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Velocity of Barnard's Star

(Quick question.) Barnard's star has radial speed tex2html_wrap_inline317 , proper motion tex2html_wrap_inline319 , and parallax 0.546''. Parallax is the angle by which a star shifts against its background when measured from the two extreme points of a baseline of tex2html_wrap_inline323 , i.e. observing the star from Earth three months apart.

  1. What is the distance to Barnard's star in pc?
  2. What is the tangential speed of Barnard's star?
  3. What is the magnitude and direction of the velocity of Barnard's star? Express the direction as an angle with respect to the line-of-sight.
  4. How far, in pc, will Barnard's star be from Earth at its point of closest approach?
  5. In how many years will it reach its point of closest approach?
A piece of trivia: before the recent discovery of extrasolar planets using the Doppler-recoil technique, Barnard's star was a favourite target of astrometric planet searches because of its proximity to Earth. (An astrometric search looks for a wobble in the path of the star across the sky.) Several of these searches even claimed success, though without confirmation. It is now known, from Doppler-recoil, that Barnard's star does not have planets -- at least, not massive ones like Jupiter.

Astronomy 7
Tue Oct 19 13:15:33 PDT 1999