CHAPTER XXVI.

THE PROBLEM OF SUN AND STAR DISTANCES.

One question had long occupied the minds of scientific men without the finding of any satisfactory answer, and this was the distance of the sun from our earth.

At length the sun had fully gained his rightful position in the minds of men as center and controller of the Solar System, and earth was fully dethroned from her old false position. In point of fact, the sun had gained _more_ than his rightful position; since he was now looked upon very much as the earth had been formerly looked upon; since he was regarded practically as the motionless Universe-Center. The earth might and did move--people had grown used to that idea--but the sun, at all events, was fixed. The sun, beyond turning upon his axis, was motionless.

Still, as to the true distance of the sun from ourselves, ignorance reigned. Tycho Brahe had made a great advance on earlier notions by placing the light-giver 4,000,000 miles away in imagination. Kepler, a quarter of a century later, increased this to 14,000,000. Galileo afterwards reverted to the 4,000,000. All this, however, was sheer guesswork.

Not till well on in the seventeenth century did Cassini make a definite attempt at actual measurement of the sun’s distance, and this attempt gave as a result some 82,000,000 miles--not far removed from the truth. But at the same period other observers gave results of 41,000,000 and 136,000,000; so for years the question still remained swathed in mist. Better modes and better instruments were required before it could receive settlement.

The measurement of the distance of objects a good way off is by means of their “parallax,” or the apparent change in their position when viewed from two different points at some distance from each other. To this method of calculating distance we have already referred.

This kind of measurement of distances is not confined to our earth’s surface alone. The distances of bright bodies in the heavens may be calculated after just the same method, provided only that the heavenly body is not too far distant to be made to change its seeming position in the sky.

Suppose you wished to find out how far off the moon is. You would have to make your observation of the moon’s exact position in the sky--of just that spot precisely where she is to be seen among heavenly scenery at a particular moment; and you would have to get somebody else to make a similar observation, at the same time, from some other part of earth, at a good distance from your post.

There are no hills or woods in the sky for the moon to be seen against; but there are plenty of stars, bright points of light far beyond the moon. If you look at her from one place, and your friend looks at her from another place a good way off, there will be a difference in your two “views.” You will see her very close to certain stars; and your friend will see her not quite so close to those stars, but closer to others. This difference of view would give the moon’s parallax.

If your observation were very careful, very exact, and if you had the precise distance between the spot where you stood, and the spot where your friend stood,--then, from that base-line, and from the two angles formed by its junction with the lines from the two ends of it straight to the moon, you might reckon how many miles away the moon is. The greater the distance between the two places of observation, the better,--as, for instance, at Greenwich and the Cape of Good Hope.

Practically, this is not nearly so simple a matter as it may sound, because our earth is always on the move, and the moon herself is perpetually journeying onward. All such motions have to be most scrupulously allowed for. So the actual measurement of moon-distance requires a great deal of knowledge and of study. Many other difficulties and complications besides these enter into the question, and have to be overcome.

Now, the sun is very much farther away than the moon, and the stumbling-blocks in the way of finding out his distance become proportionately greater and more numerous. To observe him from two parts of England, or from two parts of Europe, would give him no parallax. That is to say, there would be no change of position on his part apparent to us.

I do not say that there would be no change at all; but only that it would be so minute as to be quite unseen by human eyes, even with the help of most careful and accurate measurement. A very long base-line is needed to make the sun distinctly appear to change his position ever so little. Only the very longest base-line which can be found on earth will do for this,--nothing less than the earth’s whole diameter of nearly eight thousand miles. And I think you will see that the success of the calculation would then depend, not alone on most careful observation from two posts at the opposite sides of earth; not alone on mathematical gifts and powers of close reckoning; but also, essentially, on a true knowledge of our earth’s diameter; that is, of _the exact length of the base-line_ from which the whole calculation would have to be made, and upon which the answer would largely depend.

