5. Barnard\'s star is fourth closest known star to our Sun, and has the fastest

Question

5. Barnard's star is fourth closest known star to our Sun, and has the fastest motion across the sky of any star (10.34 arcsec/year). It has a radial speed of -108 km/s and a parallax of 546 milliarcsec. (a) What is the distance to Barnard's star in parsec? (b) What is its tangential speed in km/s? (c) What is its space velocity (in km/s) and what angle does the space velocity make with our line of sight? (d) At its closest approach to Earth, how distant in parsecs will it be? Compare this to the distance to Alpha Centauri. (e) Given its current apparent visual magnitude of 9.54, what will be its apparent visual magnitude at closest approach? How much brighter in terms of observed flux?

Explanation / Answer

1.The distance of the star is inversely proportional to parallax. d=1/p. Here p is parallax it is in milliarcsec need to change to arcsec. d=1/0.546, distance= 1.83 parsec.

2.Tangential speed (Vt)=4.74md where m= motion d= distance

Vt= 4.74*10.34*1.83 = 89.691 km/s.

3. Space velovity V2= Vr2 + Vt2 where r is radial and t is tangential velocity.

Space velocityV2 = (-108)2 + (89.691)2 = 140.38

4. Baranard star closest approach is 6 light years. so based on that barnard star having 1.8 parsec and alpha centauri having 1.34 parsec.

5. Current apparent visual magnitude is 9.54 and rightnow having 9.51 apparent magnitude.it closer to earth it may be visible in naked eye.

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