THE FIXED STARS
184. THE CONSTELLATIONS.--In the earlier chapters the student has
learned to distinguish between wandering stars (planets) and those fixed
luminaries which remain year after year in the same constellation,
shining for the most part with unvarying brilliancy, and presenting the
most perfect known image of immutability. Homer and Job and prehistoric
man saw Orion and the Pleiades much as we see them to-day, although the
precession, by changing their relation to the pole of the heavens, has
altered their risings and settings, and it may be that their luster has
changed in some degree as they grew old with the passing centuries.
[Illustration: FIG. 120.--Illustrating the division of the sky into
constellations.]
The division of the sky into constellations dates back to the most
primitive times, long before the Christian era, and the crooked and
irregular boundaries of these constellations, shown by the dotted lines
in Fig. 120, such as no modern astronomer would devise, are an
inheritance from antiquity, confounded and made worse in its descent to
our day. The boundaries assigned to constellations near the south pole
are much more smooth and regular, since this part of the sky, invisible
to the peoples from whom we inherit, was not studied and mapped until
more modern times. The old traditions associated with each constellation
a figure, often drawn from classical mythology, which was supposed to be
suggested by the grouping of the stars: thus Ursa Major is a great bear,
stalking across the sky, with the handle of the Dipper for his tail; Leo
is a lion; Cassiopeia, a lady in a chair; Andromeda, a maiden chained
to a rock, etc.; but for the most part the resemblances are far-fetched
and quite too fanciful to be followed by the ordinary eye.
185. THE NUMBER OF STARS.--"As numerous as the stars of heaven" is a
familiar figure of speech for expressing the idea of countless number,
but as applied to the visible stars of the sky the words convey quite a
wrong impression, for, under ordinary circumstances, in a clear sky
every star to be seen may be counted in the course of a few hours, since
they do not exceed 3,000 or 4,000, the exact number depending upon
atmospheric conditions and the keenness of the individual eye. Test your
own vision by counting the stars of the Pleiades. Six are easily seen,
and you may possibly find as many as ten or twelve; but however many are
seen, there will be a vague impression of more just beyond the limit of
visibility, and doubtless this impression is partly responsible for the
popular exaggeration of the number of the stars. In fact, much more than
half of what we call starlight comes from stars which are separately too
small to be seen, but whose number is so great as to more than make up
for their individual faintness.
The Milky Way is just such a cloud of faint stars, and the student who
can obtain access to a small telescope, or even an opera glass, should
not fail to turn it toward the Milky Way and see for himself how that
vague stream of light breaks up into shining points, each an independent
star. These faint stars, which are found in every part of the sky as
well as in the Milky Way, are usually called _telescopic_, in
recognition of the fact that they can be seen only in the telescope,
while the other brighter ones are known as _lucid stars_.
186. MAGNITUDES.--The telescopic stars show among themselves an even
greater range of brightness than do the lucid ones, and the system of
magnitudes (§ 9) has accordingly been extended to include them, the
faintest star visible in the greatest telescope of the present time
being of the sixteenth or seventeenth magnitude, while, as we have
already learned, stars on the dividing line between the telescopic and
the lucid ones are of the sixth magnitude. To compare the amount of
light received from the stars with that from the planets, and
particularly from the sun and moon, it has been found necessary to
prolong the scale of magnitudes backward into the negative numbers, and
we speak of the sun as having a stellar magnitude represented by the
number -26.5. The full moon's stellar magnitude is -12, and the planets
range from -3 (Venus) to +8 (Neptune). Even a very few of the stars are
so bright that negative magnitudes must be used to represent their true
relation to the fainter ones. Sirius, for example, the brightest of the
fixed stars, is of the -1 magnitude, and such stars as Arcturus and Vega
are of the 0 magnitude.
The relation of these magnitudes to each other has been so chosen that a
star of any one magnitude is very approximately 2.5 times as bright as
one of the next fainter magnitude, and this ratio furnishes a convenient
method of comparing the amount of light received from different stars.
Thus the brightness of Venus is 2.5 × 2.5 times that of Sirius. The full
moon is 2.5^{9} times as bright as Venus, etc.; only it should be
observed that the number 2.5 is not exactly the value of the _light
ratio_ between two consecutive magnitudes. Strictly this ratio is the
100^{1/5} = 2.5119+, so that to be entirely accurate we must say that
a difference of five magnitudes gives a hundredfold difference of
brightness. In mathematical symbols, if _B_ represents the ratio of
brightness (quantity of light) of two stars whose magnitudes are _m_ and
_n_, then
B = (100)^{(m-n)/5}
How much brighter is an ordinary first-magnitude star, such as Aldebaran
or Spica, than a star just visible to the naked eye? How many of the
faintest stars visible in a great telescope would be required to make
one star just visible to the unaided eye? How many full moons must be
put in the sky in order to give an illumination as bright as daylight?
How large a part of the visible hemisphere would they occupy?
187. CLASSIFICATION BY MAGNITUDES.--The brightness of all the lucid
stars has been carefully measured with an instrument (photometer)
designed for that special purpose, and the following table shows,
according to the Harvard Photometry, the number of stars in the whole
sky, from pole to pole, which are brighter than the several magnitudes
named in the table:
The number of stars brighter than magnitude 1.0 is 11
" " " " " 2.0 " 39
" " " " " 3.0 " 142
" " " " " 4.0 " 463
" " " " " 5.0 " 1,483
" " " " " 6.0 " 4,326
It must not be inferred from this table that there are in the whole sky
only 4,326 stars visible to the naked eye. The actual number is probably
50 or 60 per cent greater than this, and the normal human eye sees stars
as faint as the magnitude 6.4 or 6.5, the discordance between this
number and the previous statement, that the sixth magnitude is the limit
of the naked-eye vision, having been introduced in the attempt to make
precise and accurate a classification into magnitudes which was at first
only rough and approximate. This same striving after accuracy leads to
the introduction of fractional numbers to represent gradations of
brightness intermediate between whole magnitudes. Thus of the 2,843
stars included between the fifth and sixth magnitudes a certain
proportion are said to be of the 5.1 magnitude, 5.2 magnitude, and so on
to the 5.9 magnitude, even hundredths of a magnitude being sometimes
employed.
We have found the number of stars included between the fifth and sixth
magnitudes by subtracting from the last number of the preceding table
the number immediately preceding it, and similarly we may find the
number included between each other pair of consecutive magnitudes, as
follows:
Magnitude 0 1 2 3 4 5 6
Number of stars 11 28 103 321 1,020 2,843
4 × 3^{m} 12 36 108 324 972 2,916
In the last line each number after the first is found by multiplying the
preceding one by 3, and the approximate agreement of each such number
with that printed above it shows that on the whole, as far as the table
goes, the fainter stars are approximately three times as numerous as
those a magnitude brighter.
The magnitudes of the telescopic stars have not yet been measured
completely, and their exact number is unknown; but if we apply our
principle of a threefold increase for each successive magnitude, we
shall find for the fainter stars--those of the tenth and twelfth
magnitudes--prodigious numbers which run up into the millions, and even
these are probably too small, since down to the ninth or tenth magnitude
it is certain that the number of the telescopic stars increases from
magnitude to magnitude in more than a threefold ratio. This is balanced
in some degree by the less rapid increase which is known to exist in
magnitudes still fainter; and applying our formula without regard to
these variations in the rate of increase, we obtain as a rude
approximation to the total number of stars down to the fifteenth
magnitude, 86,000,000. The Herschels, father and son, actually counted
the number of stars visible in nearly 8,000 sample regions of the sky,
and, inferring the character of the whole sky from these samples, we
find it to contain 58,500,000 stars; but the magnitude of the faintest
star visible in their telescope, and included in their count, is rather
uncertain.
