doug@arizona.UUCP (11/17/83)
Some of you might still be interested in this discussion, or at least
in having the correct answer. I hope that anyone I might have mislead
will catch this article and understand the error of my previous ways...
What I said was far enough off the mark that I need to start over. My
sincerest apologies for not getting it right the first time.
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.
1) When does the panorama split into two disks? NEVER. All of the stars
try to crowd into the forward hemisphere, and the faster you go, the more
successful they will be. In fact, at speeds of .9999c most of the stars
normally seen will be crowded into a single disk less than a degree across,
and the remaining panorama will be taken up by those stars seen between 179
and 180 degrees from the positive x-axis.
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 accumulation. As we
approach the star it will move away from the center and as it does, its
color will become more yellow. As the star moves away from the center of view,
it will move very slowly, but seem to move faster and faster as it gets farther
away from the axis. When we pass the star, it will still appear forward of
our 90 degree mark, and at that time it will appear its true (unshifted) color.
As we pass the star will appear to speed up, moving very quickly when it goes
behind our appearant 90 degree mark.
Relation: star at rest
v * * star when
cos B + - | /| in motion v = .5c
c | / | o
cos A = --------- | / | A = 60
v | / | o
1 + - cos B | / | B = 90
c |/ A |
red shifted -> ------------+------+----> x-axis <- blue shifted
|\ |
| \ |
| \ |
| \ |
| \ |
| \| <- normal color
y-axis
Let's assume a full panorama.
* * * * this represents the forward hemisphere
* | /** when at rest in the same location
this 240 degree view * | / **
represents the rear * | / **
hemisphere | / **
* | / **
|/ 1 ***
*------------+--2--------> ***
|\ 0 deg. ***
* | \ **
| \ **
* | \ **
* | \ **
* | \**
* * * *
Pase