[Phys-l] definition of gravity

[John Denker <jsd@av8n.com>]

On 11/03/2011 01:10 PM, Robert Cohen wrote:
> When introducing F=mg, is g the gravitational field or is it the
> local "acceleration of gravity" (acceleration of an object in the
> local frame when the only force acting is gravity)?  In other words,
> does mg include the centrifugal force associated with the rotating
> frame of reference?  Might this impact how you introduce the
> material?

That's an interesting, important question.

> ... when the only force acting is gravity ...

I'm pretty sure what those words were intended to mean,
namely that "gravity" was intended to be calculated in
accordance with the law of universal gravitation:

 "gravity" = G M / r^2          [1]

However, whether or not I'm right about that, I wish to
use a different definition.  I recommend *defining*
"gravity" to be the acceleration of the chosen reference
frame (as measured by reference to freely-falling objects).

This is pretty much required for consistency with a 
modern (post-1915) understanding of what gravity is,
including the equivalence principle.  It is also required
for common-sense practical applications such as architecture.

Let's be clear:  The thing that we calculate using equation
[1] must not be considered "the" gravity (except in a few
special cases).  It is often the dominant contribution to
the gravity, but the other contributions are quite significant
in ordinary real-world applications.

I write:

 g_I = G M / r^2          [2]

where the LHS is emphatically not g but rather g_I, which
is only one contribution to g.

For the next level of detail on this, see
  http://www.av8n.com/physics/weight.htm

Most textbooks are grotesquely inconsistent about this.  They
define gravity one way in the chapter on experiments in the
lab frame (implicitly including all contributions to the frame-
acceleration) and define it another way in the chapter on 
cosmology (including only g_I).

It may be that g is numerically equal to g_I for cosmology,
if/when we choose to use a nonrotating reference frame ...
but that's an equation, not a definition.  It's a choice,
not a law of nature.  For 99% of the practical applications
students (and other folks) see in real life, g is only 
roughly approximated by g_I.


==================

To summarize:

> When introducing F=mg, is g the gravitational field or is it the
> local "acceleration of gravity" (acceleration of an object in the
> local frame when the only force acting is gravity)? 

Yes, both.  Those are the same thing, according to the
recommended definitions.

>  In other words,
> does mg include the centrifugal force associated with the rotating
> frame of reference?  Might this impact how you introduce the
> material?

The centrifugal force is *included* in the definition of g,
and in the definition of gravity.