How many first-magnitude stars would be needed to give as much light as
do the 2,843 stars of magnitude 5.0 to 6.0? How many tenth-magnitude
stars are required to give the same amount of light?
To the modern man it seems natural to ascribe the different brilliancies
of the stars to their different distances from us; but such was not the
case 2,000 years ago, when each fixed star was commonly thought to be
fastened to a "crystal sphere," which carried them with it, all at the
same distance from us, as it turned about the earth. In breaking away
from this erroneous idea and learning to think of the sky itself as only
an atmospheric illusion through which we look to stars at very different
distances beyond, it was easy to fall into the opposite error and to
think of the stars as being much alike one with another, and, like
pebbles on the beach, scattered throughout space with some rough degree
of uniformity, so that in every direction there should be found in equal
measure stars near at hand and stars far off, each shining with a luster
proportioned to its remoteness.
188. DISTANCES OF THE STARS.--Now, in order to separate the true from
the false in this last mode of thinking about the stars, we need some
knowledge of their real distances from the earth, and in seeking it we
encounter what is perhaps the most delicate and difficult problem in the
whole range of observational astronomy. As shown in Fig. 121, the
principles involved in determining these distances are not fundamentally
different from those employed in determining the moon's distance from
the earth. Thus, the ellipse at the left of the figure represents the
earth's orbit and the position of the earth at different times of the
year. The direction of the star _A_ at these several times is shown by
lines drawn through _A_ and prolonged to the background apparently
furnished by the sky. A similar construction is made for the star _B_,
and it is readily seen that owing to the changing position of the
observer as he moves around the earth's orbit, both _A_ and _B_ will
appear to move upon the background in orbits shaped like that of the
earth as seen from the star, but having their size dependent upon the
star's distance, the apparent orbit of _A_ being larger than that of
_B_, because _A_ is nearer the earth. By measuring the angular distance
between _A_ and _B_ at opposite seasons of the year (e. g., the angles
_A--Jan.--B_, and _A--July--B_) the astronomer determines from the
change in this angle how much larger is the one path than the other, and
thus concludes how much nearer is _A_ than _B_. Strictly, the difference
between the January and July angles is equal to the difference between
the angles subtended at _A_ and _B_ by the diameter of the earth's
orbit, and if _B_ were so far away that the angle _Jan.--B--July_ were
nothing at all we should get immediately from the observations the angle
_Jan.--A--July_, which would suffice to determine the stars' distance.
Supposing the diameter of the earth's orbit and the angle at _A_ to be
known, can you make a graphical construction that will determine the
distance of _A_ from the earth?
[Illustration: FIG. 121.--Determining a star's parallax.]
The angle subtended at _A_ by the radius of the earth's orbit--i. e.,
1/2 (_Jan.--A--July_)--is called the star's parallax, and this is
commonly used by astronomers as a measure of the star's distance instead
of expressing it in linear units such as miles or radii of the earth's
orbit. The distance of a star is equal to the radius of the earth's
orbit divided by the parallax, in seconds of arc, and multiplied by the
number 206265.
A weak point of this method of measuring stellar distances is that it
always gives what is called a relative parallax--i. e., the difference
between the parallaxes of _A_ and _B_; and while it is customary to
select for _B_ a star or stars supposed to be much farther off than _A_,
it may happen, and sometimes does happen, that these comparison stars as
they are called are as near or nearer than _A_, and give a negative
parallax--i. e., the difference between the angles at _A_ and _B_ proves
to be negative, as it must whenever the star _B_ is nearer than _A_.
The first really successful determinations of stellar parallax were made
by Struve and Bessel a little prior to 1840, and since that time the
distances of perhaps 100 stars have been measured with some degree of
reliability, although the parallaxes themselves are so small--never as
great as 1''--that it is extremely difficult to avoid falling into
error, since even for the nearest star the problem of its distance is
equivalent to finding the distance of an object more than 5 miles away
by looking at it first with one eye and then with the other. Too short a
base line.
189. THE SUN AND HIS NEIGHBORS.--The distances of the sun's nearer
neighbors among the stars are shown in Fig. 122, where the two circles
having the sun at their center represent distances from it equal
respectively to 1,000,000 and 2,000,000 times the distance between earth
and sun. In the figure the direction of each star from the sun
corresponds to its right ascension, as shown by the Roman numerals about
the outer circle; the true direction of the star from the sun can not,
of course, be shown upon the flat surface of the paper, but it may be
found by elevating or depressing the star from the surface of the paper
through an angle, as seen from the sun, equal to its declination, as
shown in the fifth column of the following table,
_The Sun's Nearest Neighbors_
---+------------------+----------+-------+-----+----------+---------
No.| STAR. |Magnitude.| R. A. |Dec. | Parallax.|Distance.
---+------------------+----------+-------+-----+----------+---------
1 | [a] Centauri | 0.7 | 14.5h.| -60°| 0.75" | 0.27
| | | | | |
2 | Ll. 21,185 | 6.8 | 11.0 | +37 | 0.45 | 0.46
| | | | | |
3 | 61 Cygni | 5.0 | 21.0 | +38 | 0.40 | 0.51
| | | | | |
4 | [ê] Herculis | 3.6 | 16.7 | +39 | 0.40 | 0.51
| | | | | |
5 | Sirius | -1.4 | 6.7 | -17 | 0.37 | 0.56
| | | | | |
6 | [S] 2,398 | 8.2 | 18.7 | +59 | 0.35 | 0.58
| | | | | |
7 | Procyon | 0.5 | 7.6 | + 5 | 0.34 | 0.60
| | | | | |
8 | [g] Draconis | 4.8 | 17.5 | +55 | 0.30 | 0.68
| | | | | |
9 | Gr. 34 | 7.9 | 0.2 | +43 | 0.29 | 0.71
| | | | | |
10 | Lac. 9,352 | 7.5 | 23.0 | -36 | 0.28 | 0.74
| | | | | |
11 | [s] Draconis | 4.8 | 19.5 | +69 | 0.25 | 0.82
| | | | | |
12 | A. O. 17,415-6 | 9.0 | 17.6 | +68 | 0.25 | 0.82
| | | | | |
13 | [ê] Cassiopeiæ | 3.4 | 0.7 | +57 | 0.25 | 0.82
| | | | | |
14 | Altair | 1.0 | 19.8 | + 9 | 0.21 | 0.97
| | | | | |
15 | [e] Indi | 5.2 | 21.9 | -57 | 0.20 | 1.03
| | | | | |
16 | Gr. 1,618 | 6.7 | 10.1 | +50 | 0.20 | 1.03
| | | | | |
17 | 10 Ursæ Majoris | 4.2 | 8.9 | +42 | 0.20 | 1.03
| | | | | |
18 | Castor | 1.5 | 7.5 | +32 | 0.20 | 1.03
| | | | | |
19 | Ll. 21,258 | 8.5 | 11.0 | +44 | 0.20 | 1.03
| | | | | |
20 | [o]^{2} Eridani | 4.5 | 4.2 | - 8 | 0.19 | 1.08
| | | | | |
21 | A. O. 11,677 | 9.0 | 11.2 | +66 | 0.19 | 1.08
