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From: jonab@sdcrdcf.UUCP (Jonathan Biggar)
Newsgroups: net.movies.sw
Subject: Re: Parsecs
Message-ID: <753@sdcrdcf.UUCP>
Date: Wed, 21-Dec-83 12:13:02 EST
Article-I.D.: sdcrdcf.753
Posted: Wed Dec 21 12:13:02 1983
Date-Received: Fri, 23-Dec-83 04:36:28 EST
References: <185@iwu1c.UUCP> <138@tpvax.fluke.UUCP>
Reply-To: jonab@sdcrdcf.UUCP (Jonathan Biggar)
Organization: System Development Corporation, Santa Monica
Lines: 70

In article <138@tpvax.fluke.UUCP> inc@fluke.UUCP (Gary Benson) writes:
>Are you *sure* that a parsec is a local unit of measurement? My big old
>Webster's says it is equal to a *heliocentric* paralllax of one arc
>second. It is then converted to earth radii, then to light-years. Seems to
>me that what a parsec is is a distance that you have to be away from a sun
>to observe one arc-second of parallax. Maybe a scientist who really knows,
>or someone who cares to research it more thoroughly would care to set us
>all straight...

If the position of a star when seen against the background sky changes
by one second of arc when measured from two points on the Earth's
orbit that are on the opposite sides of the sun from each other, then
the distance to that star is exactly 1 parsec.

Note that the Earth's orbit is a factor.  Because Mars (for example) has
a larger orbit diameter, a star that is one Earth parsec away will
be measured as being less than one Mars parsec away.
A Mars parsec is greater than an Earth parsec by the same
proportion that Mars' orbit is greater than the Earth's.

Proof:


			Mars' orbit
		|-------------------------|
		|                         |
		|         Earth's         |
		|          orbit          |
		|      |-----------|      |
		v      v           v      v
		A      B     O     C      D
			    Sun




				      Star
				       o




				     D'   C'      B'   A'
		 (Measured locations of the star against the background sky)

Imagine lines between A and A', B and B' etc.  (I can't draw them)
All of these lines intersect at o (the star).

1)  angle D'oA' = angle AoD and angle C'oB' = BoC
    (when two lines intersect, opposite angles are congruent.)

2)  angle ADD' = angle DD'A', angle DAA' = angle AA'D',
    angle BCC' = angle CC'B', angle CBB' = angle BB'C'
    (opposite interior angles are congruent)

3)  triangle ADo and A'D'o are similar, triangle BCo and B'C'o are similar
    (angle, angle, angle)

4)  therefore      AD         A'D'
		 ------  =  --------  =>  the measured parallax is
		   BC         B'C'        proportional to the orbit size

Therefore, for a planet whose orbit is twice the diameter of
Earth's, it's parsec is twice as long as Earth's.

Thus, the parsec is not a universal physical constant.
-- 
Jon Biggar
{allegra,burdvax,cbosgd,hplabs,ihnp4,sdccsu3,trw-unix}!sdcrdcf!jonab