Re: [Phys-l] definition of gravity

[John Mallinckrodt <ajm@csupomona.edu>]

Bernard Cleyet wrote:

> John Mallinckrodt wrote:
>
> >  Note that I didn't say and you certainly shouldn't assume that the Earths are (somehow!?) *held* with their centers 3 Earth radii apart.
>
> In that case very soon the observer would be very crushed.  

Not necessarily!

Then chuck britton wrote:

> You DID say they weren't rotating. (But didn't specify which points 
> they weren't rotating about)
> Or are they in the act of slamming together?

They're not rotating, period.  The problem doesn't specify the state of motion and doesn't need to.  They obviously have arbitrary velocities toward, away from, or around/by each other.

Then John Denker wrote:

> The question is seriously ill-posed.
>
> There are innumerable possible interpretations.  The three most
> symmetrical possibilities are:
>
> a) Static:  The planet-planet separation vector is held constant, in
> both direction and magnitude ... somehow.
>
> b) Smash:  Each planet is freely falling toward the other.
>
> c) Orbit:  Each plant is in orbit around the other, such that the
> planet-planet separation vector is changing as to direction but
> not magnitude.

Reasonable people can disagree, but I don't find a) to be a plausible interpretation.  For instance, I also didn't specify whether or not there are other large masses in the vicinity, but it seems to me that, if there were, then that fact, like the (rather remarkable!) fact of some external support preventing them from moving would have to be specified.  In the absence of such specification one must make the most reasonable assumption.  Scenario b) and c) (as well as many others) lead to the same, intended result. 

> Note:  The statement of the problem rules out rotational motion,
> but not orbital motion.  They can orbit with out spin, dos-à-dos.

Indeed.

> The statement of the problem doesn't say that the situation 
> is static ... but it doesn't say that it's not.  Assuming case (b) is 
> no more correct than assuming case (a).

See above.

> In my world, when confronted with an ill-posed question, the crucial
> first step is to clearly identify it as ill-posed.

We agree.

> I also remark that in most cases other than (a), any observer with 
> the slightest amount of sense would have noticed that the gravitational
> acceleration was time-dependent, and would report the time-dependence 
> explicitly (rather than merely quoting the instantaneous value).

Now THAT is a seriously good point!

John Mallinckrodt
Cal Poly Pomona