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Re: [Phys-l] definitions ... purely operational, or not



I won't guarantee that the following is perfectly consistent with everything I've ever written in the past, but my current taste is as follows:

1. "g" is called "the gravitational field vector." It is identical to what is often called "the acceleration due to gravity" and also sometimes called "the free-fall acceleration." Indeed, g is operationally determined as the initial acceleration of an object released from rest as measured in the reference frame of interest. It is reference-frame dependent and can vary with both position and time.

2. The "gravitational force" on a point particle is m*g. It is a reference-frame dependent vector.

3. The "weight" of a point particle or a non-rotating, extended object is the magnitude of the gravitational force on it in its own reference frame. It is what a properly calibrated, properly used scale would read. (Among other more obvious things, "proper use" of a scale includes making sure that the object being weighed is not supported against gravity by any other force including buoyant forces ... or correcting for those forces.) Weight is a scalar and is NOT reference-frame dependent, but it is generally time-dependent. Rotating extended objects don't always have a sensible weight. For instance, in some circumstances one hand may have a substantially different weight than the other.

4. Within the realm of Newtonian mechanics, the gravitational field vector may be calculated *theoretically* in the vicinity of any mass distribution as long as the tidal effects of other, external masses can be neglected as follows:

a) Go into the nonrotating center of mass frame for the system.

b) For any desired position, calculate the gravitational field vector in the CM frame as

g = G * sum[ m_i / r_i^2, toward_i]

where r_i is the distance from each point mass m_i to the point of interest and toward_i is a unit vector toward m_i from the point of interest

c) If you want the gravitational field vector in any other reference frame, use the transformation law

g_new = g_CM – a_new_wrt_CM

where a_new wrt_CM is the acceleration of the new reference frame wrt the CM frame.

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As a consequence of all of this,

A. Sufficiently compact objects (i.e., those for which g does not vary substantially over their extent) in free-fall ARE weightless, period.

B. g IS what we MEASURE it to be in our reference frame of choice, no "corrections" for centrifugal effects or anything else are necessary.

C. There is no such thing as "artificial" gravity or "artificial" weight.

D. In the nonrotating center of mass frame of the solar system, the Sun exerts a noticeable gravitational force (~.06% of the gravitational force due to the Earth) on a ball dropped in a laboratory on Earth. In the frame of the laboratory, however, the bulk* of that force vanishes and we can neglect the Sun's gravity for all practical purposes. (* There may be a tiny residual tidal effect of up to .000005% of the gravitational force due to the Earth.)

NONE of the above involves "general relativity," but it is far more in keeping with "modern" ideas about gravity--i.e. those less than 100 years old. I recognize that there are some nonstandard ideas here, but I believe I can defend them as being BOTH internally consistent AND quite sensible.

I am interested in hearing challenges to these ideas, especially #4.

John Mallinckrodt
Cal Poly Pomona