[Physics] Consequences of destroying a space elevator

Question

Suppose there is a fully functional space elevator built on Earth. The base is attached to coordinates

$
(\lambda, \varphi) = (0,0)
$

e.g., on the equator on the zero-meridian.

What would happen if we were to suddenly remove the counterweight?
At what speed would the tip hit the Earth, and at what coordinates (all approximate)?

I might be missing something, but I found this scenario exceptionally difficult to model properly.

I was trying to get general equations, so for arbitrary material, planet, etc. I suspect the equations involved will be quite messy, so please use abbreviations/substitutions/references to standard transformations etc. where possible. Ignore the atmosphere and any carts/stations/other masses attached to the elevator, assume spherical Earth, etc.

For completeness: it is a scenario described in the Mars Trilogy, by Kim Stanley Robinson. So this is purely a pet project 🙂

Answer 1

Blaise Gassend has created this simulation of "An elevator that breaks at the counterweight.":

More discussion of various possible failure modes of a space elevator:

• Blaise Gassend discusses and simulates other possible failure modes at Animation of a Broken Space Elevator by Blaise Gassend.
• Bradley Carl Edwards. "A Hoist to the Heavens". IEEE Spectrum 2005.
• Wikipedia: space elevator safety.