Where on earth do I weigh the most?

Factual Questions
1

It is commonly said around here that the closer you are to the center of a gravity source (e.g. the earth) the more you weigh. So on top of a mountain you weigh an eensy bit less than you do at sea level.

However, if I actually traveled to the center of the earth (using the magic of hypothetical) I would be weightless. The earth would be all around me and tugging equally in all directions so I’d just float there. So, being as close as I can be to the center of gravity actually does not make me heavier.

So where on earth do I weigh the most? The surface of the sphere (my guess)? Some distance in? What if we remove all the air and water from the earth would I weigh more on the sea floor (some thousands of feet below sea level if the sea were there) or in New York?

2

I think you would weigh the most at the North or South Pole. The Earth is slightly flattened at the poles, so you would be closest to the center while still having the entire mass of the earth on one side of you (and thus all pulling in the same direction).

Being in a deep canyon would get you a bit closer to the center, but I think the effect would be offset by the fact that some of the earth’s mass would be pulling you away from the center.

3

Bottom of the Marianas Trench, I should think.

4

Not taking into account your buoyancy due to being immersed in seawater – that would make you weigh about zero (after your lungs had collapsed due to the pressure).

I suspect that the greatest weight is going to be very close to sea level somewhere.

5

Nevermind

6

Yes, but because of the Earth’s rotation, you would still weigh more at the poles, even if the Earth were a perfect sphere.

And actually, you’d weigh more at the North Pole than the South, since the South Pole is considerably elevated.

7

If you weigh more at the poles than at the Equator, why doesn’t the water in the oceans flow from the Equator to the poles, under that pull of gravity?

Yes, but what if you dug a hole at the South Pole down to sea level? Wouldn’t you weigh the same there at the bottom of the hole as you would at sea level at the North Pole?

8

I understand rotation lightens people not at the poles up some but for the purposes of this thread go ahead and ignore it. I am more interested in weight changing as distance to the gravitational center changes and rotation just needlessly confuses that.

And as for the Marianas Trench go with the no water/no air on earth bit. Again that is to just focus on how distance to the center changes things without worrying about sea pressure.

9

It seems like you’d weigh the most at the point on the boundary of the convex hull of the earth’s surface which is closest to the center of gravity. That’s going to be as close as you can get without having any mass above you.

10

Nope, because at the bottom of the hole, you’re going to feel some gravitational pull upwards by all the stuff above you.

11

Depends. Where do you eat your Thanksgiving dinner?

12

About the question of whether you would weigh more if you dug a really deep hole, if the Earth were constant-density you would weigh less and less as you descended. However, the Earth isn’t homogeneous, it has a very heavy iron core and the outer parts are much lighter, so for some distance in, the pull of gravity would actually get stronger as you go down. The pull of gravity is partially offset by having mass above you, but you’re closer to that really heavy iron core which more than makes up for it.

13

The field varies from place to place, but the potential is the same everywhere at sea level (to within some minor variation due to waves, currents, and the like). Water flows from high potential to low potential, not from weak field to strong field.

The answer is still the poles. Of course, the flattening of the Earth is itself due to rotation, and the two effects (distance to the center and centrifugal force) are comparable in magnitude.

14

This is what I was thinking earlier.

Also, if you were to dig a hole, your radius will be changing. The term in the gravitational force equation is squared. However, the stuff above you will not be increasing with the square of the radius.

15

I hate to use Wikipedia as a reference for this, but I recall reading somewhere (I think it was my physics textbook) that what CurtC and Santo said is true. According to wikipedia, the point of highest gravity is at the mantle-core barrier where gravity is 10.7 m/s^2 as opposed to the 9.8 m/s^2 it is at the surface.

16

For exactly the same reason. The centrifugal force that makes you slightly lighter at the equator also slightly pulls the water from the poles.

No, because you have all that mass of ice above you.

17

For me, it’s at the doctor’s office during my annual physical.

18

Last time I saw Michio Kaku on TV, he said there’s no
such thing as the pull of gravity.

It pushes, he said.

Not kidding.

19

No, the stuff above you will be decreasing with the cube of the radius.
As stated above, in a homogenous sphere, maximum gravity is at the surface.

20

It seems to me that at the surface, if we go down a kilometer, you’re going to be taking the difference of two big numbers squared. However, the cube we’re losing is going to be a much smaller number.

Gaining:
6371[sup]2[/sup] - 6370[sup]2[/sup] = 12741

Losing:
(6371 - 6370 )[sup]3[/sup] = 1

This is a gross simplification, but I forget the formula for the volume of a chord of a sphere. Little help? I’d like to see it mathematically.

Also, as stated above, the earth is not a homogeneous sphere. We know the density of the core, and of the mantle, and of the crust; let’s put a program together that will find the gravity with respect to radius.