Parsec (pc)

Date: 10/26/2001 at 09:30:38
From: Peter Mott
Subject: km ->pc

Dear Dr.Math,

I recently bought a Casio fx-991MS calculator. One of the unit 
conversions it does is pc to km and km to pc. Would you please explain 
to me what "pc" means in this context?

Thank you very much.
Regards,
Peter

Date: 10/26/2001 at 12:36:14
From: Doctor Sarah
Subject: Re: km ->pc

Hi Peter - thanks for writing to Dr. Math.

From Russ Rowlett's _How Many? A Dictionary of Units of Measurement_

   http://www.unc.edu/~rowlett/units/dictP.html   

   parsec (pc) - 

   a non-metric unit of distance used in astronomy. As the Earth makes 
   its orbit around the Sun, nearby stars appear to shift their 
   positions in relation to the background of distant stars. The 
   shift, called the parallax of the star, is very small, less than 
   one arcsecond even for the nearest stars. If it can be measured, 
   however, then simple trigonometry can be used to find the distance 
   from the Earth to the star. One parsec is the distance at which a 
   star appears to shift its position by one arcsecond over the course 
   the time (about 3 months) in which the Earth moves a distance of 
   one astronomical unit (au) in the direction perpendicular to the 
   direction to the star. Using this unit makes it easy to compute 
   distances: the distance to a star, in parsecs, is simply one 
   divided by the amount of the parallax. If the parallax is 0.01 
   seconds, the distance is 100 parsecs. The length of 
   a parsec, divided by one astronomical unit (the radius of the 
   Earth's orbit) is the trigonometric function of the parallax called 
   the cotangent; from this relation we can compute that one parsec 
   equals 206 264.8 au. This is the same as 3.261 631 light years, 
   30.856 78 petameters (30.856 78 x 1012 kilometers), or about 
   19 173 510 000 000 miles.


- Doctor Sarah, The Math Forum
  http://mathforum.org/dr.math/