No. I am not asking for the center of Earth's map.
On average, the kg/m3 of Earth's soil is heaver than the kg/m3 of oceans, and the earth does not have a flat surface. And as we have quite some oceans on earth, this means the center of mass of earth is not exactly in 'in its middle'.
I know, the earth's crust is just a fraction of Earth's layers, as you can see in the picture above. But say if the left side of imaginary earth contains a lot of oceans, and the right side none, that that mean that the center of mass of earth is more to the right?
Here, my beautifully drawn image to create an image of my question:
Note the water on the 'left' side of Earth, and mountains on the 'Right' side of earth.
So there is no way I can really ask 'coordinates' of the exact center of mass of Earth, but which point on Earth's surface (=includes oceans) is closest to the center (of mass)?
Best Answer
I'm afraid you are still severally overestimating this fraction. Note the text "Not to scale".
The image below is for a carbon purpose, but it shows thicknesses of the layers to scale. You can't even see the crust.
Source: http://phys.org/news/2013-03-deep-carbon-quest-underway-quantity.html
Compare the crust of maximum 50 km in depth to Earth's radius of 6370 km. This is $0.7\;\%$.
If we assume sphere-shape, the volume $V=\frac43 \pi r^3$ of Earth is $V=1.0827\times 10^{12}\;\mathrm{m^3}$. The crust volume is all this subtracted all below the crust: $V=(1.0827-1.0574)\times 10^{12}\;\mathrm{m^3}=0.0253\times 10^{12}\;\mathrm{m^3}$. That is $2.3\%$.
And furthermore, presumably the density difference from ocean to mountain is not enormous.
If you have density values, multiply them onto the volumes and find the masses to compare. But a presumably tiny mass difference in a tiny volume fraction... I doubt there is any practical change of centre of mass.
Apart from the neglibility, I am not sure which answer you are looking for. Since you say mountains are denser, the centre of mass is displaced slightly towards the more mountainrich side. So are you in the same depth in the ocean at one side of Earth as you are in a mountain cave on the other side, of course the mountain cave brings you closest - though negligibly.