Question

Hello●●●●●●

What is the acceleration due to gravity at the centre of the earth ??.

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Answer 1

An acceleration due to gravity is caused by the mutual gravitational force exerted by a system of bodies between themselves.

The main fact to note is, if you imagine a massive body like the earth to be made of a very large number of theoretical hollow spheres, all of them combining to form the Earth as we know it, only the outermost sphere from our perspective defines the gravitational force exerted (including the mass of all the material inside that theoretical sphere).

That is, if you go higher out in atmosphere, the outermost sphere with radius equal to radius of the Earth will be taken into consideration to define acceleration due to gravity.

On the other hand, if you dig 'x' distance into the Earth, only the ground below you (the surface of a sphere with radius = Radius of Earth - x ) will be taken into consideration to find acceleration die to gravity. All the mass above you will have no contribution to the experienced gravitational acceleration. That is, you can say that the gravitational field due to all mass above you cancels out.

Going this way, when you reach the exact centre of the earth, all the mass of the earth will be above you and all it's gravitational influence will cancel out. Thus, when you are at the centre, there is no other theoretical hollow sphere to exert gravitational influence on you, so this condition will be an actual 'gravity free condition' and you will be able to feel no acceleration due to gravity.

Do note that it is impossible for humans to actually go to the center of the earth since going that deep (about 6400km) is not viable and the temperature of the inner core of the Earth is around 5700K (5430°C or 9800F) (same as that of surface of the Sun)

It is also interesting to note that if the Earth was hollow, but had the same mass, we would feel no change in the acceleration due to gravity (or 'g') at the surface of the Earth, but on digging and entering inside the hollow Earth, we would feel absolutely no acceleration due to gravity anywhere inside and we would simply float around (!)