An object at the exact center of the Earth experiences weightlessness
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Retrieved physics discussions and historical scientific descriptions explain that at the exact center of the Earth, gravitational pulls from surrounding mass cancel out entirely, causing an object to experience weightlessness.
# Would you be weightless at the center of the Earth?
Tags: gravity, newtonian-gravity, earth, planets, geophysics
- Score: 39
- Views: 34981
- Answers: 5
- Answered: yes
- Asked by: freeside (543 rep)
- Asked: 2011-01-03
- Edited: 2016-08-26
- Site: physics
## Question
If you could travel to the center of the Earth (or any planet), would you be weightless there?
## Answers
### Answer by John Alexiou (score: 31)
Correct. If you split the earth up into spherical shells, then the gravity from the shells "above" you cancels out, and you only feel the shells "below" you. When you are in the middle there is nothing "below" you.
Refrence from Wikipedia Gauss & Shell Theorem.
{I am using some simplistic terms, but I don't want to break out surface integrals and radial flux equations}
Edit: Although the inside of the shell will have zero gravity classically, it will also have non zero gravity relativistically. At the perfect center the forces may balance out, yielding an unstable solution, meaning that a small perturbation in position will result in forces that exaggerate this perturbation.
### Answer by inflector (score: 21)
The simplest way to think about it is that there is
The last word | New Scientist
On the pull
Question: If you could journey to the centre of the Earth, what would be the sensation of gravity at various points on the way down, and at the centre?
Answer: This problem piqued the curiosity of no less a physicist than Isaac Newton, who of course solved it in his Principia (Book 1, theorem 33). If you are at the centre of the Earth you are pulled equally in all directions, so you are in fact weightless. Higher up, at radius R from the centre, Newton found that the attractions of the materials in the hollow spherical shell of radius greater than R will all cancel one another out—a beautiful mathematical consequence of the fact that gravity decreases as the square of the distance. You feel only the pull of the mass in the sphere below you.
Newton showed that its combined pull is simply proportional to the inverse square of the distance R from the centre. The mass of this sphere is proportional to its volume, that is, R3. So, the weight you would feel, if you were foolhardy enough to descend through a homogeneous planet, would decrease in direct proportion to R3/R2 (which is equal to R) as you moved inwards, reaching zero at the centre.
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