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.