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This may very well be a question for Earth Science SE, but as it is very hypothetical, maybe pure physics is more appropriate...

Question:

Imagine we have have a wedge that tapers down into an infinitesimally small point. We can balance the wedge so that this point is orthogonal to the Earth's surface.

How heavy would the wedge need to be, so that it pushes its way (sinks) into the Earth's core? Is there even a weight (theoretically or otherwise) that could make this happen?

Would impulse be necessary in any case? Analogous to hitting a nail with a hammer.

Assumptions:

  1. the incompressibility of a solid is not considered
  2. We can add more force to the motion of the wedge (e.g. with n rocket engines) than it gets alone from its gravitational relationship with the earth.
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  • $\begingroup$ A warm welcome to Physics SE! :) I'm looking forward to see an answer including friction forces or fluid dynamics under high pressure to solve this ;) $\endgroup$
    – Stefan Bischof
    Commented Mar 12, 2016 at 16:31
  • $\begingroup$ @StefanBischof - Thanks for the welcome :) I would also tend towards fluid dynamics as a modelling tool, but also something completely different would be great! $\endgroup$
    – n1k31t4
    Commented Mar 12, 2016 at 16:32
  • $\begingroup$ Re, "incompressibility of a solid". The Earth is not a solid object; It is supposed to have a solid ball of nickel/iron at its core, and it has a very thin solid crust, but mostly it's made of hot, plastic magma and hotter fluid magma. $\endgroup$
    – Solomon Slow
    Commented Mar 15, 2016 at 13:51

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A wedge will not work. A wedge by its shape presupposes extended area behind the point, which will meet the resistance of the ground as the shape widens. A wedge is useful in latticed material, where it can break bonds and it can trigger a break by supplying the necessary energy. The ground is anything but an organized lattice. It is the reason one uses drills in disorganized solids, as in making holes in concrete, or to reach oil and water underground.

This article on new drilling technologies might give a lead .

From the list I would favor lasers, and plasma, though it would be a very dangerous environment and when going towards the core, the path would not be stable.

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