For a long while the earth’s diameter was not well known. As time went on, fresh measurements were again and again made of different portions of earth’s surface, fresh calculations following therefrom; and gradually clear conclusions were reached. A very important matter it was that they should be reached; for the semi-diameter of our earth has been adopted as a “standard measure” for the whole universe; and the slightest error in that standard measure would affect all after calculations.

When actual observations of sun-distance came to be made, innumerable difficulties arose. Foremost stood the huge amount of that distance. This made precise observations more difficult; and at the same time it made every mistake in observation so much the worse. A little mistake in observing the moon might mean only a hundred miles or so wrong in the answer; but a mistake equally small in observing the sun would lead to an error of many millions of miles.

Again, to observe the sun’s exact position among the stars, as with the moon, was not possible; because when the sun is visible, the stars are not visible. Then, too, the dazzling brightness of the sun balked the needed exactitude.

Halley had a brilliant thought before he died. He could not carry it out himself, but he left it to others as a legacy; that was, by observing the transit of Venus from two different points on the earth’s surface. At his suggestion, on the first opportunity--which was not till after his death--the above mode was tried of measuring the sun’s distance.

A certain observer, stationed on one part of earth, saw the tiny dark body of Venus take one particular line across the sun’s bright face. Another observer, standing on quite another and a far-off part of earth, saw the little dark body take quite another line across the sun’s bright face. Not that there were two little dark bodies, but that the one body was seen by different men in different places.

From these separate views of the path of Venus across the face of the sun, in connection with what was already known of the earth’s diameter, and therefore of the length of base-line between the two places, the distance of the sun was reckoned to be about 95,000,000 miles.

Since that date many fresh attempts have been made, and errors have been set right. Mercury as well as Venus has been used in this matter, and other newer modes of measurement have also been successfully tried. We know now, with tolerable accuracy, that the sun’s greater distance from earth is between 92,000,000 and 93,000,000 miles. A curious illustration of sun-distance has been offered by one writer. Sound and light, heat and sensation, all require _time_ for journeying. When a child puts his finger into a candle-flame, he immediately shrieks with pain. Yet, quickly as the cry follows the action, his brain is not really aware of the burn until a certain interval has elapsed. True, the interval is extremely minute; still it is a real interval. News of the burn has to be telegraphed from the finger, through the nerves of the arm, up to the brain; and it occupies time in transmission, though so small a fraction of a second that we can not be conscious of it.

Now, try to imagine a child on earth with an arm long enough to reach the sun. His fingers might be scorched by the raging fires there, while yet his brain on earth would remain quite unaware of the fact for about one hundred and thirty years. All through those years, sensation would be darting along the arm exactly as fast as it darts from the finger-tips of an ordinary child on earth to that child’s brain.

If the scorching began before he was one year old, he would have become a very aged man, one hundred and thirty years old, before he could know in his mind what was happening in the region of his hand. Moreover, if, on receiving the intimation, he should decide to withdraw his hand from that unpleasantly-hot neighborhood, another hundred and thirty years would elapse before the fingers could receive and act upon the message, telegraphed from the brain, through the nerves of the arm. So much for the distance of the sun from our earth!

But the stars! How far off are the stars?

The distance of the moon is a mere nothing. The distances of the planets have been found out. The distance of the sun has been measured. But the stars--those wondrous points of light, twinkling on, night after night, century after century, unchanged in position save by the seeming nightly pilgrimage of them all across the sky in company, caused only by our earth’s restless, continual whirl,--

What about the distances of the stars? Can we measure their distance by means of their parallax? This mode of measurement was tried successfully on the moon, on the planets, and on the sun. But when it was tried upon the stars, from two stations as far apart as any two stations on earth could be, the attempt was a failure. Not a ghost of parallax could be detected with any one star. Not the faintest sign of displacement was seen in the position of a single star when most critically and carefully examined.

