Name: JOHN
Status: other
Age: old
Location: N/A
Country: N/A
Date: 1999

Question:
If I dug a hole through the earth, not necessarily
through the center, what is the math derivation of the gravity in the
hole as a function of distance? If I jumped into the hole, what is the
math derivation of gravity as a function of time?

Replies:
The way to think about this problem is to separate the mass of the earth
into the sphere containing everything closer to the center than you and
the spherical shell further from the center than you. Because gravity
is an inverse-square-law force, the net force on you from all of the mass
in the spherical shell is zero. Similarly, you can replace the sphere
by a point mass (same mass) at its center. Then the acceleration on you
at any radial distance from the center is G*d*(4/3)*pi*r where G is the
gravitational constant and d is the earth's density (wrongly) assumed
constant. The answer to the second question depends on where the hole
goes.

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