| | | | | |
22 | Ll. 18,115 | 8.0 | 9.1 | +53 | 0.18 | 1.14
| | | | | |
23 | B. D. 36°, 3,883 | 7.1 | 20.0 | +36 | 0.18 | 1.14
| | | | | |
24 | Gr. 1,618 | 6.5 | 10.1 | +50 | 0.17 | 1.21
| | | | | |
25 | [b] Cassiopeiæ | 2.3 | 0.1 | +59 | 0.16 | 1.28
| | | | | |
26 | 70 Ophiuchi | 4.4 | 18.0 | + 2 | 0.16 | 1.28
| | | | | |
27 | [S] 1,516 | 6.5 | 11.2 | +74 | 0.15 | 1.38
| | | | | |
28 | Gr. 1,830 | 6.6 | 11.8 | +39 | 0.15 | 1.38
| | | | | |
29 | [m] Cassiopeiæ | 5.4 | 1.0 | +54 | 0.14 | 1.47
| | | | | |
30 | [e] Eridani | 4.4 | 3.5 | -10 | 0.14 | 1.47
| | | | | |
31 | [i] Ursæ Majoris | 3.2 | 8.9 | +48 | 0.13 | 1.58
| | | | | |
32 | [b] Hydri | 2.9 | 0.3 | -78 | 0.13 | 1.58
| | | | | |
33 | Fomalhaut | 1.0 | 22.9 | -30 | 0.13 | 1.58
| | | | | |
34 | Br. 3,077 | 6.0 | 23.1 | +57 | 0.13 | 1.58
| | | | | |
35 | [e] Cygni | 2.5 | 20.8 | +33 | 0.12 | 1.71
| | | | | |
36 | [b] Comæ | 4.5 | 13.1 | +28 | 0.11 | 1.87
| | | | | |
37 | [ps]^{5} Aurigæ | 8.8 | 6.6 | +44 | 0.11 | 1.87
| | | | | |
38 | [p] Herculis | 3.3 | 17.2 | +37 | 0.11 | 1.87
| | | | | |
39 | Aldebaran | 1.1 | 4.5 | +16 | 0.10 | 2.06
| | | | | |
40 | Capella | 0.1 | 5.1 | +46 | 0.10 | 2.06
| | | | | |
41 | B. D. 35°, 4,003 | 9.2 | 20.1 | +35 | 0.10 | 2.06
| | | | | |
42 | Gr. 1,646 | 6.3 | 10.3 | +49 | 0.10 | 2.06
| | | | | |
43 | [g] Cygni | 2.3 | 20.3 | +40 | 0.10 | 2.06
| | | | | |
44 | Regulus | 1.2 | 10.0 | +12 | 0.10 | 2.06
| | | | | |
45 | Vega | 0.2 | 18.6 | +39 | 0.10 | 2.06
---+------------------+----------+-------+-----+----------+---------
in which the numbers in the first column are those placed adjacent to
the stars in the diagram to identify them.
[Illustration: FIG. 122.--Stellar neighbors of the sun.]
190. LIGHT YEARS.--The radius of the inner circle in Fig. 122, 1,000,000
times the earth's distance from the sun, is a convenient unit in which
to express the stellar distances, and in the preceding table the
distances of the stars from the sun are expressed in terms of this
unit. To express them in miles the numbers in the table must be
multiplied by 93,000,000,000,000. The nearest star, [a] Centauri, is
25,000,000,000,000 miles away. But there is another unit in more common
use--i. e., the distance traveled over by light in the period of one
year. We have already found (§ 141) that it requires light 8m. 18s. to
come from the sun to the earth, and it is a simple matter to find from
this datum that in a year light moves over a space equal to 63,368 radii
of the earth's orbit. This distance is called a _light year_, and the
distance of the same star, [a] Centauri, expressed in terms of this
unit, is 4.26 years--i. e., it takes light that long to come from the
star to the earth.
In Fig. 122 the stellar magnitudes of the stars are indicated by the
size of the dots--the bigger the dot the brighter the star--and a mere
inspection of the figure will serve to show that within a radius of 30
light years from the sun bright stars and faint ones are mixed up
together, and that, so far as distance is concerned, the sun is only a
member of this swarm of stars, whose distances apart, each from its
nearest neighbor, are of the same order of magnitude as those which
separate the sun from the three or four stars nearest it.
Fig. 122 is not to be supposed complete. Doubtless other stars will be
found whose distance from the sun is less than 2,000,000 radii of the
earth's orbit, but it is not probable that they will ever suffice to
more than double or perhaps treble the number here shown. The vast
majority of the stars lie far beyond the limits of the figure.
191. PROPER MOTIONS.--It is evident that these stars are too far apart
for their mutual attractions to have much influence one upon another,
and that we have here a case in which, according to § 34, each star is
free to keep unchanged its state of rest or motion with unvarying
velocity along a straight line. Their very name, _fixed stars_, implies
that they are at rest, and so astronomers long believed. Hipparchus (125
B. C.) and Ptolemy (130 A. D.) observed and recorded many allineations
among the stars, in order to give to future generations a means of
settling this very question of a possible motion of the stars and a
resulting change in their relative positions upon the sky. For example,
they found at the beginning of the Christian era that the four stars,
Capella, [e] Persei, [a] and [b] Arietis, stood in a straight
line--i. e., upon a great circle of the sky. Verify this by direct
reference to the sky, and see how nearly these stars have kept the same
position for nearly twenty centuries. Three of them may be identified
from the star maps, and the fourth, [e] Persei, is a third-magnitude
star between Capella and the other two.
Other allineations given by Ptolemy are: Spica, Arcturus and [b] Bootis;
Spica, [d] Corvi and [g] Corvi; [a] Libræ, Arcturus and [z] Ursæ
Majoris. Arcturus does not now fit very well to these alignments, and
nearly two centuries ago it, together with Aldebaran and Sirius, was on
other grounds suspected to have changed its place in the sky since the
days of Ptolemy. This discovery, long since fully confirmed, gave a
great impetus to observing with all possible accuracy the right
ascensions and declinations of the stars, with a view to finding other
cases of what was called _proper motion_--i. e., a motion peculiar to
the individual star as contrasted with the change of right ascension and
declination produced for all stars by the precession.
Since the middle of the eighteenth century there have been made many
thousands of observations of this kind, whose results have gone into
star charts and star catalogues, and which are now being supplemented by
a photographic survey of the sky that is intended to record permanently
upon photographic plates the position and magnitude of every star in the
heavens down to the fourteenth magnitude, with a view to ultimately
determining all their proper motions.
The complete achievement of this result is, of course, a thing of the
remote future, but sufficient progress in determining these motions has
been made during the past century and a half to show that nearly every
lucid star possesses some proper motion, although in most cases it is
very small, there being less than 100 known stars in which it amounts
to so much as 1" per annum--i. e., a rate of motion across the sky which
would require nearly the whole Christian era to alter a star's direction
from us by so much as the moon's angular diameter. The most rapid known
proper motion is that of a telescopic star midway between the equator
and the south pole, which changes its position at the rate of nearly 9"
per annum, and the next greatest is that of another telescopic star, in
the northern sky, No. 28 of Fig. 122. It is not until we reach the tenth
place in a list of large proper motions that we find a bright lucid
star, No. 1 of Fig. 122. It is a significant fact that for the most part
the stars with large proper motions are precisely the ones shown in Fig.
122, which is designed to show stars near the earth. This connection
between nearness and rapidity of proper motions is indeed what we should
expect to find, since a given amount of real motion of the star along
its orbit will produce a larger angular displacement, proper motion, the
nearer the star is to the earth, and this fact has guided astronomers in
selecting the stars to be observed for parallax, the proper motion being
determined first and the parallax afterward.
192. THE PATHS OF THE STARS.--We have already seen reason for thinking
that the orbit along which a star moves is practically a straight line,
and from a study of proper motions, particularly their directions across
the sky, it appears that these orbits point in all possible ways--north,
south, east, and west--so that some of them are doubtless directed
nearly toward or from the sun; others are square to the line joining sun
and star; while the vast majority occupy some position intermediate
between these two. Now, our relation to these real motions of the stars
is well illustrated in Fig. 112, where the observer finds in some of the
shooting stars a tremendous proper motion across the sky, but sees
nothing of their rapid approach to him, while others appear to stand
motionless, although, in fact, they are moving quite as rapidly as are
their fellows. The fixed star resembles the shooting star in this
respect, that its proper motion is only that part of its real motion
which lies at right angles to the line of sight, and this needs to be
supplemented by that other part of the motion which lies parallel to the
line of sight, in order to give us any knowledge of the star's real
orbit.
[Illustration: FIG. 123.--Motion of Polaris in the line of sight as
determined by the spectroscope. FROST.]
193. MOTION IN THE LINE OF SIGHT.--It is only within the last 25 years
that anything whatever has been accomplished in determining these
stellar motions of approach or recession, but within that time much
progress has been made by applying the Doppler principle (§ 89) to the
study of stellar spectra, and at the present time nearly every great
telescope in the world is engaged upon work of this kind. The shifting
of the lines of the spectrum toward the violet or toward the red end of
the spectrum indicates with certainty the approach or recession of the
star, but this shifting, which must be determined by comparing the
star's spectrum with that of some artificial light showing corresponding
lines, is so small in amount that its accurate measurement is a matter
of extreme difficulty, as may be seen from Fig. 123. This cut shows
along its central line a part of the spectrum of Polaris, between wave
lengths 4,450 and 4,600 tenth meters, while above and below are the
corresponding parts of the spectrum of an electric spark whose light
passed through the same spectroscope and was photographed upon the same
plate with that of Polaris. This comparison spectrum is, as it should
be, a discontinuous or bright-line one, while the spectrum of the star
is a continuous one, broken only by dark gaps or lines, many of which
have no corresponding lines in the comparison spectrum. But a certain
number of lines in the two spectra do correspond, save that the dark
line is always pushed a very little toward the direction of shorter wave
lengths, showing that this star is approaching the earth. This spectrum
was photographed for the express purpose of determining the star's
motion in the line of sight, and with it there should be compared Figs.
124 and 125, which show in the upper part of each a photograph obtained
without comparison spectra by allowing the star's light to pass through
some prisms placed just in front of the telescope. The lower section of
each figure shows an enlargement of the original photograph, bringing
out its details in a way not visible to the unaided eye. In the enlarged
spectrum of [b] Aurigæ a rate of motion equal to that of the earth in
its orbit would be represented by a shifting of 0.03 of a millimeter in
the position of the broad, hazy lines.
[Illustration: FIG. 124.--Spectrum of [b] Aurigæ.--PICKERING.]
Despite the difficulty of dealing with such small quantities as the
above, very satisfactory results are now obtained, and from them it is
known that the velocities of stars in the line of sight are of the same
order of magnitude as the velocities of the planets in their orbits,
ranging all the way from 0 to 60 miles per second--more than 200,000
miles per hour--which latter velocity, according to Campbell, is the
rate at which [m] Cassiopeiæ is approaching the sun.
The student should not fail to note one important difference between
proper motions and the motions determined spectroscopically: the latter
are given directly in miles per second, or per hour, while the former
are expressed in angular measure, seconds of arc, and there can be no
direct comparison between the two until by means of the known distances
of the stars their proper motions are converted from angular into linear
measure. We are brought thus to the very heart of the matter; parallax,
proper motion, and motion in the line of sight are intimately related
quantities, all of which are essential to a knowledge of the real
motions of the stars.
[Illustration: FIG. 125.--Spectrum of Pollux.--PICKERING.]
194. STAR DRIFT.--An illustration of how they may be made to work
together is furnished by some of the stars--which make up the Great
Dipper--[b], [g], [e], and [z] Ursæ Majoris, whose proper motions have
long been known to point in nearly the same direction across the sky and
to be nearly equal in amount. More recently it has been found that these
stars are all moving toward the sun with approximately the same
velocity--18 miles per second. One other star of the Dipper, [d] Ursæ
Majoris, shares in the common proper motion, but its velocity in the
line of sight has not yet been determined with the spectroscope. These
similar motions make it probable that the stars are really traveling
together through space along parallel lines; and on the supposition
that such is the case it is quite possible to write out a set of
equations which shall involve their known proper motions and motions in
the line of sight, together with their unknown distances and the unknown
direction and velocity of their real motion along their orbits. Solving
these equations for the values of the unknown quantities, it is found
that the five stars probably lie in a plane which is turned nearly
edgewise toward us, and that in this plane they are moving about twice
as fast as the earth moves around the sun, and are at a distance from us
represented by a parallax of less than 0.02"--i. e., six times as great
as the outermost circle in Fig. 122. A most extraordinary system of
stars which, although separated from each other by distances as great as
the whole breadth of Fig. 122, yet move along in parallel paths which it
is difficult to regard as the result of chance, and for which it is
equally difficult to frame an explanation.
[Illustration: FIG. 126.--The Great Dipper, past, present, and future.]
The stars [a] and [ê] of the Great Dipper do not share in this motion,
and must ultimately part company with the other five, to the complete
destruction of the Dipper's shape. Fig. 126 illustrates this change of
shape, the upper part of the figure (_a_) showing these seven stars as
they were grouped at a remote epoch in the past, while the lower
section (_c_) shows their position for an equally remote epoch in
the future. There is no resemblance to a dipper in either of these
configurations, but it should be observed that in each of them the stars
[a] and [ê] keep their relative position unaltered, and the other five
stars also keep together, the entire change of appearance being due to
the changing positions of these two groups with respect to each other.
This phenomenon of groups of stars moving together is called _star
drift_, and quite a number of cases of it are found in different parts
of the sky. The Pleiades are perhaps the most conspicuous one, for here
some sixty or more stars are found traveling together along similar
paths. Repeated careful measurements of the relative positions of stars
in this cluster show that one of the lucid stars and four or five of the
telescopic ones do not share in this motion, and therefore are not to be
considered as members of the group, but rather as isolated stars which,
for a time, chance to be nearly on line with the Pleiades, and probably
farther off, since their proper motions are smaller.
To rightly appreciate the extreme slowness with which proper motions
alter the constellations, the student should bear in mind that the
changes shown in passing from one section of Fig. 126 to the next
represent the effect of the present proper motions of the stars
accumulated for a period of 200,000 years. Will the stars continue to
move in straight paths for so long a time?
