Radial velocity as a function of distance from the Sun, d, along a given line of sight.The upper curve is typical of I between 0 and 90°.The maximum vr corresponds to the point at which the line of sight passes closest to the galactic center.The close point with vr = 0 corresponds to local material, and the far point with vr = 0 corresponds to our line of sight crossing the Sun's orbit. Inside the Sun's orbit, each vr (except for the maximum) occurs twice.The lower curve is typical of values of I between 90° and 180°. All of these points are outside the Sun's orbit, so each circle is crossed only once, and each vr is reached only once. [F rancoise Combes, Observatoire de Meudon]

point of closest approach to the galactic center. This point is called the subcentral point. Of all the material along this line of sight, the material at the subcentral point produces the largest vr. As we go beyond the subcentral point, we are recrossing orbits, and vr becomes smaller. Eventually, vr reaches zero, when the Sun's orbit is crossed again. For points beyond the Sun's orbit, ^(R) < 00. This means that vr is negative and increases in absolute value as d increases.

For Í > 270° (the fourth quadrant), the behavior of vr is similar to that in the first quadrant, except that when vr is positive in the first quadrant it is negative in the fourth quadrant, and when it is negative in the first quadrant it is positive in the fourth quadrant.

In the second quadrant (90° <£ < 180°), all lines of sight pass only through material outside the Sun's orbit. There is no maximum vr; it just increases with d. The behavior in the third quadrant is the negative of that in the second quadrant.

We can also find an expression for the relative transverse velocity. This will produce proper motions. The relative velocity is given by vT = v(R) sin (90° - 6) - v0 sin (90° - £)

From Fig. 16.6 we see that

R cos 6 = R0 cos £ - d (16.14) Substituting this into equation (16.12) gives vT = fi(R)[R0 cos £ - d] - R0n0 cos £ (16.15) Grouping the terms with cos £ gives vT = [fl(R) - fi0]R0 cos £ - H(R) d (16.16)

The quantity R0, our distance from the galactic center, is determined from studies of the distribution of globular clusters, and more recently from the studies of clusters of masers near the galactic center. For approximately 20 years prior to 1985, the generally accepted value was 10.0 kpc. However, data accumulated by 1985 suggest a smaller value. As of 1985, the International Astronomical Union started recommending the value

By using an agreed upon value, astronomers can be sure that they are using the same values when they compare their studies of various aspects of galactic structure. Prior to 1985, the adopted value for v0, the orbital speed about the galactic center, was 250 km/s. The value recommended in 1985, to go with the new R0, is v0 = 220 km/s

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