Thus there was a transit in June, 1761, then another 8 years after, in June, 1769. The next occurred 113-1/2 years less 8 years, _i.e._, 105-1/2 years after the preceding, in December, 1874; the next in December, 1882. The next will be in June, 2004, and June, 2012. At these eagerly antic.i.p.ated epochs, astronomers watch the transit of Venus across the Sun at two terrestrial stations as far as possible removed from each other, marking the two points at which the planet, seen from their respective stations, appears to be projected at the same moment on the solar disk. This measure gives the width of an angle formed by two lines, which starting from two diametrically opposite points of the Earth, cross upon Venus, and form an identical angle upon the Sun. Venus is thus at the apex of two equal triangles, the bases of which rest, respectively, upon the Earth and on the Sun. The measurement of this angle gives what is called the parallax of the Sun--that is, the angular dimension at which the Earth would be seen at the distance of the Sun.
[Ill.u.s.tration: FIG. 83.--Measurement of the distance of the Sun.]
Thus, it has been found that the half-diameter of the Earth viewed from the Sun measures 8.82". Now, we know that an object presenting an angle of one degree is at a distance of 57 times its length.
The same object, if it subtends an angle of a minute, or the sixtieth part of a degree, indicates by the measurement of its angle that it is 60 times more distant, _i.e._, 3,438 times.
Finally, an object that measures one second, or the sixtieth part of a minute, is at a distance of 206,265 times its length.
Hence we find that the Earth is at a distance from the Sun of 206,265/8.82--that is, 23,386 times its half-diameter, that is, 149,000,000 kilometers (93,000,000 miles). This measurement again is as precise and certain as that of the Moon.
I hope my readers will easily grasp this simple method of triangulation, the result of which indicates to us with absolute certainty the distance of the two great celestial torches to which we owe the radiant light of day and the gentle illumination of our nights.
The distance of the Sun has, moreover, been confirmed by other means, whose results agree perfectly with the preceding. The two princ.i.p.al are based on the velocity of light. The propagation of light is not instantaneous, and notwithstanding the extreme rapidity of its movements, a certain time is required for its transmission from one point to another. On the Earth, this velocity has been measured as 300,000 kilometers (186,000 miles) per second. To come from Jupiter to the Earth, it requires thirty to forty minutes, according to the distance of the planet. Now, in examining the eclipses of Jupiter"s satellites, it has been discovered that there is a difference of 16 minutes, 34 seconds in the moment of their occurrence, according as Jupiter is on one side or on the other of the Sun, relatively to the Earth, at the minimum and maximum distance. If the light takes 16 minutes, 34 seconds to traverse the terrestrial orbit, it must take less than that time, or 8 minutes, 17 seconds, to come to us from the Sun, which is situated at the center. Knowing the velocity of light, the distance of the Sun is easily found by multiplying 300,000 by 8 minutes, 17 seconds, or 497 seconds, which gives about 149,000,000 kilometers (93,000,000 miles).
Another method founded upon the velocity of light again gives a confirmatory result. A familiar example will explain it: Let us imagine ourselves exposed to a vertical rain; the degree of inclination of our umbrella will depend on the relation between our speed and that of the drops of rain. The more quickly we run, the more we need to dip our umbrella in order not to meet the drops of water. Now the same thing occurs for light. The stars, disseminated in s.p.a.ce, shed floods of light upon the Heavens. If the Earth were motionless, the luminous rays would reach us directly. But our planet is spinning, racing, with the utmost speed, and in our astronomical observations we are forced to follow its movements, and to incline our telescopes in the direction of its advance. This phenomenon, known under the name of _aberration_ of light, is the result of the combined effects of the velocity of light and of the Earth"s motion. It shows that the speed of our globe is equivalent to 1/10000 that of light, _i.e._, = about 30 kilometers (19 miles) per second. Our planet accordingly accomplishes her revolution round the Sun along an orbit which she traverses at a speed of 30 kilometers (better 29-1/2) per second, or 1,770 kilometers per minute, or 106,000 kilometers per hour, or 2,592,000 kilometers per day, or 946,080,000 kilometers (586,569,600 miles) in the year. This is the length of the elliptical path described by the Earth in her annual translation.
The length of orbit being thus discovered, one can calculate its diameter, the half of which is exactly the distance of the Sun.
We may cite one last method, whose data, based upon attraction, are provided by the motions of our satellite. The Moon is a little disturbed in the regularity of her course round the Earth by the influence of the powerful Sun. As the attraction varies inversely with the square of the distance, the distance may be determined by a.n.a.lyzing the effect it has upon the Moon.
Other means, on which we will not enlarge in this summary of the methods employed for determinations, confirm the precisions of these measurements with certainty. Our readers must forgive us for dwelling at some length upon the distance of the orb of day, since this measurement is of the highest importance; it serves as the base for the valuation of all stellar distances, and may be considered as the meter of the universe.
This radiant Sun to which we owe so much is therefore enthroned in s.p.a.ce at a distance of 149,000,000 kilometers (93,000,000 miles) from here.
Its vast brazier must indeed be powerful for its influence to be exerted upon us to such a manifest extent, it being the very condition of our existence, and reaching out as far as Neptune, thirty times more remote than ourselves from the solar focus.
