# Gravitational Singularity

considering the earth as a sphere, at the centre of the earth, by the equation F = G*m1*m2/r^2 , the gravitational pull experienced would be infinite . so assuming that we built a tunnel from 2 ends of the earth through the centre, and a person jumps into the tunnel. till the centre of the earth, he would experience free-fall. after the point where the gravitational pull becomes infinity, what happens to the man?

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phinds
Gold Member
2019 Award
considering the earth as a sphere, at the centre of the earth, by the equation F = G*m1*m2/r^2 , the gravitational pull experienced would be infinite . so assuming that we built a tunnel from 2 ends of the earth through the centre, and a person jumps into the tunnel. till the centre of the earth, he would experience free-fall. after the point where the gravitational pull becomes infinity, what happens to the man?
There is no mass acting gravitationally on the center of the earth, so your premise is incorrect.

EDIT: actually, that's a simplification. There IS mass acting there but it all cancels out.

There is no mass acting gravitationally on the center of the earth, so your premise is incorrect.

EDIT: actually, that's a simplification. There IS mass acting there but it all cancels out.
can you explain this to me a bit? i'm just a beginner

phinds
Gold Member
2019 Award
can you explain this to me a bit? i'm just a beginner
The math is a bit complex but the concept's pretty simple. Think about it this way: You weigh a certain amount on the surface of the Earth. Now let's move you to a point 100 miles inside the surface. All of the mass above you is very close and pulling you in one direction. The mass below you is greater but most of it is farther away, so your weight is somewhat less. Now go 1000 miles inside. The imbalance is different and basically you are getting much lighter. When you get to the center, all the mass around you is pulling you evenly in all directions, so you are weightless.

The math is a bit complex but the concept's pretty simple. Think about it this way: You weigh a certain amount on the surface of the Earth. Now let's move you to a point 100 miles inside the surface. All of the mass above you is very close and pulling you in one direction. The mass below you is greater but most of it is farther away, so your weight is somewhat less. Now go 1000 miles inside. The imbalance is different and basically you are getting much lighter. When you get to the center, all the mass around you is pulling you evenly in all directions, so you are weightless.
thank you. i'm just a 10th grade student and this helped a lot

jtbell
Mentor
Divide up the earth into a lot of little equal-mass pieces, mentally. Each piece exerts a gravitational force on the object whose strength depends on the mass of the piece and how far it is from the object, and whose direction depends on where the piece is located relative to the object. The net gravitational force is the sum of the forces from all those little pieces.

For an object at the center of the earth, every piece of the earth in one direction from the object has a corresponding piece in the opposite direction at the same distance, so their gravitational forces are in opposite directions and cancel (add to zero).

For an object outside the earth's surface, the forces from all those little pieces add up and give a net force which is the same as if you collapsed all the mass of the earth into a single point at the center. In order to prove this, Isaac Newton invented integral calculus. (At least, that's the story I read somewhere.)

(added: phinds beat me to it while I was refilling my coffee. )

phinds