Stargazing: Past and Present

by Sir Norman Lockyer

The uses of the position micrometer as it is called are very various. In examination of the sun it is used to ascertain the position of spots on the surface, and the rate of their motion and change. The lunar craters require mapping, and their distances and bearing from certain fixed points measuring, for this then the position micrometer comes into use.

The varying diameters and the inclinations of the axes of the planets and the periods of revolution of the satellites are determined, and the position of their orbits fixed, in like manner. When a comet appears it is of importance to determine not only the direction of its motion among the stars, but the position of its axis of figure, and the angles of position and dimensions of its jets. The following diagram gives an example of the manner in which the position of its axis of figure is determined. First the nucleus is made to run along the fixed wire, so that it may be seen that the north vernier truly reads zero under this condition; if it does not its index error is noted. The system of wires is then rotated till one of the wires passes through the nucleus and fairly bisects the dark part behind the nucleus.

Fig. 161.—Measurement of the Angle of Position of the Axis of Figure of a Comet, a a, positions of fixed wire when the north vernier is at zero; d d position of movable wire under like conditions; a´ a´, d´ d´, positions of these wires which enable the angle of position of the comet’s axis to be measured. The angle a a´ or d d´ is the angle required.

It need scarcely be said that these observations are also of importance with reference to the motion of the binary stars, those compound bodies, those suns revolving round each other, the discovery of which we owe to the elder Herschel. We may thus have two stars a small distance apart; at another time we may have them closer still; and at another we may have them gradually separating, with their relative position completely changed. By means of the wire micrometer and the arrangement for turning the system of wires into different positions with regard to the parallel of declination, we have a means of determining the positions occupied by the binary stars in all parts of their apparent orbit, as well as their distances in seconds of arc. It is found, however, by experience that the errors of observation made in estimating distances are so large, relatively to the very small quantities measured, that it is absolutely necessary to make the determination of the orbit depend chiefly on the positions. And this is done in the following way.

Fig. 162.—Double Star Measurement, a a, b b, first position of fixed, double wire when the vernier reads 0°, and the star runs between the wires; c c, d d, first position of movable wires. a´ a´, b´ b´, new position of fixed double wire which determines the angle of position; c´ c´, d´ d´, new positions of the movable wires which measure the distance.

It is possible, by knowing the position angles at different dates, to find the angular velocity, and since the areas described by the radius vector are equal in equal times, the length of the radius vector must vary inversely as the square root of the angular velocity, and by taking a number of positions on the orbit of known angular velocity, we can set off radii vectores, and construct an ellipse, or part of one, by drawing a curve through the ends of the radii vectores; and from the part of the ellipse so constructed it is possible to make a good guess at the remainder. The angular size of this ellipse is obtained from the average of all the measures of distance of the stars. This ellipse is then the apparent ellipse described by the star, and the form and position of the true ellipse can be constructed from it from the consideration of the position of the larger star (which must really be the focus), with reference to the focus of the apparent ellipse; for if an ellipse be seen or projected on a plane other than its own, its real foci will no longer coincide with the foci of the projected ellipse.

The methods adopted in practice, for which we must refer the reader to other works on the subject, are, however, much more laborious and lengthy than the above outline, which is intended merely to show the possibility, or the faint outline of a method of constructing the real ellipse. When the real ellipse or orbit is known, it is then of course possible to predict the relative positions of the two components. Let us consider in some little detail the actual work of measuring a double star.

A useful form for entering observations upon, as taken, is the following, which is copied from one actually used.