195. THE SUN'S WAY.--Another and even more interesting application of
proper motions and motions in the line of sight is the determination
from them of the sun's orbit among the stars. The principle involved is
simple enough. If the sun moves with respect to the stars and carries
the earth and the other planets year after year into new regions of
space, our changing point of view must displace in some measure every
star in the sky save those which happen to be exactly on the line of the
sun's motion, and even these will show its effect by their apparent
motion of approach or recession along the line of sight. So far as their
own orbital motions are concerned, there is no reason to suppose that
more stars move north than south, or that more go east than west; and
when we find in their proper motions a distinct tendency to radiate from
a point somewhere near the bright star Vega and to converge toward a
point on the opposite side of the sky, we infer that this does not come
from any general drift of the stars in that direction, but that it marks
the course of the sun among them. That it is moving along a straight
line pointing toward Vega, and that at least a part of the velocities
which the spectroscope shows in the line of sight, comes from the motion
of the sun and earth. Working along these lines, Kapteyn finds that the
sun is moving through space with a velocity of 11 miles per second,
which is decidedly below the average rate of stellar motion--19 miles
per second.
196. DISTANCE OF SIRIAN AND SOLAR STARS.--By combining this rate of
motion of the sun with the average proper motions of the stars of
different magnitudes, it is possible to obtain some idea of the average
distance from us of a first-magnitude star or a sixth-magnitude star,
which, while it gives no information about the actual distance of any
particular star, does show that on the whole the fainter stars are more
remote. But here a broad distinction must be drawn. By far the larger
part of the stars belong to one of two well-marked classes, called
respectively Sirian and solar stars, which are readily distinguished
from each other by the kind of spectrum they furnish. Thus [b] Aurigæ
belongs to the Sirian class, as does every other star which has a
spectrum like that of Fig. 124, while Pollux is a solar star presenting
in Fig. 125 a spectrum like that of the sun, as do the other stars of
this class.
Two thirds of the sun's near neighbors, shown in Fig. 122, have spectra
of the solar type, and in general stars of this class are nearer to us
than are the stars with spectra unlike that of the sun. The average
distance of a solar star of the first magnitude is very approximately
represented by the outer circle in Fig. 122, 2,000,000 times the
distance of the sun from the earth; while the corresponding distance for
a Sirian star of the first magnitude is represented by the number
4,600,000.
A third-magnitude star is on the average twice as far away as one of the
first magnitude, a fifth-magnitude star four times as far off, etc.,
each additional two magnitudes doubling the average distance of the
stars, at least down to the eighth magnitude and possibly farther,
although beyond this limit we have no certain knowledge. Put in another
way, the naked eye sees many Sirian stars which _may_ have "gone out"
and ceased to shine centuries ago, for the light by which we now see
them left those stars before the discovery of America by Columbus. For
the student of mathematical tastes we note that the results of Kapteyn's
investigation of the mean distances (_D_) of the stars of magnitude
(_m_) may be put into two equations:
For Solar Stars, D = 23 × 2^{m/2}
For Sirian Stars, D = 52 × 2^{m/2}
where the coefficients 23 and 52 are expressed in light years. How long
a time is required for light to come from an average solar star of the
sixth magnitude?
197. CONSEQUENCES OF STELLAR DISTANCE.--The amount of light which comes
to us from any luminous body varies inversely as the square of its
distance, and since many of the stars are changing their distance from
us quite rapidly, it must be that with the lapse of time they will grow
brighter or fainter by reason of this altered distance. But the
distances themselves are so great that the most rapid known motion in
the line of sight would require more than 1,000 years (probably several
thousand) to produce any perceptible change in brilliancy.
The law in accordance with which this change of brilliancy takes place
is that the distance must be increased or diminished tenfold in order to
produce a change of five magnitudes in the brightness of the object, and
we may apply this law to determine the sun's rank among the stars. If it
were removed to the distance of an average first-, or second-, or
third-magnitude star, how would its light compare with that of the
stars? The average distance of a third-magnitude star of the solar type
is, as we have seen above, 4,000,000 times the sun's distance from the
earth, and since 4,000,000 = 10^{6.6}, we find that at this distance the
sun's stellar magnitude would be altered by 6.6 × 5 magnitudes, and
would therefore be -26.5 + 33.0 = 6.5--i. e., the sun if removed to the
average distance of the third-magnitude stars of its type would be
reduced to the very limit of naked-eye visibility. It must therefore be
relatively small and feeble as compared with the brightness of the
average star. It is only its close proximity to us that makes the sun
look brighter than the stars.
The fixed stars may have planets circling around them, but an
application of the same principles will show how hopeless is the
prospect of ever seeing them in a telescope. If the sun's nearest
neighbor, [a] Centauri, were attended by a planet like Jupiter, this
planet would furnish to us no more light than does a star of the
twenty-second magnitude--i. e., it would be absolutely invisible, and
would remain invisible in the most powerful telescope yet built, even
though its bulk were increased to equal that of the sun. Let the student
make the computation leading to this result, assuming the stellar
magnitude of Jupiter to be -1.7.
198. DOUBLE STARS.--In the constellation Taurus, not far from Aldebaran,
is the fourth-magnitude star [th] Tauri, which can readily be seen to
consist of two stars close together. The star [a] Capricorni is plainly
double, and a sharp eye can detect that one of the faint stars which
with Vega make a small equilateral triangle, is also a double star.
Look for them in the sky.
In the strict language of astronomy the term double star would not be
applied to the first two of these objects, since it is usually
restricted to those stars whose angular distance from each other is so
small that in the telescope they appear much as do the stars named above
to the naked eye--i. e., their angular separation is measured by a few
seconds or fractions of a single second, instead of the six minutes
which separate the component stars of [th] Tauri or [a] Capricorni.
There are found in the sky many thousands of these close double stars,
of which some are only optically double--i. e., two stars nearly on line
with the earth but at very different distances from it--while more of
them are really what they seem, stars near each other, and in many cases
near enough to influence each other's motion. These are called _binary_
systems, and in cases of this kind the principles of celestial mechanics
set forth in Chapter IV hold true, and we may expect to find each
component of a double star moving in a conic section of some kind,
having its focus at the common center of gravity of the two stars.
We are thus presented with problems of orbital motion quite similar
to those which occur in the solar system, and careful telescopic
observations are required year after year to fix the relative positions
of the two stars--i. e., their angular separation, which it is customary
to call their _distance_, and their direction one from the other, which
is called _position angle_.
199. ORBITS OF DOUBLE STARS.--The sun's nearest neighbor, [a] Centauri,
is such a double star, whose position angle and distance have been
measured by successive generations of astronomers for more than a
century, and Fig. 127 shows the result of plotting their observations.
Each black dot that lies on or near the circumference of the long
ellipse stands for an observed direction and distance of the fainter of
the two stars from the brighter one, which is represented by the small
circle at the intersection of the lines inside the ellipse. It appears
from the figure that during this time the one star has gone completely
around the other, as a planet goes around the sun, and the true orbit
must therefore be an ellipse having one of its foci at the center
of gravity of the two stars. The other star moves in an ellipse of
precisely similar shape, but probably smaller size, since the dimensions
of the two orbits are inversely proportional to the masses of the two
bodies, but it is customary to neglect this motion of the larger star
and to give to the smaller one an orbit whose diameter is equal to the
sum of the diameters of the two real orbits. This practice, which has
been followed in Fig. 127, gives correctly the relative positions of the
two stars, and makes one orbit do the work of two.
