MEASUREMENT OF STAR DISTANCES.
Until the days of Sir William Herschel, little attention was bestowed
upon the universe of distant stars. Before his advent the interest
of astronomers had been mainly centered in the sun and his revolving
worlds. The “fixed stars” were indeed studied, as such, with a certain
amount of care, and numberless efforts were made to discover their
distances from earth; but the thought of a vast Starry System, in which
our little Solar System should sink to a mere point by comparison with
its immensity, had not yet dawned.
With larger and yet larger telescopes of his own making, Herschel
studied the whole Solar System, and especially the nature of sun-spots,
the rings of Saturn, the various motions of attendant moons, together
with countless other details. He enlarged the system by the discovery
of another planet outside Saturn--the planet Uranus, till then unknown.
These were only first steps. The work which he did in respect of the
Solar System was as nothing compared with the work which he did among
the stars. His work in our system was supplementary to other men’s
labors; his work among the stars was the beginning of a new era. Like
many before him, he, too, sought eagerly to find star-parallax, and he,
too, failed. Not yet had instruments reached a degree of finish which
should permit measuring operations of so delicate a nature.
Although he might not detect star-parallax, he sprang a mine upon the
older notions of star-fixity. He shook to its very foundations the
sidereal astronomy of the day,--the theory, long held, of a motionless
universe, motionless stars, and a rotating but otherwise motionless
sun. He did away with the mental picture, then widely believed in,
of vast interminable fixity and stillness, extending through space,
varied only by a few little wandering worlds. As he swept the skies,
and endeavored to gauge the fathomless depths, and vainly pursued the
search for the parallax of one star after another, he made a great and
unlooked-for discovery. This was in connection with double-stars.
Double-stars had long been known, and were generally recognized. But
whether the doubleness were purely accidental, due merely to the fact
of two stars happening to lie almost in the same line of sight, as
viewed from earth, or whether any real connection existed between
the two, no man living could say. Indeed, so long as all stars were
regarded as utter fixtures, the question was of no very great interest.
But light dawned as Herschel watched. He found the separate stars in a
certain pair to be moving. Each from time to time had slightly, very
slightly, changed its place. Then, at least, if all other stars in
the universe were fixed, those two were not fixed. He watched on, and
gradually he made out that their motions were steady, were systematic,
and were connected the one with the other. That was one of the first
steps towards breaking down the olden notion, so widely held, of a
fixed and unchanging universe.
Another double-star, and yet another, responded to Herschel’s intense
and careful searching. These other couples, too, were revolving, not
separately, but in company; journeying together round one center; bound
together apparently by bonds of gravitation, even as our sun and his
planets are bound together.
Other stars besides binary stars are found to move with a real and
not merely a seeming movement. Viewed carelessly, the stars do indeed
appear to remain fixed in changeless groups; fixed even through
centuries. But, to exceedingly close watching and accurate measurement,
many among them are distinctly _not_ fixed; many among them can be
actually seen to move.
Of course the observed motions are very small and slow. One may be
found to creep over a space as wide as the whole full moon in the
course of three hundred or four hundred years; and this is rapid
traveling for a star in earth’s sky! Another will perhaps cross a space
one-tenth or one-twentieth or one-fiftieth of the moon’s width in one
hundred years.
Such motions had never been carefully noted or examined, until Herschel
came to do away with the old received notions of star-fixity. Happily,
Herschel was no slave to “received ideas.” Like Galileo in earlier
times, he wished to “prove all things” personally, anxious only to find
out what was the truth. And he found that the stars were _not_ fixed!
He found that numbers of them were moving. He conjectured that probably
all the rest were moving also; that in place of a fixed universe of
changeless stars we have a whirling universe of rushing suns.
Herschel could not, of course, watch any one star for a hundred years,
much less for several centuries. But in a very few years he could, by
exceedingly close measurement, detect sufficient motion to be able to
calculate how long it would take a certain star to creep across a space
as wide as the full moon.
