Re: [Phys-l] Weightless

[John Denker <jsd@av8n.com>]

On 11/21/2006 10:42 AM, Rauber, Joel wrote:

> | I understand that lots of people (including apparently the folks at
> | NIST) want weight to be the same thing as gravitational 
> | force, but I have yet to hear one compelling reason for that. 
> |  
>
> That's not how I read the following:
>
> "According to NIST (http://physics.nist.gov/Pubs/SP811/sec08.html) - the
> closest we have in the US to an "official definition": 
>
>
> "In science and technology, the weight of a body in a particular
> reference frame is defined as the force that gives the body an
> acceleration equal to the local acceleration of free fall in that
> reference frame . . ."
>
> Doesn't this say that the weight of an astronaught is zero in the rest
> frame of the orbiting shuttle, since the local free-fall acceleration is
> zero in that frame.  Therefore the force to give it that acceleration is
> zero, i.e. weightless??

It is conventional and IMHO reasonable to say that the astronaut
is weightless in the reference frame comoving with the orbiting
spacecraft.

The only slight risk of confusion arises when we try to connect
"weight" with "force of gravity".  The question is whether the "force
of gravity" should include:
 a) all types of acceleration of the reference frame, in accordance
  with the equivalence principle, or
 b) only the GM/r^2 acceleration, in accordance with the law of
  "universal" gravitation.

In each case, the ideas are clear;  AFAICT the only problem arises
from ambiguous terminology;  what do we mean by _gravity_?  There
two reasonable but inequivalent answers.

If we are confused by this, talking amongst ourselves, just imagine
how confused the students must be!

Many textbooks are shamelessly inconsistent about this.  In the
chapter on universal gravitation they use the terms one way, and
then in other chapters, including anything that involves practical
weighing, they use the terms the other way.

The only way I know to get out of the mess is to define better
terminology.  As I mentioned earlier today, I get a lot of mileage
out of the terms
  -- N-down (Newtonian down, directed toward the center of the
   earth),  and
  -- E-down (Einsteinian down, as defined by a freely-falling
   particle).

Perhaps we can extend this and define N-gravity and E-gravity.  The
astronauts in orbit have no E-gravity relative to the spacecraft
frame, but N-gravity still accelerates them toward the center of
the earth.

ISTM that in almost all practical situations, when people talk about
gravity they mean E-gravity.  Physicists are sometimes interested in
discussing N-gravity separately, and it is common to discuss N-gravity
in introductory classes, in connection with the GmM/r^2 law.

I understand that it would be simple and elegant if "the" gravity
were defined to be equal to N-gravity ... but such a definition would
be very unconventional and very impractical.