Astronomy for Amateurs

the Sun. The annual parallax of a star is the angle under which one would see the radius, or half-diameter, of the terrestrial orbit from it. This radius of 149,000,000 kilometers (93,000,000 miles) is indeed, as previously observed, the unit, the meter of celestial measures. The angle is of course smaller in proportion as the star is more distant, and the apparent motion of the star diminishes in the same proportion. But the stars are all so distant that their annual displacement of perspective is almost imperceptible, and very exact instruments are required for its detection. Fig. 84.—Small apparent ellipses described by the stars as a result of the annual displacement of the Earth. The researches of the astronomers have proved that there is not one star for which the parallax is equal to that of another. The minuteness of this angle, and the [Pg 307]extraordinary difficulties experienced in measuring the distance of the stars, will be appreciated from the fact that the value of a second is so small that the displacement of any star corresponding with it could be covered by a spider's thread. A second of arc corresponds to the size of an object at a distance of 206,265 times its diameter; to a millimeter seen at 206 meters' distance; to a hair, 1⁄10 of a millimeter in thickness, at 20 meters' distance (more invisible to the naked eye). And yet this value is in excess of those actually obtained. In fact:—the apparent displacement of the nearest star is calculated at 75⁄100 of a second (0.75″), i.e., from this star, α of Centaur, the half-diameter of the terrestrial orbit is reduced to this infinitesimal dimension. Now in order that the length of any straight line seen from the front be reduced until it appear to subtend no more than an angle of 0.75″, it must be removed to a distance 275,000 times its length. As the radius of the terrestrial orbit is 149,000,000 kilometers (93,000,000 miles), the distance which separates α of Centaur from our world must therefore = 41,000,000,000,000 kilometers (25,000,000,000,000 miles). And that is the nearest star. We saw in Chapter II that it shines in the southern hemisphere. The next, and one that can be seen in our latitudes, is 61 of Cygnus, which floats in the Heavens 68,000,000,000,000 kilometers[Pg 308] (42,000,000,000,000 miles) from here. This little star, of fifth magnitude, was the first of which the distance was determined (by Bessel, 1837–1840). All the rest are much more remote, and the procession is extended to infinity. We can not conceive directly of such distances, and in order to imagine them we must again measure space by time. In order to cover the distance that separates us from our neighbor, α of Centaur, light, the most rapid of all couriers, takes 4 years, 128 days. If we would follow it, we must not jump from start to finish, for that would not give us the faintest idea of the distance: we must take the trouble to think out the direct advance of the ray of light, and associate ourselves with its progress. We must see it traverse 300,000 kilometers (186,000 miles) during the first second of the journey; then 300,000 more in the second, which makes 600,000 kilometers; then once more 300,000 kilometers during the third, and so on without stopping for four years and four months. If we take this trouble we may realize the value of the figure; otherwise, as this number surpasses all that we are in the habit of realizing, it will have no significance for us, and will be a dead letter. If some appalling explosion occurred in this star, and the sound in its flight of 340 meters (1,115 feet) per[Pg 309] second were able to cross the void that separates us from it, the noise of this explosion would only reach us in 3,000,000 years. A train started at a speed of 106 kilometers (65 miles) per hour would have to run for 46,000,000 years, in order to reach this star, our neighbor in the celestial kingdom. The distance of some thirty of the stars has been determined, but the results are dubious. The dazzling Sirius reigns 92,000,000,000,000 kilometers (57,000,000,000,000 miles), the pale Vega at 204,000,000,000,000. Each of these magnificent stars must be a huge sun to burn at such a distance with such luminosity. Some are millions of times larger than the Earth. Most of them are more voluminous than our Sun. On all sides they scintillate at inaccessible distances, and their light strays a long while in space before it encounters the Earth. The luminous ray that we receive to-day from some pale star hardly perceptible to our eyes—so enormous is its distance—may perhaps bring us the last emanation of a sun that expired thousands of years ago. If these methods have been clear to my readers, they may also be interested perhaps in knowing the means employed in weighing the worlds. The process[Pg 310] is as simple and as clear as those of which we have been speaking. Weighing the stars! Such a pretension seems Utopian, and one asks oneself curiously what sort of balance the astronomers must have adopted in order to calculate the weight of Sun, Moon, planets or stars. Here, figures replace weights. Ladies proverbially dislike figures: yet it would be easier for some society dame to weigh the Sun at the point of her pen, by writing down a few columns of figures with a little care, than to weigh a 12 kilogram case of fruit, or a dress-basket of 35 kilos, by direct methods. Weighing the Sun is an amusement like any other, and a change of occupation. If the Moon were not attracted by the Earth, she would glide through the Heavens along an indefinite straight line, escaping at the tangent. But in virtue of the attraction that governs the movements of all the Heavenly bodies, our satellite at a distance of 60 times the terrestrial half-diameter revolves round us in 27 days, 7 hours, 43 minutes, 111⁄2 