Digging down into the earth puts you closer to its center of mass...?

Question

DIGGING DOWN INTO THE EARTH PUTS YOU CLOSER
TO ITS CM(CENTER OF MASS). YOU MIGHT THEREFORE THINK THAT
DIGGING DOWN INCREASES THE PULL OF GRAVITY
ON YOU (YOUR WEIGHT), BUT ACTUALLY THE
OPPOSITE IS TRUE. WHY?

Answer 1

Look at at as a whole.
It is not the center that attracts you it is the mass and we compute the forces as an inverse square of the distance from center to center of gravities between the masses in question.

Also

the closer you get to the center the smaller the mass therefore the pull gets diminished.

and finally

as you move towards the center of the Earth the masses you are passing by begin to act upon you. Finally when you reach the center the sum of the forces acting upon you becomes zero (symmetry)

I hope it helps ;-)

Answer 2

Actually, as you dig down the mass which you have passed does NOT pull you back up. Just like being inside a hollow sphere of mass, the net gravity is zero anywhere inside the shell. That's because if you're closer to one side of the shell, that shell exerts greater forcer per unit on you, but there are more units on the OTHER side of the shell which all pull with less strength but more units to perfectly cancel out.

In other words, the only mass you need to consider as you dig down is the mass left beneath you, so the volume*density calculation changes because the volume is simply the radius of wherever YOU are to the center of the earth, and decreasing the volume of the sphere under decreases the mass. Decreasing the mass of the object interacting with you decreases the gravitational force it exerts on you.

Answer 3

The center of mass isn't the issue.
The entire earth has to be considered as it is the entire earth that contributes to the gravity of a planet.

As you dig closer to the core, there is less mass to pull you "down" and in addition, there is now mass above you that is exerting a pull and mass to the sides that is basically canceled because of you position relative to its force.

Answer 4

Promethius got it most right. The inverse square law of gravitational attraction changes suddenly at the surface to a linear curve which is zero at the center of the earth and g at the surface. Just like a spring. From which you can deduce the period of vibration of a body falling down the hole (and through to the other side) and rebounding to its starting point. About 84 min round trip.

Answer 5

Mass and gravity are concentrated at the center of the earth as long as you are above the surface.
When you penetrate the surface it does not hold true because of the mass and gravity between you and the surface.

Answer 6

because as you go further down, you have less mass pulling you down, whereas you increase the mass pulling you up. Everything you have dug through is now asserting it's own gravitational pull upon you, in fact pulling you a little bit away from the center, making you seem lighter.

Answer 7

At a undeniable element the rigidity of gravity from the middle of the earth could triumph over the device's engines. Ask this question in an engineering dialogue board for some fairly solid solutions.

Answer 8

Perhaps it's not the center of mass where you find the strongest gravity? Perhaps it's the larger mass itself, and thus the outer part of the object?

Answer 9

the question is moot; you will never be able to dig down far enough.

Answer 10

if you on it logically then it is wrong,as we reach near the centre of any object the gravitational pull also increases.