High School Gravity in the center of the Earth (a confusion)

[Allen_Wolf]

I have learned that the gravity at the center of the Earth is zero. I guess its because it gets balanced as the force from all the sides are equal in magnitude and opp in direction. But several land forms throughout the world having different masses could cause a distortion which could make an imbalance on the gravity at the centre of the earth. I mean there will be some gravity at the center right?. Then why is it said to be zero ?

 

[rootone]

I think that although there are parts of the crust which are composed of marginally denser material than other parts, the crust is a very small part of the overall volume of the planet, so it's contribution to the where lies the center of gravity for the planet is negligible.

 

[drvrm]

But several land forms throughout the world having different masses could cause a distortion which could make an imbalance on the gravity at the centre of the earth. I mean there will be some gravity at the center right?. Then why is it said to be zero ?

actually when you theorize the whole situation an uniform average density and spherical shape is taken as a model.
but when you get to real situation the changes in gravitational force will be observed on the Earth's surface also due to uneven mass formations that's why the real shape is different and due to geological changes in such a great/large time span of cooling and spinning a semi-equilibrium has been attained -therefore in equilibrium condition of real Earth the g=0 may get shifted - but in all rough model calculations we take the gravity to be zero at the centre as the shift may not be so large to account for.
another example is we take Earth as inertial frame - non accelerating system in usual calculations of speeds on Earth but when actual rotational effects become important we treat Earth as accelerating frame.

 

[Khashishi]

Physics is all about approximations. (Queue the spherical cow joke.) It's not wrong to make an approximation, unless yourv application requires a level of accuracy higher than the approximation allows.

How accurately do you need to know the gravity at the center of the Earth? (How do you even define where the center is?)

 

[PeroK]

I have learned that the gravity at the center of the Earth is zero. I guess its because it gets balanced as the force from all the sides are equal in magnitude and opp in direction. But several land forms throughout the world having different masses could cause a distortion which could make an imbalance on the gravity at the centre of the earth. I mean there will be some gravity at the center right?. Then why is it said to be zero ?

Perhaps you could define the centre of the Earth as the point where gravity is 0.

 

[David Lewis]

Then I think that would be the earth-moon barycenter.