Kapteyn\'s star is a nearby star, but closer examination shows it to be a visito
ID: 1770591 • Letter: K
Question
Kapteyn's star is a nearby star, but closer examination shows it to be a visitor from our Galaxy's halo, unlike other nearby stars which are orbiting the Galactic center in the disk. Look up its parallax ( in mas), proper motion components (Ho cos & in mas/yr), and radial velocity (v, in km/s) from SIMBAD. 2. Use the proper motion components to determine the total proper motion in the plane of our sky in mas/yr Show that the tangential velocity of the star can be given by vt=4.74 () kms where is in mas/yr and is in mas. Calculate the tangential velocity of Kapteyn's Star. Specify magnitude in km/s and direction as the angle N of E (Ha cos is measured in the eastern direction and is measured north for positive values. Further, Ha cos is the corrected angular motion in our sky in the E-W direction, so the correction for the cos term has already been applied). Using the radial and tangential velocities, determine the space velocity of Kapteyn's Star with respect to the Sun in km/s and mph. A. -1 B. C. D.Explanation / Answer
Solution of part (d)
Let
Tangential velocity =Vt
Radial Velocity=Vr
Now
Vt= 4.74 µ / p = 4.74 (7.67 arcsec/yr) / (0.225 arcsec) = 162 km/s
The net velocity is the resultant of tangential velocity and radial velocity
Therefore
v = sqrt [ vt2 + vr2] = sqrt [ (162)2 + (226)2 ] = 278 km/s
Because the velocity is positive, it is moving away from the Sun.
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