I defined gravitational mass as the ratio of the gravitational force
acting on an object to the local strength of the gravitational field.
I believe that this definition of gravitational mass is correct, but I
did not clearly define "gravitational field".
I assume that the gravitational mass of an object is constant. If I cut
off a piece of an object to fix a hole in my roof, it is no longer the
same object, and its gravitational mass is no longer the same. If I
spill spaghetti sauce on an object, it is no longer the same object, and
its gravitational mass is no longer the same. (I'm sure the reader can
imagine many other processes, some of them much more subtle, that would
change the constitution of an object. ;-)
I also assume that the gravitational field due to one or more objects
depends only on their configuration.
Begin by placing an object in the gravitational field due to one or more
other objects. Initially, other effects, such as electromagnetic
interactions, should be minimized to isolate gravitational effects. Use
the elongation or compression of a coiled spring, or the deformation of
some other constraint to measure the force acting on the object.
Next move the object to another position (perhaps very far from the
previous position, near very different objects) and repeat the force
measurement. If the deformation of the constraint (e.g., elongation or
compression of a coiled spring) is different, then the strength of the
gravitational field is different.
After many such measurements, a standard unit of gravitational field
strength can be defined.
The concept of gravitational field can be extended to more complicated
physical situations by analogy.
The validity of these approximations and the usefulness of the concept
gravitational field are determined by the agreement between calculations
made using the concept of gravitational field and experimental
measurements.
Daniel Crowe
Oklahoma School of Science and Mathematics
Ardmore Regional Center
dcrowe@sotc.org
-----Original Message-----
From: Forum for Physics Educators [mailto:PHYS-L@list1.ucc.nau.edu] On
Behalf Of Jack Uretsky
Sent: Tuesday, October 19, 2004 2:39 PM
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: [PHYS-L] Mass
<snip>
2. I object to Dan Crowe's definition of "gravitation mass" because it
is
circular. "Force" and "field" are not independent concepts. The circle
closes when I recall that the gravitational field is the force per unit
mass.