[Illustration: FIG. 127.--The orbit of [a] Centauri.--SEE.]
In Fig. 127 the bright star does not fall anywhere near the focus of the
ellipse marked out by the smaller one, and from this we infer that the
figure does not show the true shape of the orbit, which is certainly
distorted, foreshortened, by the fact that we look obliquely down upon
its plane. It is possible, however, by mathematical analysis, to find
just how much and in what direction that plane should be turned in order
to bring the focus of the ellipse up to the position of the principal
star, and thus give the true shape and size of the orbit. See Fig. 128
for a case in which the true orbit is turned exactly edgewise toward the
earth, and the small star, which really moves in an ellipse like that
shown in the figure, appears to oscillate to and fro along a straight
line drawn through the principal star, as shown at the left of the
figure.
In the case of [a] Centauri the true orbit proves to have a major
axis 47 times, and a minor axis 40 times, as great as the distance of
the earth from the sun. The orbit, in fact, is intermediate in size
between the orbits of Uranus and Neptune, and the periodic time of the
star in this orbit is 81 years, a little less than the period of Uranus.
[Illustration: FIG. 128.--Apparent orbit and real orbit of the double
star 42 Comæ Berenicis.--SEE.]
200. MASSES OF DOUBLE STARS.--If we apply to this orbit Kepler's Third
Law in the form given it at page 179, we shall find--
a^3 / T^2 = (23.5)^3 / (81)^2 = k (M + m),
where _M_ and _m_ represent the masses of the two stars. We have already
seen that _k_, the gravitation constant, is equal to 1 when the masses
are measured in terms of the sun's mass taken as unity, and when _T_ and
_a_ are expressed in years and radii of the earth's orbit respectively,
and with this value of _k_ we may readily find from the above equation,
_M_ + _m_ = 2.5--i. e., the combined mass of the two components of
[a] Centauri is equal to rather more than twice the mass of the
sun. It is not every double star to which this process of weighing can
be applied. The major axis of the orbit, _a_, is found from the
observations in angular measure, 35" in this case, and it is only when
the parallax of the star is known that this can be converted into the
required linear units, radii of the earth's orbit, by dividing the
angular major axis by the parallax; 47 = 35" ÷ 0.75".
Our list of distances (§ 189) contains four double stars whose periodic
times and major axes have been fairly well determined, and we find in
the accompanying table the information which they give about the masses
of double stars and the size of the orbits in which they move:
---------------------+-------+-------+----------+-------
STAR. | Major | Minor | Periodic | Mass.
| axis. | axis. | time. |
---------------------+-------+-------+----------+-------
[a] Centauri | 47 | 40 | 81 y. | 2
70 Ophiuchi | 56 | 48 | 88 | 3
Procyon | 34 | 31 | 40 | 3
Sirius | 43 | 34 | 52 | 4
---------------------+-------+-------+----------+-------
The orbit of Uranus, diameter = 38, and Neptune, diameter = 60, are of
much the same size as these double-star orbits; but the planetary orbits
are nearly circular, while in every case the double stars show a
substantial difference between the long and short diameters of their
orbits. This is a characteristic feature of most double-star orbits, and
seems to stand in some relation to their periodic times, for, on the
average, the longer the time required by a star to make its orbital
revolution the more eccentric is its orbit likely to prove.
Another element of the orbits of double stars, which stands in even
closer relation to the periodic time, is the major axis; the smaller the
long diameter of the orbit the more rapid is the motion and the shorter
the periodic time, so that astronomers in search of interesting
double-star orbits devote themselves by preference to those stars whose
distance apart is so small that they can barely be distinguished one
from the other in the telescope.
Although the half-dozen stars contained in the table all have orbits of
much the same size and with much the same periodic time as those in
which Uranus and Neptune move, this is by no means true of all the
double stars, many of which have periods running up into the hundreds if
not thousands of years, while a few complete their orbital revolutions
in periods comparable with, or even shorter than, that of Jupiter.
201. DARK STARS.--Procyon, the next to the last star of the preceding
table, calls for some special mention, as the determination of its mass
and orbit stands upon a rather different basis from that of the other
stars. More than half a century ago it was discovered that its proper
motion was not straight and uniform after the fashion of ordinary stars,
but presented a series of loops like those marked out by a bright point
on the rim of a swiftly running bicycle wheel. The hub may move straight
forward with uniform velocity, but the point near the tire goes up and
down, and, while sharing in the forward motion of the hub, runs
sometimes ahead of it, sometimes behind, and such seemed to be the
motion of Procyon and of Sirius as well. Bessel, who discovered it, did
not hesitate to apply the laws of motion, and to affirm that this
visible change of the star's motion pointed to the presence of an unseen
companion, which produced upon the motions of Sirius and Procyon just
such effects as the visible companions produce in the motions of double
stars. A new kind of star, dark instead of bright, was added to the
astronomer's domain, and its discoverer boldly suggested the possible
existence of many more. "That countless stars are visible is clearly no
argument against the existence of as many more invisible ones." "There
is no reason to think radiance a necessary property of celestial
bodies." But most astronomers were incredulous, and it was not until
1862 that, in the testing of a new and powerful telescope just built, a
dark star was brought to light and the companion of Sirius actually
seen. The visual discovery of the dark companion of Procyon is of still
more recent date (November, 1896), when it was detected with the great
telescope of the Lick Observatory. This discovery is so recent that the
orbit is still very uncertain, being based almost wholly upon the
variations in the proper motion of the star, and while the periodic time
must be very nearly correct, the mass of the stars and dimensions of the
orbit may require considerable correction.
The companion of Sirius is about ten magnitudes and that of Procyon
about twelve magnitudes fainter than the star itself. How much more
light does the bright star give than its faint companion? Despite the
tremendous difference of brightness represented by the answer to this
question, the mass of Sirius is only about twice as great as that of its
companion, and for Procyon the ratio does not exceed five or six.
The visual discovery of the companions to Sirius and Procyon removes
them from the list of dark stars, but others still remain unseen,
although their existence is indicated by variable proper motions or by
variable orbital motion, as in the case of [z] Cancri, where one
of the components of a triple star moves around the other two in a
series of loops whose presence indicates a disturbing body which has
never yet been seen.
202. MULTIPLE STARS.--Combinations of three, four, or more stars close
to each other, like [z] Cancri, are called multiple stars, and
while they are far from being as common as are double stars, there is a
considerable number of them in the sky, 100 or more as against the more
than 10,000 double stars that are known. That their relative motions are
subject to the law of gravitation admits of no serious doubt, but
mathematical analysis breaks down in face of the difficulties here
presented, and no astronomer has ever been able to determine what will
be the general character of the motions in such a system.
[Illustration: FIG. 129.--Illustrating the motion of a spectroscopic
binary.]
