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5 The Motion of Stars
In addition to the daily (diurnal) motion of the sky as a whole, the stars move (very slowly) on the celestial sphere with respect to each other. This motion is called proper motion , and is commonly denoted by the symbol .
The motion of stars can be decomposed into a radial component (along the line of sight) and a transverse component that changes its position on the celestial sphere. It is the transverse component that produces the proper motion: the radial component of motion changes the distance of the star from us, but does change its location on the celestial sphere.
5.1 Proper Motion
The proper motion itself is composed of two components: a change in the right ascension and a change in the declination of the star. The following figure illustrates.
Direction to sta r
Star Earth
Celestial spher e
Proper motion (^) Change in declinatio n
Change in right ascension
Celestial sphere
The 5 stars with the largest proper motion are listed in the following table
Star Change in R. A. Change in Dec Proper Motion (arcsec/yr) (arcsec/yr) (arcsec/yr) Barnard’s Star 0:79784 10.32693 10. Kapteyn’s Star 6.50605 5:73139 8. Groombridge 1830 4.00369 5:81300 7. Lacaille 9352 6.76726 1.32666 6. CD-37d 15492 5.63407 2:33794 6.
Example: Proper motion of Barnard’s Star
Barnard’s Star has the largest proper motion of any star. How long will it take for Barnard’s star to change its position relative to other stars on the celestial sphere by an angle equal to the diameter of the Moon? The diameter of the Moon is about (^12)
ı D 1800 arcsec. It will take Barnard’s Star 1800 arcsec 10:3 arcsec yr ^1
' 175 yr
to move the diameter of the Moon. Most other stars move much more slowly than this on the celestial sphere.
Show OJTA animation 2.7 for proper motion of Barnard’s Star.
5.2 Space Velocities
The true velocity of a star is called its space velocity. The space velocity vs may be resolved into a radial velocity vr along the line of sight and a transverse velocity vt perpendicular to the line of sight. The space velocity and its components are illustrated in the following figure.
vr
v (^) t vs
Earth Star
Their lengths are related by the Pythagorean theorem.
5.3 Motion of the Sun Relative to the Stars
The Sun is in motion, just like other stars. It partakes of the general rotation of the galaxy (the spiral Milky Way). The Milky Way rotates once in about 225 million years, which corresponds to an average velocity for the Sun of about 220 km s ^1 (the Sun covers a distance of about 4 AU in one year because of this motion). The space velocities that we measure for stars then correspond to deviations from this average motion for stars near the Sun.
The Solar Apex and Antapex With respect to the local field of stars, the Sun is moving at 19.7 km s ^1 toward a point in the constellation Hercules (near the star Vega, which is in Lyra) that is called the solar apex. It will take us a while to get to Vega though; it is 26.5 ly away! The point on the opposite side of the sky away from which the Sun appears to be moving is called the solar antapex.