From step to step he passed on, never weary of his toil. He sought to
gauge the Milky Way, and to form some notion of its shape. He noted
a general drift of stars to right and to left, which seemed to speak
of a possible journey of our sun through space, with all the planets
of the Solar System. He flung himself with ardor into the study of
star-clusters and of nebulæ. He saw, with an almost prophetic eye, the
wondrous picture of a developing universe--of nebulæ growing slowly
into suns, and of suns cooling gradually into worlds--so far as to
liken the heavens to a piece of ground, containing trees and plants in
every separate stage of growth.
And still the search for star parallax went on, so long pursued in
vain. No longer base-line than that of the diameter of earth’s yearly
orbit lay within man’s reach. But again and yet again the attempt was
made. Instruments were improved, and measurements became ever more
delicate; and at length some small success crowned these persistent
endeavors. The tiny sounding-line of earth, lowered so often into the
mysterious depths of space, did at last “touch bottom.”
Herschel died, full of years and honors, in 1822; and some ten years
later three different attempts proved, all to some extent, and almost
at the same date, successful. Bessel, however, was actually the first
in point of time; and his attempt was upon the double-star, 61 Cygni;
not at all a bright star, but only just visible to the naked eye.
There are stars and stars, enough to choose from. The difficulty
always was, which to select as a subject for trial with any reasonable
prospect of a good result. Some astronomers held that the brightest
stars were the most hopeful, since they were probably the nearest; and
of course the nearer stars would show parallax more readily, because
their parallax would be the greater. But certain very bright stars
indeed are now known to be far more distant than certain very dim stars.
Again, some astronomers thought that such stars as could be perceived
to move most rapidly in the course of years would be the most hopeful
objects to attack, since the more rapid movement might be supposed to
mean greater nearness, and so greater ease of measurement. But some
stars, seen to move rapidly, are now known to be more distant than
others which are seen to move more sluggishly. So neither of these two
rules could altogether be depended on; yet both were, on the whole, the
best that could be followed, either separately or together.
The star 61 Cygni is not one of the brighter stars, but it is one of
those stars which can be seen to travel most quickly across the sky in
the course of a century. Therefore it was selected for a trial; and
that trial was the first to meet with success.
For 61 Cygni was found to have an apparent parallax; in other words,
its tiny seeming journey through the year, caused by our earth’s great
journey round the sun, could be detected. Small as the star-motion
was, it might, through careful measurement, be perceived. And, in
consequence, the distance of the star from earth could be measured.
Not measured with anything like such exactitude as the measurements
of sun-distance, but with enough to give a fair general notion of
star-distance.
One success was speedily followed by others. By a few others,--not by
many. Among the thousands of stars which can be seen by the naked eye,
one here and one there responded faintly to the efforts made. One here
and one there was found to stir slightly in the sky, when viewed from
earth’s summer and winter positions, or from her spring and autumn
positions, in her yearly pathway round the sun.
It was a very, very delicate stir on the part of the star. Somewhat
like the difference in position which you might see in a penny a
few miles off, if you looked at it first out of one window and then
out of another window in the same house. You may picture the penny
as radiantly bright, shining through pitch darkness; and you may
picture yourself as looking at it through a telescope. But even so,
the apparent change of position in the penny, viewed thus, would be
exceedingly minute, and exceedingly difficult to see.
There are two ways of noting this little seeming movement on the part
of a star in the sky.
Either its precise place in the sky may be observed--its exact
position, as in a map of the heavens--or else its place may be noted
as compared with another more distant star, near to it in the sky,
though really far beyond. Parallax, if visible, would make it alter its
precise place in the sky. Parallax, if visible, would bring it nearer
to or farther from any other star more distant than itself from earth.
The more distant star would have a much smaller parallax--probably
so small as to be invisible to us--and so it would do nicely for a
“comparison star.”
The first of these methods was the first tried; and the second was the
first successful.
