From: cflatter@nrao.edu (Chris Flatters)
Subject: Re: The Hole Story
Reply-To: cflatter@nrao.edu
Organization: NRAO
Date: Fri, 18 Dec 1992 16:50:29 GMT

In article 17157@stortek.com, pg@sanitas.stortek.com (Paul Gilmartin) writes:
>Tom Van Flandern (metares@well.sf.ca.us) wrote:
> 
>:      First, here's what is true.  Light propagates through the solar system
>: at lightspeed, taking minutes to hours to reach the planets.  When light from
>: the Sun applies a force, for example, the Poynting-Robertson effect, that
>: force seems to come from the Sun's retarded position, as one logically
>: expects.  As a direct consequence, dust in the inner solar system slowly
>: spirals into the Sun, since delayed forces are non-central forces and always
>: change the angular momentum of an orbit.
>: 
>:      Gravity, by contrast, always appears to act from the true, instantaneous
>: position of the bodies involved.  It never appears to associate with retarded
>: positions.  And the Sun's gravity does not change the angular momentum of the
>: planets.  By direct observation, the directions of the Sun's arriving photons
>: at the Earth and the direction of its gravitational force on the Earth are
>: not parallel, since one comes from the retarded position and the other from
>: the true position.
>    [ ... ]
>:      Now, the interpretation.  In GR, the static gravitational fields of
>                                            ^^^^^^
>I'm curious (and naive).  Does the Coulomb potential around a static electric
>charge appear retarded or instantaneous?  In other words, does an electric
>charge in orbit spiral in because of the Poynting-Robertson effect?
>I know it spirals in because it radiates because of centripetal acceleration,
>but I suppose this is analogous to binary neutron stars losing orbital
>energy to gravitational radiation, which you don't attribute to
>retarded potential.

Disregard most of what Tom is saying.  Tom is trying is confusing the effects
of a field with those of a propagating wave.

If you want to calculate the gravitational potential at the Earth (say) using GR
you would use retarded potentials to do the necessary integrations in the most
general way.  You would find that the gravitational force on the Earth is
directed towards the point in space where the Sun was about 8 minutes ago
(the light travel time between the Sun and the Earth).  In the reference frame
of the solar system this is a near as makes no difference to the point in space
where the Sun is now so we can ignore the retardation.

The correct analogy in terms of electromagnetism is not to consider the
direction of the force acting on the Earth due to light from the Sun
(the Poynting-Robertson effect is due to the fact that light has a
non-zero momentum) but to consider the what would happen if the Sun
had a net positive charge and the Earth had a net positive charge.  In this
case the force on the Earth would again be directly towards the Sun.

Now: going back to the beginning.  Light from the Sun does not appear
to come directly from the Sun but appears to come from a direction that
is shifted slightly forward of the Earth (defining forward by the
instantaneous motion of the Earth) in the reference frame of an
observer moving with the Earth.  This is simple aberation and has
nothing to do with retarded potentials (in the Sun's reference frame
you could say that the Earth is running into the side of the light);
the apparent direction from which the light comes is not the direction
of the retarded position of the Sun.  Since light has momentum and the
light comes from slightly in front of the Earth there is a slight
slowing of the Earth.  This effect is significant for small particles
and dust does indeed spiral inwards towards the Sun because of it.  The
effect is real: Tom's explanation is garbled.

The gravitational analogue of light is gravitation radiation
(gravitational waves).  If the Sun is emitting gravitational radiation
it will also be subject to abberation due to the Earth's motion.  It
will also exert a small force on the Earth (much smaller than that due
to the light from the Sun) which will tend to slow the Earth in its
orbit.  Gravitational radiation is also refracted by a gravitational
field in the same way that light is.

	Chris Flatters
	cflatter@nrao.edu



Xref: sparky sci.astro:13220 sci.physics:21328