Then arose a brilliant thought! What of earth’s yearly journey round the sun? If a base-line of 8,000 miles were not enough, compared with the great distance of the stars, this at least remained. Our earth at midsummer is somewhere about 185,000,000 miles away from where she is at midwinter, comparing her position with that of the sun, and reckoning him to be at rest.

In reality, the sun is not at rest, but is in ceaseless motion, carrying with him, wherever he goes, the whole Solar System with as much ease as a train carries its passengers. Those passengers are truly in motion, yet, with regard merely to the train, they are at rest. So each member of the Solar System--attached to the sun, not by Ptolemaic bars, but by the bond of gravity--is borne along by him through space; yet, with respect to each member of that system, the central sun is always and absolutely at rest.

At one time of the year, our earth is on one side of the sun, over 92,000,000 miles distant. Six months later, the earth is on the other side of the sun, not quite 93,000,000 miles away from him in that opposite direction. Twice 93,000,000 comes to 186,000,000. This line, therefore--the diameter of the earth’s whole yearly orbit, may be roughly stated as about 185,000,000 of miles in length.

Here surely was a base-line fit to give parallax to any star--or, rather, to make parallax visible in the case of any star. For it is, after all, a question, not of fact, but of visibility; not of whether the thing _is_, but of whether we are able to _see_ it.

As the earth journeys on her annual tour round the sun, following a slightly elliptic pathway, the diameter of which is about 185,000,000 miles, each star in the sky must of necessity undergo a change of position, however minute, performing a tiny apparent annual journey in exact correspondence with the earth’s great annual journey.

The question is not, Does the star do this? but, Can we _see_ the star do this? Its apparent change of position may be so infinitesimal, through enormous distance, that no telescopes or instruments yet made by man can possibly show it to us.

The star-motion of which I am now speaking is purely a seeming movement, not real. Be very clear on this point in your mind. _Real_ star-movements, though suspected earlier, were not definitely surmised--one may even say “discovered”--until the year 1718, by Halley. And though Cassini in 1728 referred to this discovery of Halley’s, yet very little was heard about the matter until the days of Herschel. Only _apparent_ star-motions were generally understood and accepted.

The first and simplest of such seeming star-motions is one which we can all see--the nightly journey of the whole host of stars, caused by our earth’s whirl upon her axis.

The second is also simple, but by no means also easily seen. Astronomers reasoned out the logical necessity for such an apparent motion long before it could be perceived. As far back as the days of Copernicus it was felt that if the Copernican System were true, if the earth in very deed traveled round the sun, then the stars ought to change their positions in the sky when viewed from different parts of earth’s annual journey. Observations were taken, divided by six months of time and by one hundred and eighty-five millions of miles of space. And the stars stirred not!

Stupendous as was this base-line, it proved insufficient. So much _more_ stupendous was the distance of the stars that the base-line sank to nothing, and once again parallax could not be detected. Not that the seeming change of position in the star did not take place, but that human eyes were unable to see it, human instruments were unable to register it.

There lies the gist of the matter. If the change of position can be observed, well and good! The length of the base-line being known, the distance of the star may be mathematically calculated. For the size of the tiny apparent path, followed in a year by the star, is and must be exactly proportioned to the distance of the star from that base-line. If the tiny oval be so much larger, then the star is known to be so much nearer. If the tiny oval be so much smaller, then the star is known to be so much farther away.

But when not the minutest token could be discovered of a star’s position in the sky being in the least degree affected by the earth’s great annual change of position, astronomers were at a loss. There was absolutely nothing to calculate from. The star was a motionless point to earth. The whole yearly orbit of earth was a motionless point to the star. One slender beam of light united the two. Reckoners had nothing to stand upon.

It is interesting to know that Copernicus had actually, long before, suggested this as a possible explanation of the absence of star-parallax. He thought that astronomers might fail altogether to find it, because the stars might be “at a practically infinite distance” from our earth.