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Re: [Phys-l] definition of gravity



On 11/07/2011 05:16 PM, Robert Cohen wrote:
I've thought about JD's response below and am a little confused. So it
is *incorrect* to say that GM/r2 is equal to the strength of the
gravitational field (of the object of mass M at the distance r from its
center)?

Well, it might be incorrect, or it might not. At best it is
unclear and unsafe to call GM/r^2 "the" gravity. I prefer to
write

g_I = G M / r^2

and to call g_I the /primary/ gravity as opposed to "the" gravity.

The point is that according to a modern (post-1915) view of
gravity, it is frame-dependent. You can always find a frame
where "the" gravity (g) is GM/r^2 ... but you can also find
plenty of frames where it is not.

Two obvious examples include
a) the ordinary terrestrial frame, where the direction and
magnitude of "the" gravity (g) differ from g_I by smallish
but nontrivial amounts, and
b) the frame comoving with the space station, where "the"
gravity (g) ... in that frame ... differs from g_I by 100%.

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

The gravitational field g(r) is commonly called "the
acceleration of gravity" and I don't have a problem with
that.

The point is to remind people that g(r) is an acceleration
field (as opposed to, say, a force field).

Quite commonly g is not the only acceleration acting on any
given object, which can be confusing to students ... but changing
the terminology will not help with this problem. The problem
arises from not considering all the force-vectors acting on the
object ... or _equivalently_ not considering all the acceleration-
vectors acting on the object.

∑ F_i = m ∑ a_i

where one of the a_i is the acceleration of gravity. You can
add acceleration vectors as easily as you add force vectors.