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From: matt@oddjob.UChicago.UUCP (Matt Crawford)
Newsgroups: net.physics,net.astro
Subject: Re: RE: FLASHING QUASARS (the last word ?)
Message-ID: <285@oddjob.UChicago.UUCP>
Date: Sun, 10-Jun-84 14:57:58 EDT
Article-I.D.: oddjob.285
Posted: Sun Jun 10 14:57:58 1984
Date-Received: Mon, 11-Jun-84 00:33:53 EDT
References: <3560@fortune.UUCP>
Organization: U. Chicago: Astronomy & Astrophysics
Lines: 39

Yes, a system can be made to flash with period P and still be larger than 
c*P, but only certain observers will see the flashing.  As an example
consider a square sheet which emits from all points with an intensity that
varies periodically with a period P = 1 second.  Let the square have an
edge of length L = (10 sec) * c = 3*10^9 meters.  Let an observer be
located a distance d from the center of the square on a line perpendicular
to the square.  The points on the square farthest from the observer are the
corners, at a distance d' = d + L^2/4d + ... .  This can be made
arbitrarily close to d make making d sufficiently larger than L.  To have
d'-d < (0.1 sec)*c it suffices to make d > (250 sec)*c = 7.5*10^10 meters.
Under these conditions, if the square switches between full intensity and
zero intensity with a period of 1 second, the observer will see the
pulsation, but with the transition from bright to dark smeared out over a
tenth of a second.

Consider another observer the same distance from the center of the square
but 30 degrees off the perpendicular.  The center of the edge nearest to
this observer is (247.54 sec)*c away while the center of the farthest edge is
(252.54 sec)*c away.  This difference of five seconds of light travel time
(a bit more for the far corners) will cause the observer not to see
simultaneous pulsation but an average brightness, unless the observing
instruments are sufficiently powerful to discern the bands of light and dark.
Increasing the distance of the second observer will not reduce the time
difference to less than 5 seconds.

Diagram: (distances in light-seconds)

        |          <- 250 ->
     10 |-------------------------------O 1st observer
        |

                                       O 2nd observer

If the object is spherical the ideas are the same, except that there are NO
positions outside the sphere from which all points on the surface of the
sphere are arbitrarily close to being equidistant.
___________________________________________________________
Matt		University	ARPA: crawford@anl-mcs.arpa
Crawford	of Chicago	UUCP: ihnp4!oddjob!matt