seconds, continually leaving the straight line to approach the Earth, and describing an almost circular orbit in space. If at any moment we trace an arc of the lunar orbit, and if a tangent is taken to this arc, the deviation from the[Pg 311] straight line caused by the attraction of our planet is found to be 11⁄3 millimeter per second. This is the quantity by which the Moon drops toward us in each second, during which she accomplishes 1,017 meters of her orbit. On the other hand, no body can fall unless it be attracted, drawn by another body of a more powerful mass. Beings, animals, objects, adhere to the soil, and weigh upon the Earth, because they are constantly attracted to it by an irresistible force. Weight and universal attraction are one and the same force. On the other hand, it can be determined that if an object is left to itself upon the surface of the Earth, it drops 4.90 meters during the first second of its fall. We also know that attraction diminishes with the square of the distance, and that if we could raise a stone to the height of the Moon, and then abandon it to the attraction of our planet, it would in the first second fall 4.90 meters divided by the square of 60, or 3,600—that is, of 11⁄3 millimeters, exactly the quantity by which the Moon deviates from the straight line she would pursue if the Earth were not influencing her. The reasoning just stated for the Moon is equally applicable to the Sun. [Pg 312] The distance of the Sun is 23,386 times the radius of the Earth. In order to know how much the intensity of terrestrial weight would be diminished at such a distance, we should look, in the first place, for the square of the number representing the distance—that is, 23,386 multiplied by itself, = 546,905,000. If we divide 4.90 meters, which represents the attractive force of our planet, by this number, we get 9⁄1,000,000 of a millimeter, and we see that at the distance of the Sun, the Earth's attraction would really be almost nil. Now let us do for our planet what we did for its satellite. Let us trace the annual orbit of the terrestrial globe round the central orb, and we shall find that the Earth falls in each second 2.9 millimeters toward the Sun. This proportion gives the attractive force of the Sun in relation to that of the Earth, and proves that the Sun is 324,000 times more powerful than our world, for 2.9 millimeters divided by 0.000,009 equals 324,000, if worked out into the ultimate fractions neglected here for the sake of simplicity. A great number of stars have been weighed by the same method. Their mass is estimated by the movement of a satellite round them, and it is by this method that we are able to affirm that Jupiter is 310 times heavier than[Pg 313] the Earth, Saturn 92 times, Neptune 16 times, Uranus 14 times, while Mars is much less heavy, its weight being only two-thirds that of our own. The planets which have no satellites have been weighed by the perturbations which they cause in other stars, or in the imprudent comets that sometimes tarry in their vicinity. Mercury weighs very much less than the Earth (only 6⁄100) and Venus about 8⁄10. So the beautiful star of the evening and morning is not so light as her name might imply, and there is no great difference between her weight and our own. As the Moon has no secondary body submitted to her influence, her weight has been calculated by reckoning the amount of water she attracts at each tide in the ocean, or by observing the effects of her attraction on the terrestrial globe. When the Moon is before us, in the last quarter, she makes us travel faster, whereas in the first quarter, when she is behind, she delays us. All the calculations agree in showing us that the orb of night is 81 times less heavy than our planet. There is nearly as much difference in weight between the Earth and the Moon as between an orange and a grape. Not content with weighing the planets of our system, astronomers have investigated the weight of the stars. How have they been enabled to ascertain the quantity[Pg 314] of matter which constitutes these distant Suns—incandescent globes of fire scattered in the depths of space? They have resorted to the same method, and it is by the study of the attractive influence of a sun upon some other contiguous neighboring star, that the weight of a few of these has been calculated. Of course this method can only be applied to those double stars of which the distance is known. It has been discovered that some of the tiny stars that we can hardly see twinkling in the depths of the azure sky are enormous suns, larger and heavier than our own, and millions of times more voluminous than the Earth. Our planet is only a grain of dust floating in the immensity of Heaven. Yet this atom of infinity is the cradle of an immense creation incessantly renewed, and perpetually transformed by the accumulated centuries. And what diversity exists in this army of worlds and suns, whose regular harmonious march obeys a mute order.... But we have as yet said nothing about weight on the surface of the worlds, and I see signs of impatience in my readers, for after so much simple if unpoetical demonstration, they will certainly ask me for the explanation that will prove to them that a kilogram transported to Jupiter or Mars would weigh more or less than here. [Pg 315] Give me your attention five minutes longer, and I will restore your faith in the astronomers. It must not be supposed that objects at the surface of a world like Jupiter, 310 times heavier than our own, weigh 310 times more. That would be a serious error. In that case we should have to assume that a kilogram transported to the surface of the Sun would there weigh 324,000 times more, or 324,000 kilograms. That would be correct if these orbs were of the same dimensions as the Earth. But to speak, for instance, only