# All astrophysicists would curse me for this!

Classical Mechanics Level 3

Imagine if the Earth was in the shape of a perfect cube instead of an imperfect sphere (geoid as we call it), how many maximum number of points would have been there in our cubical Earth that would have the same value of acceleration due to gravity?

Details and assumptions:

• Consider all points you can take on a regular cube (on faces, on edges and on vertices).
• The value of acceleration due to gravity need not be same as the standard value $$g = 9.8 ~ms^{-2}$$.
• Consider all points on a particular face of the cubical Earth to be at zero elevation/depression w.r.t. the surface level (no geographical imperfections).
• All vertices and edges are perfectly steep and sharp and have no imperfections.
• Neglect any other forces of the Universe except the Earth's own force of gravity.
• Neglect rotation and revolutions of Earth. It is completely still.

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