It is on account of its great distance that the Sun appears to us no larger than the Moon, which is only 384,000 kilometers (238,000 miles) from here, and is itself illuminated by the brilliancy of this splendid orb.
No terrestrial distance admits of our conceiving of this distance. Yet, if we a.s.sociate the idea of s.p.a.ce with the idea of time, as we have already done for the Moon, we may attempt to picture this abyss. The train cited just now would, if started at a speed of a kilometer a minute, arrive at the Sun after an uninterrupted course of 283 years, and taking as long to return to the Earth the total would be 566 years.
Fourteen generations of stokers would be employed on this celestial excursion before the bold travelers could bring back news of the expedition to us.
Sound is transmitted through the air at a velocity of 340 meters (1,115 feet) per second. If our atmosphere reached to the Sun, the noise of an explosion sufficiently formidable to be heard here would only reach us at the end of 13 years, 9 months. But the more rapid carriers, such as the telegraph, would leap across to the orb of day in 8 minutes, 17 seconds.
Our imagination is confounded before this gulf of 93,000,000 miles, across which we see our dazzling Sun, whose burning rays fly rapidly through s.p.a.ce in order to reach us.
And now let us see how the distances of the planets were determined.
We will leave aside the method of which we have been speaking; that now to be employed is quite different, but equally precise in its results.
It is obvious that the revolution of a planet round the Sun will be longer in proportion as the distance is greater, and the orbit that has to be traveled vaster. This is simple. But the most curious thing is that there is a geometric proportion in the relations between the duration of the revolutions of the planets and their distances. This proportion was discovered by Kepler, after thirty years of research, and embodied in the following formula:
"The squares of the times of revolution of the planets round the Sun (the periodic times) are proportional to the cubes of their mean distances from the Sun."
This is enough to alarm the boldest reader. And yet, if we unravel this somewhat incomprehensible phrase, we are struck with its simplicity.
What is a square? We all know this much; it is taught to children of ten years old. But lest it has slipped your memory: a square is simply a number multiplied by itself.
Thus: 2 2 = 4; 4 is the square of 2.
Four times 4 is 16; 16 is the square of 4.
And so on, indefinitely.
Now, what is a cube? It is no more difficult. It is a number multiplied twice by itself.
For instance: 2 multiplied by 2 and again by 2 equals 8. So 8 is the cube of 2. 3 3 3 = 27; 27 is the cube of 3, and so on.
Now let us take an example that will show the simplicity and precision of the formula enunciated above. Let us choose a planet, no matter which. Say, Jupiter, the giant of the worlds. He is the Lord of our planetary group. This colossal star is five times (precisely, 5.2) as far from us as the Sun.
Multiply this number twice by itself 5.2 5.2 5.2 = 140.
On the other hand, the revolution of Jupiter takes almost twelve years (11.85). This number multiplied by itself also equals 140. The square of the number 11.85 is equal to the cube of the number 5.2. This very simple law regulates all the heavenly bodies.
Thus, to find the distance of a planet, it is sufficient to observe the time of its revolution, then to discover the square of the given number by multiplying it into itself. The result of the operation gives simultaneously the cube of the number that represents the distance.
To express this distance in kilometers (or miles), it is sufficient to multiply it by 149,000,000 (in miles 93,000,000), the key to the system of the world.
Nothing, then, could be less complicated than the definition of these methods. A few moments of attention reveal to us in their majestic simplicity the immutable laws that preside over the immense harmony of the Heavens.
But we must not confine ourselves to our own solar province. We have yet to speak of the stars that reign in infinite s.p.a.ce far beyond our radiant Sun.
Strange and audacious as it may appear, the human mind is able to cross these heights, to rise on the wings of genius to these distant suns, and to plumb the depths of the abyss that separates us from these celestial kingdoms.
Here, we return to our first method, that of triangulation. And the distance that separates us from the Sun must serve in calculating the distances of the stars.
The Earth, spinning round the Sun at a distance of 149,000,000 kilometers (93,000,000 miles), describes a circ.u.mference, or rather an ellipse, of 936,000,000 kilometers (580,320,000 miles), which it travels over in a year. The distance of any point of the terrestrial orbit from the diametrically opposite point which it pa.s.ses six months later is 298,000,000 kilometers (184,760,000 miles), _i.e._, the diameter of this...o...b..t. This immense distance (in comparison with those with which we are familiar) serves as the base of a triangle of which the apex is a star.
The difficulty in exact measurements of the distance of a star consists in observing the little luminous point persistently for a whole year, to see if this star is stationary, or if it describes a minute ellipse reproducing in perspective the annual revolution of the Earth.
If it remains fixed, it is lost in such depths of s.p.a.ce that it is impossible to gage the distance, and our 298,000,000 kilometers have no meaning in view of such an abyss. If, on the contrary, it is displaced, it will in the year describe a minute ellipse, which is only the reflection, the perspective in miniature, of the revolution of our planet round 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.
[Ill.u.s.tration: 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 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, [alpha] 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 [alpha] 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 lat.i.tudes, is 61 of Cygnus, which floats in the Heavens 68,000,000,000,000 kilometers (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 s.p.a.ce by time.