Re: [Phys-l] definition of gravity

["Robert Cohen" <Robert.Cohen@po-box.esu.edu>]

I just wanted to make sure that JD was saying the gravitational field is dependent on one's reference frame.  I know that the "local acceleration of gravity" (g) is [I just didn't realize the two were equivalent].

This was news to me so I just want to make sure I understand it correctly.

Follow-up question: does it matter whether I say "Earth's gravitational field" or "locally measured gravitational field"?  For example, is it appropriate to say the Earth's gravitational field is zero at the location of the space shuttle orbit?

Robert A. Cohen, Department of Physics, East Stroudsburg University 
570.422.3428   rcohen@esu.edu    http://www.esu.edu/~bbq 

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Monday, November 07, 2011 7:52 PM
To: Forum for Physics Educators
Subject: 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.