Stephen A. Lawrence wrote: It's a very cute example. [... cute example: A spherical chamber cut out of a uniformly dense planet ...] I ran across it here:
http://www.geocities.com/physics_world/gr/grav_cavity.htm <snip> The field at any point inside a uniform sphere of density rho is F = -(4/3)*pi*G*rho*R where "R" is the _radius vector_ from the center of the sphere to the point where we're finding the field. For the big sphere, let the radius vector be R1. For the small (cut-out) sphere let the radius vector be R2. (Note that they point from different origins, but that's OK, all we care about are the direction and length.) Then the net field anywhere inside the small (cut-out) sphere will be F(total) = -(4/3)*pi*G*rho*(R1 - R2) But (R1 - R2) is a _constant_, and is just the vector from the center of the big sphere to the center of the small sphere. So the force is also a constant, proportional to the distance between the spheres' centers, pointing along the line which connects the small sphere's center to the big sphere's center. ----------------------------------- Not so. R1 and R2 are NOT the actual radii of the spheres, but the radii to the point of measurement. This is because any spherical shell of constant density has no net gravitational effect on an object within it, so you only need the mass of the spherical volume with radius equal to your distance from the center of mass. Thus I can measure the gravitational field strength along a constant radius from the center of the large sphere (R1 constant) but at different locations within the volume of the small sphere (R2 variable) and achieve different results. Merlyn Magickal Engineer and Technical Metaphysicist __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
