Is there gravity at the center of earth?

Question

And if so, which way will it pull?

So you are saying that a person will float? Let's say a perfect round hole is dug precisely in the center. If a person enters it, will he be stuck floating in the center?

Answer 1

Yes, there is gravity at the center of the earth, but it would exert the same force in all directions at once, resulting in a net acceleration of zero. Therefore, yes, you would float in the same manner as if you were in outer space.

Answer 2

The geometric center of the Earth, the mass center of the Earth, and the center of Gravity of the Earth are three different things. They are located also at three different spots.

If you were at the exact center of gravity... where the mass distribution and distance from mass cancel out on all sides of you, you would in fact remain static... or float if you will.

Gravity will be pulling from you on all sides equally and thus the net force on you would be zero. Of course because you are not a point mass and cannot be treated as such, you would also have to be oriented in such a way that your mass was distributed perfectly in the gravity field such that there were no gravity moments or gradients applied on you.

To answer your question, there is gravity everywhere. Anything with mass has gravity. Gravity can be quantitatively found and has a direct correlation with the mass of the body and the distance you are from it. However, it has yet to be qualitatively explained. The most prevalent theory suggest gravity bends space time and thus turns straight lines into curved ones in space... This is seen in gravitational lensing effects as the light from stars is morphed and "bent" around planets and stars.

Answer 3

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That equation you cited (g=GM/r^2) is for a point mass. It is also good for a spherical source when you are outside the sphere. It doesn't work inside the sphere. The gravitational field induced by a spherical shell is zero everywhere inside the sphere. So if you are at the center of the earth, you are "inside" all of the shells that make up the volume of the earth, so the field is zero. This is obvious just from symmetry. You're pulled equally in every direction. This analysis assumes that the earth is perfectly spherical. Of course it isn't, so you will have a g-field due to the assymmetries. But it will be very small for sure.

Answer 4

Say you dig a hole through the Earth from one side to the other. Drop a ball into it, and you think the ball would be suspended in the middle. However that's not true, the ball would actually oscillate back and forth. The ball would go the the other side, slow down at the surface, then come back to you, and the process repeats. Some of you say "well the forces cancel at the center so the ball should be suspended", but you seem to be forgetting "a body in motion stays in motion unless acted upon by an outside force". While you're right that no force acts on the ball at the center, the ball wasn't stationary to begin with, it was moving, therefore it'll continue it's course of motion until it gets off center and forces begin pulling it.

Answer 5

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RE:
Is there gravity at the center of earth?
And if so, which way will it pull?

Answer 6

If you were at the center of the Earth, you would be the point that every other thing on earth is attracted to. You would be the most attractive person on Earth.

Answer 7

The force due to gravity will be zero at the center of the earth. The symmetries dictate this.

Answer 8

If you were in a hollow sphere in the exact center of Earth, the mass of Earth would be evenly distributed around you, therefore also the gravitational forces generated. If the sphere were small compared to your body size, you'd experience microgravity (weightlessness), similiar to aboard an unaccelerating spaceship. If the sphere were much larger than your body size, you'd feel a slight tugging toward the nearest wall of it, i.e, you'd exhibit a weight of grams or ounces, depending on the size of the sphere, being completely weightless only when you were in the exact center of the sphere.

(Added after your additional details) -

Yes, if you jumped into such a well you would have to climb or be lifted out:

There's air in the well. Terminal velocity for a human in Earth freefall is in the range of about 100 (if your fall flat, arms and legs extended) to 200 miles per hour (if you "dive", body and limbs straight). If it weren't for the fact that the density of the air wouldn't be constant with depth, you'd maintain close to this speed for the first few hours (remember, it's 4000 miles to the center from here), until you were deep enough that a significant percentage of the mass of Earth was behind you. Then you'd gradually begin slowing down due to air friction versus the decreasing net gravitational force on you. After a couple of days of this, you'd be approaching the center of Earth at about the same speed as a feather falling through the air.

But if you factor into your well the fact that air pressure will increase by a factor of about 10 for every 10 miles down you go, you'll figure that you're going to have real trouble even get close to the center. The reasoning is this: at sea level, the volume of air equal to the volume of a person (about 3 cubic feet maybe) weighs about 0.006 pounds. Every 10 miles down you go, that same volume will weigh 10 times more. If I have it figured right (anyone out there???), somewhere between about 40 and 50 miles down the air density will equal that of water. You will float at that point just as if you were in water. Swimming down much further will be increasingly difficult since unlike water, the density of the air will still keep increasing with depth, making your bouyancy progressively more difficult to overcome.

The only way to be able to fall all the way to the center would be to seal and apply vacuum to your well. Then when you jumped in with your spacesuit on, no air or air friction will slow you down. If the vacuum was close to perfect, you'd accelerate at a 1G rate to thousands of miles per hour within minutes (100 seconds at 1G = 32ft/sec^2 =3200ft/sec~= 0.6mps=2182mph), Gradually, this rate of acceleration will decrease as more of the mass of Earth becomes behind you, becoming 0 as you pass through the center, then gradually tending to reverse your acceleration to the point where your speed would be zero just about time you hit surface level on the opposite side (you did dig ALL the way through, right?). Then you would start falling back again, and if your vacuum were perfect, continue this cycle indefinitely.

BTW, finding the solution for speed as you pass through the center or the time it would take to get there (hint: well under 1 hour) makes for an interesting calculus "related rates" problem.

Answer 9

Yes, if you had a hollow, air-conditioned, lava-proof cavity in the center of the Earth, you'd float in it. And in fact, you would't have to be exactly in the center---the gravitational force is zero everywhere in the cavity, even if it is quite large. This assumes that the Earth's shape, and the cavity's shape, are spherical. (Actually they can be similar tri-axial ellipsoids, but a sphere is a degenerate example of a tri-axial ellipsoid.)

Answer 10

No there is no gravity.Acc to formula
g1=g(1-d/R)here we will put d=R i.e radius of earth.(d is depth)