Re: gravitation conserves momentum

[John Denker <jsd@MONMOUTH.COM>]

At 09:11 AM 10/21/99 -0700, Leigh Palmer wrote:
> I must ask, how do you account for the momentum component in the
> gravitational field in the laboratory? I know of no term used in
> elementary physics which does this. I am thinking of a term
> analogous to the energy term mgh.

What's wrong with mgt?

It's the obvious partner to mgh.  At the non-elementary level there's more
to the story (momentum is a vector, and momentum-transport is a tensor) but
at the elementary level that seems to solve the problem you pose.

> It is possible to use the law
> of conservation of energy in the Earthbound laboratory by
> adopting this (do you call it fictitious?) energy term in the
> reckoning. I don't recall hearing about a momentum counterpart.
> Instead we usually apply conservation of momentum only over the
> brief interval from "just before the collision" to "just after
> the collision", not a very satisfactory situation in my view.
> Why not invent a "gravitational potential impulse" account by
> virtue of which a particle builds up credit (m*g*delta t in the
> downward direction) in a momentum account by merely existing for
> an interval of time?

Indeed, why not?  Consider it done.  Lots of other people consider it
satisfactory.

> I'm not advocating the introduction of this fiction into the
> curriculum; I'm merely pointing out that something must be done
> to save the appearances of the law of conservation of momentum
> if one is to use it in a noninertial frame such as the Earthbound
> laboratory over a finite time interval.

Yes, something needed to be done, but it was done many years ago.  Note the
form of the gravitation law;  the magitude of the force is
        |Force(on m due to M)| = G M m / r^2
and note that multiplication is commutative.
        |Force(on M due to m)| = G m M  / r^2 = |Force(on m due to M)|
and when we consider the direction of the force this is a correct (yet
elementary) demonstration that gravitation conserves momentum.

> Contrary to John Denker's
> vehement protestations, tables, chairs, and even floors are
> needed in Earthbound laboratories to provide the necessary force
> to maintain a state of zero vertical momentum in many objects.

Anybody who bothered to read what I actually wrote will know that what I
really said at 06:38 AM 10/21/99 -0400 was:
> 1) Our need for tables and chairs provides absolutely no evidence for
> nonconservation of momentum.

Which remains true.

Gravitation does not violate conservation of momentum.


______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com