From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Spin
Organization: Computer Science Department,  Stanford University.
Date: Tue, 29 Sep 1992 06:56:40 GMT

In article <1992Sep29.003556.3472@sjsumcs.sjsu.edu> b5249-23@mathcs.sjsu.edu (Kurt Stocklmeir) writes:
>John Baez
> his article
>
>You must be doing a lot of homework at MIT.  By the time you get
>out, you will be worn down and not ever be able to do any good research.
>
>Gravitational Action        Constant
>Gravitation                 Misner Thorne Wheller P. 177 and other parts
>Look at any books about computer programs of finding paths of planets
>in a solar system.  All componets of gravity have an infinite velocity.

Ah, so *that's* why Ephem.4.21 isn't correctly predicting lunar star
grazes.  :-)

Seriously, if gravity has finite velocity, its effects given the
organization of our solar system are third order and beyond the reach
of any measurement we can hope to do today.  And those effects are
*way* below the size of errors arising with the polynomial models
typically used in computer programs to approximate (nonpolynomial)
orbits.

A first order effect would be the influence of the sun's gravity on the
planets.  But a graviton, or at least gravity wave, from the sun
arriving here on earth appears to come from the sun's present position
(in contrast to a graviton from earth arriving at the sun, which
appears to the sun to come from where the earth was 8 minutes
earlier).  Planets have a second order effect on the Sun's motion
(where this "order" is in terms of the ratio of planetary mass to solar
mass), but this effect is further scaled back to third order by virtue
of planetary orbital velocities being well below the speed of light.
Planets have a mutual effect on each other's orbits, but this is still
third order: the sun dominates, and they are still slow relative to
each other.

If we had chosen our parents more carefully so as to be born in a solar
system with a binary star, we might find it easier to determine the
velocity of gravity experimentally than with good old Sol.  In a binary
system the gravity from each component should arrive at the other
component delayed by several seconds, whence it should appear to be
coming not from the center of the "transmitting" star, but where that
center was a few seconds earlier.  While this isn't much of a
displacement, it might be just enough to be measurable with enough
technology, care, and time.

One might think that a whole galaxy would offer even more such
opportunities.  However n bodies for n >= 3 introduces an unpredictable
chaotic element into the data that is likely to completely drown out
the small finite-gravity-speed perturbation we are trying to detect.

So my conjecture is that a binary star gives the optimal experimental
conditions for measuring the velocity of gravity.  (If this weren't
Usenet I'd have to call this a question, not having paid my dues.
Usenet doesn't have dues, a nice feature, that.)

Anyone care to express strong opinions either way on this question?

-- 
=================================================== In short, I am floundering
Vaughan Pratt   pratt@cs.Stanford.EDU  415-494-2545 around and don't take what
=================================================== I say seriously.