that the cancellation only applies to those portions of a planet that are currently above the point at which we'd like to know the force of gravity. A common mistake is assuming that entering any shell causes the gravitational force to drop to zero rather than that that shell's gravitational force drops to zero.

As a practical example, I can go into a 1 mile deep mine and gravity (assuming uniform density, etc), ought to be about 1/4000th weaker as a result because there is now a 1 mile thick shell of earth that I am inside. If I travel down to 3 miles, then there would be a 3 mile thick shell and my weight would have been reduced by about 3/4000ths compared to the surface. In neither case would we expect the gravitational force to drop to zero.

(I realize that nobody made this mistake, I'm just commenting on it as a note for those to whom it is a new idea.)

 

[Towlie]

What often winds up confusing students...

Ironically, that's exactly what wound up confusing my 7th grade science teacher.

He insisted that gravity continues to increase as you approach the center of the Earth and reaches a maximum when you reach the center. My question of "Which way is down then?" was totally lost on him. It took me an extreme amount of work to finally prove that I was right and he was wrong.

 

[Uncayimmy]

What often winds up confusing students when they try to apply the shell theorem is that the cancellation only applies to those portions of a planet that are currently above the point at which we'd like to know the force of gravity. A common mistake is assuming that entering any shell causes the gravitational force to drop to zero rather than that that shell's gravitational force drops to zero.

I don't want to take this off-topic, so I'll just post a link to an interesting article that touches on the subject.

What happens if you fall into a tube through the earth.

 

[MattusMaximus]

I think that was his point.

Doh!

 

[Towlie]

What happens if you fall into a tube through the earth.

As a side note, you might be interested in knowing that in less than three months, the U.S. National Debt will equal a stack of $100 bills with a height equal to the length of that tube.

(Mathematics and references will be provided on request.)

 

[PitPat]

I don't want to take this off-topic, so I'll just post a link to an interesting article that touches on the subject.

What happens if you fall into a tube through the earth.

Don't want to take this further off topic, but this reminded me of a short Neil DeGrasse Tyson segment I saw recently which demonstrates this, for those of you who, like me, prefer movin' pictures over those pesky written words.


Requires Quicktime

http://www.teachersdomain.org/asset/oer08_vid_gravitynsn/