"acceleration due to gravity"

[Leigh Palmer <palmer@SFU.CA>]

> OK, Jim, I'll bite. What's wrong with "acceleration due to gravity"?
>
> Paul O. Johnson
> Collin County College

As Chuck Britton only slightly jocularly reminded us, the "acceleration of
gravity" commonly subsumes the centrifugal acceleration. It is a term
appropriate only to the laboratory frame on Earth's surface, a quantity
which can be measured by students in the lab. I guess Jim's point is that,
since it is not really a "purely" gravitational acceleration, we shouldn't
call it that. However, in the context of the principle of equivalence, we
recognize that there is no real distinction between the two components in
the lab frame. There is no way to measure how much is "purely" gravitational
and how much is "fictitious". g (a vector quantity) is the gravitational
field in the laboratory. It manifests itself as the initial acceleration of
any body falling freely from rest in the laboratory frame.

While we don't find the prevalent conventions confusing, I can understand
why a student might consider them so. When I introduce this topic I suppress
mention of the centrifugal force when I introduce weight, defining it simply
as the reading on a scale (or spring balance). I then tell them weight is
the product of an object's mass and the gravitational field at the weight's
position, the latter being g in the laboratory on Earth's surface. In the
orbiting Space Shuttle the gravitational field is nearly zero, so we say the
astronauts inside are weightless, or very nearly so. All of these statements
conform to both scientific and common cultural understanding.

When I introduce simple Newtonian gravity I tell them that weight is caused
by gravity (or is attributable to gravity) which we can calculate using the
law of universal gravitation, a conscious lie. Later on I let on to them
that there are numerous complications to this picture (the figure and
inhomogeneity of the Earth, the centrifugal and Coriolis forces, the
influence of the Moon and Sun) which require examination because they have
measurable consequences in the laboratory. Scientific rigor is restored
before the students leave my course, and I have only had to tell one lie on
the way to the end, a lie which was corrected.

I like my approach better than the traditional approach, as for example in
Sears & Zemansky (1952). They define weight as follows:

 "The force of gravitational attraction which the earth exerts on a body
  is called the *weight* of the body."

Now a definition can't be a lie, so I'll let them have that one. Let's see
where it puts them later on, however. S&Z do not acknowledge the influence
of the Sun and Moon on weight. Modern gravimeters must take these fields
into account. The centrifugal force is added later in the text, and the
combination of that force with gravity is called the "apparent weight", a
source of confusion which never arises when I use my definition. When I
refer to an astronaut walking on the Moon I say he weighs much less on the
Moon than he does on earth; S&Z refer to his apparent weight. It is
noteworthy that the astronaut also has a weight on the Moon in S&Z terms,
but it is directed toward Earth! Astronauts in orbit are not weightless in
S&Z terms; they merely have no apparent weight, contrary to what is said
in the vulgar media.

Needless to say, I like my approach better than the traditional one. My
definition of weight is an operational definition; the traditional
definition is needlessly abstract.

Leigh