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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.

Tim Mooney



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