203. SPECTROSCOPIC BINARIES.--In the year 1890 Professor Pickering, of
the Harvard Observatory, announced the discovery of a new class of
double stars, invisible as such in even the most powerful telescope,
and producing no perturbations such as have been considered above, but
showing in their spectrum that two or more bodies must be present in the
source of light which to the eye is indistinguishable from a single
star. In Fig. 129 we suppose _A_ and _B_ to be the two components of a
double star, each moving in its own orbit about their common center of
gravity, _C_, whose distance from the earth is several million times
greater than the distance between the stars themselves. Under such
circumstances no telescope could distinguish between the two stars,
which would appear fused into one; but the smaller the orbit the more
rapid would be their motion in it, and if this orbit were turned
edgewise toward the earth, as is supposed in the figure, whenever the
stars were in the relative position there shown, _A_ would be rapidly
approaching the earth by reason of its orbital motion, while _B_ would
move away from it, so that in accordance with the Doppler principle the
lines composing their respective spectra would be shifted in opposite
directions, thus producing a doubling of the lines, each single line
breaking up into two, like the double-sodium line _D_, only not spaced
so far apart. When the stars have moved a quarter way round their orbit
to the points _A´_, _B´_, their velocities are turned at right angles to
the line of sight and the spectrum returns to the normal type with
single lines, only to break up again when after another quarter
revolution their velocities are again parallel with the line of sight.
The interval of time between consecutive doublings of the lines in the
spectrum thus furnishes half the time of a revolution in the orbit. The
distance between the components of a double line shows by means of the
Doppler principle how fast the stars are traveling, and this in
connection with the periodic times fixes the size of the orbit, provided
we assume that it is turned exactly edgewise to the earth. This
assumption may not be quite true, but even though the orbit should
deviate considerably from this position, it will still present the
phenomenon of the double lines whose displacement will now show
something less than the true velocities of the stars in their orbits,
since the spectroscope measures only that component of the whole
velocity which is directed toward the earth, and it is important to note
that the real orbits and masses of these _spectroscopic binaries_, as
they are called, will usually be somewhat larger than those indicated by
the spectroscope, since it is only in exceptional cases that the orbit
will be turned exactly edgewise to us.
The bright star Capella is an excellent illustration of these
spectroscopic binaries. At intervals of a little less than a month the
lines of its spectrum are alternately single and double, their maximum
separation corresponding to a velocity in the line of sight amounting to
37 miles per second. Each component of a doubled line appears to be
shifted an equal amount from the position occupied by the line when it
is single, thus indicating equal velocities and equal masses for the two
component stars whose periodic time in their orbit is 104 days. From
this periodic time, together with the velocity of the star's motion, let
the student show that the diameter of the orbit--i. e., the distance of
the stars from each other--is approximately 53,000,000 miles, and that
their combined mass is a little less than that of [a] Centauri, provided
that their orbit plane is turned exactly edgewise toward the earth.
There are at the present time (1901) 34 spectroscopic binaries known,
including among them such stars as Polaris, Capella, Algol, Spica, [b]
Aurigæ, [z] Ursæ Majoris, etc., and their number is rapidly increasing,
about one star out of every seven whose motion in the line of sight is
determined proving to be a binary or, as in the case of Polaris,
possibly triple. On account of smaller distance apart their periodic
times are much shorter than those of the ordinary double stars, and
range from a few days up to several months--more than two years in the
case of [ê] Pegasi, which has the longest known period of any star of
this class.
Spectroscopic binaries agree with ordinary double stars in having masses
rather greater than that of the sun, but there is as yet no assured case
of a mass ten times as great as that of the sun.
204. VARIABLE STARS.--Attention has already been drawn (§ 23) to the
fact that some stars shine with a changing brightness--e. g., Algol, the
most famous of these _variable stars_, at its maximum of brightness
furnishes three times as much light as when at its minimum, and other
variable stars show an even greater range. The star [o] Ceti has
been named Mira (Latin, _the wonderful_), from its extraordinary range
of brightness, more than six-hundred-fold. For the greater part of the
time this star is invisible to the naked eye, but during some three
months in every year it brightens up sufficiently to be seen, rising
quite rapidly to its maximum brilliancy, which is sometimes that of a
second-magnitude star, but more frequently only third or even fourth
magnitude, and, after shining for a few weeks with nearly maximum
brilliancy, falling off to become invisible for a time and then return
to its maximum brightness after an interval of eleven months from the
preceding maximum. In 1901 it should reach its greatest brilliancy about
midsummer, and a month earlier than this for each succeeding year. Find
it by means of the star map, and by comparing its brightness from night
to night with neighboring stars of about the same magnitude see how it
changes with respect to them.
The interval of time from maximum to maximum of brightness--331.6 days
for Mira--is called the star's period, and within its period a star
regularly variable runs through all its changes of brilliancy, much as
the weather runs through its cycle of changes in the period of a year.
But, as there are wet years and dry ones, hot years and cold, so also
with variable stars, many of them show differences more or less
pronounced between different periods, and one such difference has
already been noted in the case of Mira; its maximum brilliancy is
different in different years. So, too, the length of the period
fluctuates in many cases, as does every other circumstance connected
with it, and predictions of what such a variable star will do are
notoriously unreliable.
205. THE ALGOL VARIABLES.--On the other hand, some variable stars
present an almost perfect regularity, repeating their changes time after
time with a precision like that of clockwork. Algol is one type of these
regular variables, having a period of 68.8154 hours, during six sevenths
of which time it shines with unchanging luster as a star of the 2.3
magnitude, but during the remaining 9 hours of each period it runs down
to the 3.5 magnitude, and comes back again, as is shown by a curve in
Fig. 130. The horizontal scale here represents hours, reckoned from the
time of the star's minimum brightness, and the vertical scale shows
stellar magnitudes. Such a diagram is called the star's light curve, and
we may read from it that at any time between 5h. and 32h. after the time
of minimum the star's magnitude is 2.32; at 2h. after a minimum the
magnitude is 2.88, etc. What is the magnitude an hour and a half before
the time of minimum? What is the magnitude 43 days after a minimum?
[Illustration: FIG. 130.--The light curve of Algol.]
The arrows shown in Fig. 130 are a feature not usually found with light
curves, but in this case each one represents a spectroscopic
determination of the motion of Algol in the line of sight. These
observations extended over a period of more than two years, but they are
plotted in the figure with reference to the number of hours each one
preceded or followed a minimum of the star's light, and each arrow shows
not only the direction of the star's motion along the line of sight, the
arrows pointing down denoting approach of the star toward the earth, but
also its velocity, each square of the ruling corresponding to 10
kilometers (6.2 miles per second). The differences of velocity shown by
adjacent arrows come mainly from errors of observation and furnish some
idea of how consistent among themselves such observations are, but there
can be no doubt that before minimum the star is moving away from the
earth, and after minimum is approaching it. It is evident from these
observations that in Algol we have to do with a spectroscopic binary,
one of whose components is a dark star which, once in each revolution,
partially eclipses the bright star and produces thus the variations in
its light. By combining the spectroscopic observations with the
variations in the star's light, Vogel finds that the bright star, Algol,
itself has a diameter somewhat greater than that of the sun, but is of
low density, so that its mass is less than half that of the sun, while
the dark star is a very little smaller than the sun and has about a
quarter of its mass. The distance between the two stars, dark and
bright, is 3,200,000 miles. Fig. 129, which is drawn to scale, shows the
relative positions and sizes of these stars as well as the orbits in
which they move.
The mere fact already noted that close binary systems exist in
considerable numbers is sufficient to make it probable that a certain
proportion of these stars would have their orbit planes turned so nearly
edgewise toward the earth as to produce eclipses, and corresponding to
this probability there are already known no less than 15 stars of the
Algol type of eclipse variables, and only a beginning has been made in
the search for them.
