A Text-Book of Astronomy

by George C. Comstock

The student should not fail to note one important difference between proper motions and the motions determined spectroscopically: the latter are given directly in miles per second, or per hour, while the former are expressed in angular measure, seconds of arc, and there can be no direct comparison between the two until by means of the known distances of the stars their proper motions are converted from angular into linear measure. We are brought thus to the very heart of the matter; parallax, proper motion, and motion in the line of sight are intimately related quantities, all of which are essential to a knowledge of the real motions of the stars.

194. Star drift.—An illustration of how they may be made to work together is furnished by some of the stars—which make up the Great Dipper—β, γ, ϑ, and ζ Ursæ Majoris, whose proper motions have long been known to point in nearly the same direction across the sky and to be nearly equal in amount. More recently it has been found that these stars are all moving toward the sun with approximately the same velocity—18 miles per second. One other star of the Dipper, δ Ursæ Majoris, shares in the common proper motion, but its velocity in the line of sight has not yet been determined with the spectroscope. These similar motions make it probable that the stars are really traveling together through space along parallel lines; and on the supposition that such is the case it is quite possible to write out a set of equations which shall involve their known proper motions and motions in the line of sight, together with their unknown distances and the unknown direction and velocity of their real motion along their orbits. Solving these equations for the values of the unknown quantities, it is found that the five stars probably lie in a plane which is turned nearly edgewise toward us, and that in this plane they are moving about twice as fast as the earth moves around the sun, and are at a distance from us represented by a parallax of less than 0.02"—i. e., six times as great as the outermost circle in [Fig. 122]. A most extraordinary system of stars which, although separated from each other by distances as great as the whole breadth of [Fig. 122], yet move along in parallel paths which it is difficult to regard as the result of chance, and for which it is equally difficult to frame an explanation.

The stars α and η of the Great Dipper do not share in this motion, and must ultimately part company with the other five, to the complete destruction of the Dipper's shape. [Fig. 126] illustrates this change of shape, the upper part of the figure (a) showing these seven stars as they were grouped at a remote epoch in the past, while the lower section (c) shows their position for an equally remote epoch in the future. There is no resemblance to a dipper in either of these configurations, but it should be observed that in each of them the stars α and η keep their relative position unaltered, and the other five stars also keep together, the entire change of appearance being due to the changing positions of these two groups with respect to each other.

This phenomenon of groups of stars moving together is called star drift, and quite a number of cases of it are found in different parts of the sky. The Pleiades are perhaps the most conspicuous one, for here some sixty or more stars are found traveling together along similar paths. Repeated careful measurements of the relative positions of stars in this cluster show that one of the lucid stars and four or five of the telescopic ones do not share in this motion, and therefore are not to be considered as members of the group, but rather as isolated stars which, for a time, chance to be nearly on line with the Pleiades, and probably farther off, since their proper motions are smaller.

To rightly appreciate the extreme slowness with which proper motions alter the constellations, the student should bear in mind that the changes shown in passing from one section of [Fig. 126] to the next represent the effect of the present proper motions of the stars accumulated for a period of 200,000 years. Will the stars continue to move in straight paths for so long a time?

195. The sun's way.—Another and even more interesting application of proper motions and motions in the line of sight is the determination from them of the sun's orbit among the stars. The principle involved is simple enough. If the sun moves with respect to the stars and carries the earth and the other planets year after year into new regions of space, our changing point of view must displace in some measure every star in the sky save those which happen to be exactly on the line of the sun's motion, and even these will show its effect by their apparent motion of approach or recession along the line of sight. So far as their own orbital motions are concerned, there is no reason to suppose that more stars move north than south, or that more go east than west; and when we find in their proper motions a distinct tendency to radiate from a point somewhere near the bright star Vega and to converge toward a point on the opposite side of the sky, we infer that this does not come from any general drift of the stars in that direction, but that it marks the course of the sun among them. That it is moving along a straight line pointing toward Vega, and that at least a part of the velocities which the spectroscope shows in the line of sight, comes from the motion of the sun and earth. Working along these lines, Kapteyn finds that the sun is moving through space with a velocity of 11 miles per second, which is decidedly below the average rate of stellar motion—19 miles per second.