Question

if gravitational force increases with the inverse of the distance squared, does it mean the force is near infinite as distance approches 0?

Answer 1

according to te equation we get infinity but it doesnt mean that it is infinite..it is undefined at 0 distance...thats why we call infinity with other name undefined..if the force is infinite it is absurd the whole universe will collapse if you merge two rocks!!

Answer 2

same is the case if you talk about center of charge, electric field is also inversely proportional to the square of distance ...so electric field should be infinite at center..but it ain't so...

Answer 3

At the center of the earth, you would not feel any gravity. This is because the gravitational pull from every region of the earth is exactly counteracted by the gravitational pull from the corresponding region on the opposite side of you. This all adds up to a great bug zero.

Answer 4

well it may be undefined at exactly 0 distance, but what about 0.0000001 distance?, applying the formula it would certainly raise a big number.

Answer 5

at exactly zero gravity is also zero because of equal forces from all the sides , cancels out and resultant gravity is zero at the center

Answer 6

the only explanation to this I can think of is that maybe it does approach infinity but it only happens for an infinitesimal amount of time which implies nothing extraordinary.

Answer 7

there is no infinite gravity ...just follow a basic free body diagram at the center of earth ..and you're gonna get zero gravity..that is at the center of earth a body will be having damped oscillation and finally stable , with no gravity

Answer 8

ok well, gravity does the trick, but what about those of electrostatics? if you only had 2 opposite charged particles, they also use the inversely proportional to the square of the distance between them.

Answer 9

see that's the different thing ...now you're talking about center of two charges it's a system...and distance between charges can't be zero ..because here, to keep the system stable charges will be at a certain minimum distance and if they will come closer forces between them will act in reverse direction (you can study potential energy curve)

Answer 10

you mean two oppositely charged particles (one + another -) will start repelling each other after they surpass a certain limiting distance?, like bounce off each other as if they were same charge? wouldn't they keep on bouncing off and back again indefinitely forever?

Answer 11

yes exactly after surpassing a certain distance they will repel to get a position on minimum potential energy and they won't keep bouncing ...as soon as they reach that distance at which potential energy is minimum they will be stable...and bouncing is in case of gravity..that is if you will reach at the center of earth then bouncing will occur

Answer 12

ok I can live with that explanation. Thank you. And just out of curiosity, how is that bouncing with gravity? for example if you managed to build a tunnel or a hole that went straight to the center of the earth passed through it and to the other side of it, drop some object into it, wouldnt it just fall and exit through the other end, or would it bounce as you implied?

Answer 13

well i manage to create a cavity or a hole and if i am dropping something there then the component of gravity at the other side will definitely try to pull it on its side but the opposite side will also apply force (gravitational force) to hold it back ..therefore object will keep swinging back and forth... you can see that both the component will keep pulling object at its side...

Answer 14

oh ok, yes that is what I believed would happen, I thought that by "bouncing" you meant falling till reaching the center and then bounce off back to the same place where the object was dropped.

Answer 15

now only one more thing, if you dont mind

Answer 16

no no...it will oscillate about the center of earth (you can consider center of earth as mean position of the oscillation)

Answer 17

you've been very generous sharing your time to this conversation

Answer 18

i love discussing concepts because i too have learned something from this

Answer 19

lets imagine the earth now were hollow, meaning there is only empty space surrounded by a rocky shell, it a perfect spherical earth.

Answer 20

You have argued that if you were at the center of the earth there would be 0 gravity, which i think works exactly the same with the hollow earth

Answer 21

it would because it is equally attracted in all directions so the net force rests in 0

Answer 22

right?

Answer 23

right

Answer 24

ok now what if you were not exactly at the center, lets say halfway between the surface and the center, what happens?

Answer 25

then at that point you will be attracted towards the center...but as soon as you'll reach the center then gravity will work on you in all the directions and resultant force on you will be zero

Answer 26

you mean it would accelerate towards the center and then make full stop at it?

Answer 27

yes...it will be accelerated at center but at center due to it's inertia it will swing back an forth...that's why i said it will oscillate..

Answer 28

ok ok, but why is it attracted towards the center if in the center there is nothing? wouldn't it be attracted to the surface walls which are the real source of attraction?

Answer 29

see physically at center of earth there is a molten material..it's nothing like the center of earth is hollow....so it is obviously attracted to the surface...

Answer 30

that is one theory I had too, but I would like you to consider (and later discuss) the other theory I had which I am beginning to believe true: Maybe there is 0 gravity anywhere inside the hollow earth because the side that is closer pulls you stronger than the other farther side, but it is compensated by the larger surface that the other side has. So the forces all along might sum 0.

Answer 31

let me draw this