Gravitational Acceleration with Spherical Hole · CAP 1999 #A25

Physics · mechanics

Problem

In the film Armageddon, astronauts land on an asteroid and are able to walk around "normally" due to the gravitation of the large rock. Suppose that a spherical asteroid has a mass M and a radius R. A spherical hole of radius R/2 is excavated from the asteroid as shown. What is the gravitational acceleration at a point on the surface of the asteroid at a point just above the excavation? [Figure: Diagram showing spherical asteroid with radius R and excavated hole of radius R/2] (a) GMR2\frac{GM}{R^2} (b) GM2R2\frac{GM}{2R^2} (c) GM8R2\frac{GM}{8R^2} (d) 7GM8R2\frac{7GM}{8R^2}

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