To find star-distance through star-parallax sounds quite simple,
when one thinks of the general principle of it. Just merely the
question of a base-line, accurately measured; and of two angles,
accurately observed; and of another angle, a good way off, accurately
calculated,--all resting on the slight seeming change of position in
a certain distant object, watched from two different positions, about
185,000,000 miles apart.
Quite simple, is it not? Only, when one comes to realize that the
“change of position” is about equal to the change of position in a
penny piece, miles away, looked at from two windows in one house,--then
the difficulty grows.
Besides this, one has to remember all the “corrections” necessary,
before any true result can be reached.
A penny piece, miles away, seen from two windows, would be difficult
enough as a subject for measurement. But, at least, the penny would
be at rest; and you yourself would be at rest; and light would pass
instantaneously from it to you; and there would be no wobbling and
nodding motions of everything around to add to your perplexities.
In the measurement of star-parallax, all these things have to be
considered and allowed for; all have to be put out of the question, as
it were, before any correct answer is obtained.
The refraction of light must be considered; because that displaces the
star, and makes it seem to us to be where it is not. And the aberration
of light must be considered; because, in a different way, that does the
same thing, making the star seem to take a little journey in the course
of the year. And the precession, or forward motion, of the equinoxes,
and nutation, or vibratory motion, have both to be separately
considered; because they, too, affect the apparent position of every
star in the sky.
To watch the star in comparison with another star is easier than
merely to note its exact position in the sky; for the other star--the
“companion-star”--is equally with itself affected by refraction of
light and by aberration of light. But, then, another question comes in
seriously: whether or no the companion-star shows any parallax also;
since, if it does, that parallax must be carefully calculated and
allowed for.
So the measurement of star-distance, even when parallax can be
detected, is by no means a light or easy matter. On the contrary, it
bristles with difficulties. It is a most complicated operation, needing
profound knowledge, accurate observation, trained powers of reasoning
and calculation.
Nothing short of what has been termed “the terrific accuracy” of the
present day could grapple with the truly tremendous difficulties of
this problem of star-distance. It has, however, been grappled with,
and grappled with successfully. We now know, not indeed with anything
like exactitude, yet with reasonable certainty, the distances of a good
many stars, as expressed roughly in round number of “about” so many
trillions of miles.[3] We have at least learned enough to gain some
notion of the immeasurable distances of countless other stars, lying
far beyond reach of earth’s longest measuring-line.
[3] The diameter of the moon as seen from the earth is equal to
one thousand eight hundred and sixty eight seconds of space. When
the parallax of a star is ascertained, it is a simple matter to
calculate the distance of the star by the use of the following table.
If the star shows a displacement of one second in space, or one
eighteen-hundred-and-sixty-eighth part of the width of the moon, that
star is distant two hundred and six thousand two hundred and sixty-five
times the distance of the earth from the sun.
An angle of 1″ is equivalent to 206,265 times 93,000,000 of miles.
“ “ “ 0″.9 “ “ “ 229,183 “ “ “ “
“ “ “ 0″.8 “ “ “ 257,830 “ “ “ “
“ “ “ 0″.7 “ “ “ 294,664 “ “ “ “
“ “ “ 0″.6 “ “ “ 343,750 “ “ “ “
“ “ “ 0″.5 “ “ “ 412,530 “ “ “ “
“ “ “ 0″.4 “ “ “ 515,660 “ “ “ “
“ “ “ 0″.3 “ “ “ 687,500 “ “ “ “
“ “ “ 0″.2 “ “ “ 1,031,320 “ “ “ “
“ “ “ 0″.1 “ “ “ 2,062,650 “ “ “ “
“ “ “ 0″.0 “ “ “ Immeasurable.
The nearest star, Alpha Centauri, shows a parallax of less than one
second (0″.75). The farthest star, the distance of which has been
ascertained, is 1830 Groombridge, which shows a parallax of only
0″.045, and is distant 4,583,000 times earth’s distance from the sun,
or 426 trillions of miles.
The very thought of such unimaginable depths of space, of suns beyond
suns “in endless range,” toned down by simple distance to mere
quivering specks of light, is well-nigh overwhelming.