What does a person weigh at the center of the Earth?

[jammieg]

?

[HallsofIvy]

That's pretty trivial isn't it? Since the gravitational attraction is spherically symmetric, there is no net pull and so no weight.

[jammieg]

Yes it seems very trivial but then maybe not...

[brum]

are we assuming a point mass?

then, yes, it is trivial.


otherwise, if it's not a point mass but a human body, would that change things?

[franznietzsche]

Originally posted by brum
are we assuming a point mass?

then, yes, it is trivial.


otherwise, if it's not a point mass but a human body, would that change things?

well it would..in a way. You'd get tidal forces on parts farther away from the center having a greater net pull on them, so the body would oscillate over the center point, unless it was placed so that the two centers of gravity coincided exactly. Also as it oscillates, becaseu we are dealing with reall objects energy would be lost and the person would settle to the point where the two centers of gravity coincided, thus weighing over all nothing because there is zero net force.

[jammieg]

So at the center of the Earth I shouldn't weigh anything, that sounds true, as to it being trivial it's trivial if one assumes it's trivial, but then what did they tell me in school heat was I don't remember?

[ShawnD]

Since gravity is caused by mass and being at the centre would mean all the mass is surrounding you; wouldn't you be torn apart by gravity?

[Chi Meson]

Originally posted by ShawnD
Since gravity is caused by mass and being at the centre would mean all the mass is surrounding you; wouldn't you be torn apart by gravity?

No, since each and every particle of you would be equally pulled in all directions, the net force on each particle would be zero.

You would instead be crushed by the enormous pressure. Since pressure is not a vector it does not "cancel out." Of course you would not be able to exist in the molten core of the earth anyway, so as long as we begin with fantastical assumptions we should stay within "ideal" circumstances: net force (from the earth) is zero.

[pmb_phy]

Originally posted by jammieg
?

For a person to exist at the center of the Earth there must be a cavity hollowed out for him to fit into. If you hollow out a spherical cavity then there will be no gravitational forces througout the cavity and hence no tidal forces. Therefore the person would be weightless where weight is defined as the force required to support a body in a gravitational field

[jammieg]

Why is the center of the Earth a molten core?

[rocketcity]

For a perfectly spherical cavity in the center of perfectly spherical Earth, it shouldn't matter whether you're a point mass or not. Draw a Gaussian surface just inside the cavity: no mass-enclosed, and spherical symmetry lets you pull F outside the integral. Result: the magnitude of the force is zero divided by something.

So you could anywhere in that spherical cavity, even right next to the wall, without a problem.

Is the same also true if there's a cylindrical shaft going (perfectly) from one side of the earth to the other?

In our non-perfect world, I suspect the magnitude of the force vector would still be very small, hardly enough to rip you apart. Mount Everest, for example, would be tugging you towards Asia with nothing comparable to counteract it, but the force would be tiny. Nearby perturbations wouldn't be massive enough to matter; distant ones would get killed by the one-over-r-squared.

P

[russ_watters]

Originally posted by jammieg
Why is the center of the Earth a molten core? Heat.

[HallsofIvy]

Originally posted by jammieg
Why is the center of the Earth a molten core?
In order to keep you from standing there and testing what we have told you.

[jammieg]

That's one possibility although that would suggest some huge conspiracy with little green men running around and it's sounds like the start of another good movie or book but, I think it more likely to start first that it is a theory.

[pmb_phy]

Originally posted by HallsofIvy
In order to keep you from standing there and testing what we have told you. [:D]