Astronomy for Amateurs by Camille Flammarion (mini ebook reader .TXT) 📕

This radiant Sun to which we owe so much is therefore enthroned in space 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 associate the idea of space 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 space 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 space 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 circumference, 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 passes six months later is 298,000,000 kilometers (184,760,000 miles), i.e., the diameter of this orbit. 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 space 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.