Re: [Phys-l] definition of gravity

[John Mallinckrodt <ajm@csupomona.edu>]

Bill Nettles wrote:

> Can/should the acceleration of the frame of reference that is at rest with respect to "one" be due to a gravitational field?

First you'd need to define what you mean by "the acceleration of the frame of reference."  I'm supposing that you envision something like a frame attached to the space station "accelerating due to the Earth's gravitational field."  But that acceleration is measured in another reference frame, one attached to the Earth, which is itself accelerating wrt lots of other very reasonable reference frames so this could go downhill quickly.  It's better and FAR easier to *define* "THE acceleration of a (local) frame of reference" as its acceleration wrt to (locally) freely-falling objects.  If you do that, then the gravitational field in that (local) reference frame is simply the vector opposite of its own acceleration, i.e., the acceleration of freely-falling objects wrt it.

Here's a question that might be instructive to work out:  

Suppose you have two non-rotating Earth's with a center to center distance of 3 Earth radii.  What gravitational field (in terms of g, the gravitational field on an isolated non-rotating Earth) would be determined by a person standing at the point on the surface of one of the Earths that is closest to the other Earth?  Is it the same as the acceleration that person observes for an object dropped to the ground?

John Mallinckrodt
Cal Poly Pomona