[Illustration: FIG. 131.--The light curve of [b] Lyræ.]
206. VARIABLES OF THE [b] LYRÆ TYPE.--In addition to these there is a
certain further number of binary variables in which both components are
bright and where the variation of brightness follows a very different
course. Capella would be such a variable if its orbit plane were
directed exactly toward the earth, and the fact that its light is not
variable shows conclusively that such is not the position of the orbit.
Fig. 131 represents the light curve of one of the best-known variable
systems of this second type, that of [b] Lyræ, whose period is 12 days
21.8 hours, and the student should read from the curve the magnitude of
the star for different times during this interval. According to Myers,
this light curve and the spectroscopic observations of the star point to
the existence of a binary star of very remarkable character, such as is
shown, together with its orbit and a scale of miles, in Fig. 132. Note
the tide which each of these stars raises in the other, thus changing
their shapes from spheres into ellipsoids. The astonishing dimensions of
these stars are in part compensated by their very low density, which is
less than that of air, so that their masses are respectively only 10
times and 21 times that of the sun! But these dimensions and masses
perhaps require confirmation, since they depend upon spectroscopic
observations of doubtful interpretation. In Fig. 132 what relative
positions must the stars occupy in their orbit in order that their
combined light should give [b] Lyræ its maximum brightness? What
position will furnish a minimum brightness?
[Illustration: FIG. 132.--The system of [b] Lyræ.--MYERS.]
207. VARIABLES OF LONG AND SHORT PERIODS.--It must not be supposed that
all variable stars are binaries which eclipse each other. By far the
larger part of them, like Mira, are not to be accounted for in this way,
and a distinction which is pretty well marked in the length of their
periods is significant in this connection. There is a considerable
number of variable stars with periods shorter than a month, and there
are many having periods longer than 6 months, but there are very few
having periods longer than 18 months, or intermediate between 1 month
and 6 months, so that it is quite customary to divide variable stars
into two classes--those of long period, 6 months or more, and those of
short period less than 6 months, and that this distinction corresponds
to some real difference in the stars themselves is further marked by the
fact that the long-period variables are prevailingly red in color, while
the short-period stars are almost without exception white or very pale
yellow. In fact, the longer the period the redder the star, although it
is not to be inferred that all red stars are variable; a considerable
percentage of them shine with constant light. The eclipse explanation of
variability holds good only for short-period variables, and possibly not
for all of them, while for the long-period variables there is no
explanation which commands the general assent of astronomers, although
unverified hypotheses are plenty.
The number of stars known to be variable is about 400, while a
considerable number of others are "suspected," and it would not be
surprising if a large fraction of all the stars should be found to
fluctuate a little in brightness. The sun's spots may suffice to make it
a variable star with a period of 11 years.
The discovery of new variables is of frequent occurrence, and may be
expected to become more frequent when the sky is systematically explored
for them by the ingenious device suggested by Pickering and illustrated
in Fig. 133. A given region of the sky--e. g., the Northern Crown--is
photographed repeatedly upon the same plate, which is shifted a little
at each new exposure, so that the stars shall fall at new places upon
it. The finally developed plate shows a row of images corresponding to
each star, and if the star's light is constant the images in any given
row will all be of the same size, as are most of those in Fig. 133; but
a variable star such as is shown by the arrowhead reveals its presence
by the broken aspect of its row of dots, a minimum brilliancy being
shown by smaller and a maximum by larger ones. In this particular case,
at two exposures the star was too faint to print its image upon the
plate.
[Illustration: FIG. 133.--Discovery of a variable star by means of
photography.--PICKERING.]
208. NEW STARS.--Next to the variable stars of very long or very
irregular period stand the so-called _new_ or _temporary stars_, which
appear for the most part suddenly, and after a brief time either vanish
altogether or sink to comparative insignificance. These were formerly
thought to be very remarkable and unusual occurrences--"the birth of a
new world"--and it is noteworthy that no new star is recorded to have
been seen from 1670 to 1848 A. D., for since that time there have been
no less than five of them visible to the naked eye and others
telescopic. In so far as these new stars are not ordinary variables
(Mira, first seen in 1596, was long counted as a new star), they are
commonly supposed due to chance encounters between stars or other cosmic
bodies moving with considerable velocities along orbits which approach
very close to each other. The actual collision of two dark bodies moving
with high velocities is clearly sufficient to produce a luminous
star--e. g., meteors--and even the close approach of two cooled-off
stars, might result in tidal actions which would rend open their crusts
and pour out the glowing matter from within so as to produce temporarily
a very great accession of brightness.
The most famous of all new stars is that which, according to Tycho
Brahe's report, appeared in the year 1572, and was so bright when at its
best as to be seen with the naked eye in broad daylight. It continued
visible, though with fading light, for about 16 months, and finally
disappeared to the naked eye, although there is some reason to suppose
that it can be identified with a ruddy star of the eleventh magnitude in
the constellation Cassiopeia, whose light still shows traces of
variability.
No modern temporary star approaches that of Tycho in splendor, but in
some respects the recent ones surpass it in interest, since it has been
possible to apply the spectroscope to the analysis of their light and to
find thereby a much more complex set of conditions in the star than
would have been suspected from its light changes alone.
One of the most extraordinary of new stars, and the most brilliant one
since that of Tycho, appeared suddenly in the constellation Perseus in
February, 1901, and for a short time equaled Capella in brightness. But
its light rapidly waned, with periodic fluctuations of brightness like
those of a variable star, and at the present time (September, 1902) it
is lost to the naked eye, although in the telescope it still shines like
a star of the ninth or tenth magnitude.
By the aid of powerful photographic apparatus, during the period of its
waning brilliancy a ring of faint nebulous matter was detected
surrounding the star and drifting around and away from it much as if a
series of nebulæ had been thrown off by the star at the time of its
sudden outburst of light. But the extraordinary velocity of this nebular
motion, nearly a billion miles per hour, makes such an explanation
almost incredible, and astronomers are more inclined to believe that the
ring was merely a reflection of the star's own light from a cloud of
meteoric matter, into which a rapidly moving dark star plunged and,
after the fashion of terrestrial meteors, was raised to brilliant
incandescence by the collision. If we assume this to be the true
explanation of these extraordinary phenomena, it is possible to show
from the known velocity with which light travels through space and from
the rate at which the nebula spread, that the distance of Nova Persei,
as the new star is called, corresponds to a parallax of about one
one-hundredth of a second, a result that is, in substance, confirmed by
direct telescopic measurements of its parallax.
Another modern temporary star is Nova Aurigæ, which appeared suddenly in
December, 1891, waned, and in the following April vanished, only to
reappear three months later for another season of renewed brightness.
The spectra of both these modern Novæ contain both dark and bright lines
displaced toward opposite ends of the spectrum, and suggesting the
Doppler effect that would be produced by two or more glowing bodies
having rapid and opposite motions in the line of sight. But the most
recent investigations cast discredit on this explanation and leave the
spectra of temporary stars still a subject of debate among astronomers,
with respect both to the motion they indicate and the intrinsic nature
of the stars themselves. The varying aspect of the spectra suggested at
one time the sun's chromosphere, at another time the conditions that are
present in nebulæ, etc.