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Path: utzoo!linus!security!genrad!decvax!harpo!eagle!mhuxl!houxm!ihnp4!arizona!doug
From: doug@arizona.UUCP
Newsgroups: net.physics
Subject: Traveling Down That Long Lonesome Highway...
Message-ID: <5957@arizona.UUCP>
Date: Tue, 8-Nov-83 10:24:36 EST
Article-I.D.: arizona.5957
Posted: Tue Nov  8 10:24:36 1983
Date-Received: Thu, 10-Nov-83 02:47:32 EST
Organization: CS Dept, U of Arizona, Tucson
Lines: 50


I thought these questions might be of interest.  Before I answer them,
let me set up a hypothetical case.  Since we are talking about a vehical
in motion, let's designate the x-axis as the direction of travel, i.e. 
the NJ turnpike.  We are also talking about two angles, the angle that an
object appears to be at when we are in motion, let's call it A, and when
we are at rest, let's call that angle B.  Let's measure them with respect 
to the x-axis.  So if we are stopped at some point O, then a star that 
appears to be B degrees away from the x-axis will appear to be A degrees 
away when we pass over the same point, traveling along the x-axis at 
velocity v.  Now for your questions.  

1) When does the panorama split into two disks?  There will be a separation
of two degrees between the edges of the two disks when v = .0175 c .

2) Where is the dividing line and which stars appear in each disk?  The
dividing line is the y-z plane, and any stars with angle B < 90 degrees
will be in the forward disk, and B > 90 degrees will be in the aft disk.

3) What does a passing star look like?  Let's assume that we start observing
this star while still quite aways off, it's reasonably close to the direction
of travel, and it emits predominantly yellow light.  It will appear bluish
in color, and will be close to the center of the forward disk.  As we 
approach the star it will move away from the center and as it does, its
color will become more yellow.  When we pass the star, it will be on the
edge of the disk and it will be yellow.  If it is too far away to discern
as a disk, then it will appear to become a tiny cresent and at the same 
time it will appear as a cresent on the aft disk.  It will remain in the 
same position on the aft disk as on the forward disk.  If it's at 3:00 on 
one disk, it will be at 9:00 on the other (9:00 touches 3:00 when they 
wrap around).  As we move away from the star it moves to the center of 
the aft disk and becomes reddish.

  Relation:                star at rest
                  v             *      * star when
          cos B + -     d|\     |     /| in motion   v = .5c
                  c     i| \    |    / |                   o
  cos A = ---------     s|  \   |   /  |             A = 60
              v         k|   \  |  /   |                   o
          1 + - cos B    |    \ | /    |             B = 90
              c         o|     \|/ A   |                   
  red shifted   ->  ----f+------+------+----> x-axis <- blue shifted
                         |     /|\     |
                        v|    / | \    |
                        i|   /  |  \   |
                        e|  /   |   \  |
                        w| /    |    \ |
                         |/     |     \| <- normal color
                             y-axis 
                                                          Pase