Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Depth of Gravity
Name: JOHN
Status: other
Age: old
Location: N/A
Country: N/A
Date: 1999 

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?

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

Click here to return to the Physics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (, or at Argonne's Educational Programs

Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory