Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: little gee and its sign



In the context of:
> > I've always thought g was the local gravitational field.

Tim O'Donnell wrote:
> I think it is, but in many (most) localities that value is
> close to 9.80 m/s/s, so it is considered a constant.

That's overstating it in a couple of ways.

1) The thing I call g is *not* constant to 3 sig digs.
http://cires.colorado.edu/~bilham/Absgdata.html
I see values greater than 9.82 and less than 9.78.

2) The thing I call g is *not* purely gravitational in origin. Almost, but
not quite. See below.

At 11:57 AM 9/29/01 -0700, Bernard Cleyet wrote:
I think this is part of the problem -- the inability to distinguish
between local and universal constants. When I was young... G was
called the Universal gravitational constant, is it still?

Sure. Big G is no problem.

A much more salient problem is that we don't have a good vernacular name
for little g. Calling it "gravitational" tempts people to write things like
g = G M / R^2 (eeeck!)
which is inconsistent with the way g is actually used. The magnitude of
the inconsistency is not huge, but it isn't negligible, and the conceptual
point is important in any case.

Operationally, g(x) is the acceleration of a free particle (at location x)
relative to the chosen reference frame.
-- The person who _uses_ g or _measures_ g doesn't know and doesn't care
how much of the local g value is due to purely-gravitational effects and
how much is due to acceleration of the reference frame. It's impossible in
principle to tell the difference.
-- In contrast, some other person who is trying to _calculate_ g from
first principles must add up the purely-gravitational contributions,
centrifugal contributions, and whatnot.
-- A careful multi-point measurement can sort out the various
contributions (purely gravitational versus other) but this is an advanced
topic (upper-division undergrad level or higher).

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

In any case, we need a good name for g. Saying
g = free-particle acceleration field
is correct, but seems a bit awkward. Maybe we can invent a name such as
g = ponderative field (from an ancient word for weight).
Another possibility is
g = gravitoidal field (literally: gravity-like),
which is ugly but gets the point across.