Читать книгу Star-land: Being Talks With Young People About the Wonders of the Heavens - Robert S. Ball - Страница 7

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I shall so often have to speak of the distances of the celestial bodies that I may once for all explain how it is that we have been able to discover what these distances are. This would be a very puzzling matter if we were to try and describe it fully, but the principle of the method is not at all difficult. Do you know why you have been provided with two eyes? It is undoubted that one of the reasons is to aid you in estimating distances. You see this boy (Fig.4) judges of the distance of his finger by the inclination of his two eyes when directed at it. In a similar way we judge of the distance of a heavenly body by making observations on it from two different stations.

Fig.4.—Two Eyes are better than One.

Fig.5.—How we measured the Height of the Ball.

I shall illustrate our method of measuring the actual distance of a body in the heavens by showing you how we can find the height of that large india-rubber ball which is hanging from the ceiling. Of course, I do not intend to have a measuring tape from the ball itself, because I want to solve the problem on the same principle as that by which we measure the distance of the sun or of any other celestial body which we cannot reach. I will ask the aid of a boy and a girl, who will please stand one at each end of the lecture table. The apparatus we shall want is very simple; it consists of two cards and a pair of scissors. The boy will kindly shape his card to such an angle that when he holds it to his eye one side of the angle shall point straight at the little girl, and the other side shall point straight at the ball, just as you see in the picture (Fig.5). The girl will also please do the same with her card, so that along one side she just sees the little boy’s face, while the other side points up to the ball. It will be necessary to cut these angles properly. If the angle be too big, then when one side points to the boy’s face, the other will be directed above the ball. If the angle on the card be too small, then one side will be directed below the ball, while the other is pointed to the boy. The whole accuracy of our little observations depends upon cutting the card angles properly. When they have been truly shaped it will be easy to find the distance of the ball. We first take a foot rule and measure the length of our table from one of our young friends to the other. That length is twelve feet, and to discover the distance of the ball we must make a drawing. We get a sheet of paper, and first rule a line twelve inches long. That will represent the length of the table, it being understood that each inch of the drawing is to correspond to a foot of the actual table. Let the end where the girl stood be marked B, and that of the boy, A, and now bring the cards and place them on the line just as shown in the figure. The card the girl has shaped is to be put so that the corner of it lies at B, and one edge along B A. Then the boy’s card is to be so put that its corner is at A and one edge along A B. Next with a pencil we rule lines on the other edges of the cards, taking care that they are kept all the time in their proper positions. These two lines carried on will meet at C; and this must be the position of the ball on the scale of our little sketch. It only now remains to take the foot rule and measure on the drawing the length from A to C. I find it to be twenty inches, and I have so arranged it that the distance from B to C is the same.

Fig.6.—This is what we wanted the Cards for.

I do not intend to trouble you much with Euclid in these lectures, but as many of my young friends have learned the sixth book, I will just refer to the well-known proposition, which tells us that the lengths of the corresponding sides of two similar triangles are proportional. We have here two similar triangles. There is the big one with the boy at one corner, the girl at the other, and the ball overhead. Here is the small triangle which we have just drawn. These triangles are similar because they have got the same angles, and it was to insure that they should have the same angles that we were so careful in shaping the cards. As these two triangles are similar, their sides must be proportional. We have agreed that the line A B, which is twelve inches long, is to represent the length of the table between the little boy and girl. Hence the distance, A C, must, on the same scale, be the interval between the ball and the boy at the end. This is twenty inches on the drawing, and therefore the actual distance from the end of the table to the ball is twenty feet.

Hence you see that without going up to the ball or having a string from it, or in any other way making direct communication with it, we have been able to ascertain how far up in the air the ball is actually hung. This simple illustration explains the principle of the method by which astronomers are able to learn the distances of the different celestial bodies from the earth. You must think of the sun, the moon, and the stars as globes supported in some manner over our heads, and we seek to discover their distances from measurements of angles made at the ends of a base-line.

Fig.7.—This would be our Base-line when finding the Sun’s Distance.

Of course, astronomers must choose two stations which are far more widely separated than are those in our little experiment. In fact, the greater the interval between the two stations, the better. Astronomers require a much longer distance than from one side of this room to the other, or from one side of London to the other side. If it were merely a balloon at which we were looking, then, when one observer at one side of London and another at the opposite side shaped their cards carefully, we should be able to tell the height of the balloon very easily. But as the sun is so much further off than any balloon could ever be, we must separate the observers much more widely. Even the breadth of England would not be enough, so we have to make them separate more and more until they are as widely divided as it is possible for any two people on this earth to be. One astronomer takes up his position at A (Fig.7), and the other at the opposite side at B, so that they can both see the sun. They are obliged to use a much more accurate way of measuring the angles than by cutting out cards with pairs of scissors; and as the astronomer at A is not able to see his friend at B, it becomes no easy matter to measure the angles accurately. However, we shall not now trouble ourselves about such difficulties. It may suffice for the present to know that the angles are measured by delicate and very accurate instruments used by astronomers. They will not, indeed, make a little sketch such as sufficed for our purpose. They make a calculation which is a much more accurate way of effecting true measurement. The astronomers know the size of the earth, and thus they know how many thousands of miles lie between the two stations where the observations are made. This distance means in their calculation just what the length of the table did in our sketch. From each end of the line they set off an angle just as we did, and the astronomer must use the principle of similar triangles which he finds in Euclid, just we had to do. At last, when they have calculated the sides of their triangle, they obtain the distance of the sun.