negligible compared to the mass of the sun, and it is for this reason
that they appear to revolve about the _center_ of the sun. As a
matter of fact, no body in the universe revolves about the _exact
geometrical center_ of another body, but two mutually attracting
bodies revolve in orbits about their common center of gravity, which
always lies between the two bodies on the line connecting them and
at a distance from each of them that is in inverse proportion to the
mass of the body. The moon does not revolve about the _center of the
earth_, but about the _center of gravity_ of the earth and moon,
which lies on the line connecting the two bodies and at a distance
from the earth's center that is one eighty-first of the distance
from the center of the earth to the center of the moon, since this
represents the ratio of the masses of the two bodies. This center
of gravity of the earth and moon, lies, then, about two thousand
miles from the earth's center, and about this point both earth and
moon trace out orbits of revolution that are identical in form and
differ only in size. In the same way each of the planets of the
solar system revolves about the center of gravity of itself and the
sun, but the mass of the sun is so far in excess of the combined
masses of all the planets that we may consider, for all practical
purposes, that the planets revolve about the sun's center, the center
of gravity of the system being within the sun, just as the center of
gravity of the earth and moon is within the earth.
Prof. T. J. J. See found from the investigation of forty binary star
orbits that the average eccentricity of double star orbits is twelve
times as great as the average eccentricity of a planetary orbit, and
that the masses of the component suns never differ very greatly. The
center of gravity of a binary system, therefore, lies at a great
distance from the centers of the stars, and about this point, as a
focus, the stars move in orbits that are exactly similar in form but
differ in size in inverse proportion to the ratio of the masses.
Since the orbits of binaries are, moreover, very highly eccentric,
the two suns are, as we have said, anywhere from two to nineteen
times nearer to each other at periastron than they are at "apastron."
We have spoken so far only of systems of two associated suns, but
many systems exist in which three or more sun-like bodies are in
revolution about a common center of gravity. Frequently two fairly
close suns are in revolution about a common center of gravity, in a
period, say, of fifty or sixty years, while a third sun revolves at
a comparatively great distance about the center of gravity of itself
and the first pair in a period of several hundred years. Or possibly
the third sun also possesses a close attendant and the two pairs
revolve in a period of great length about a common center of gravity.
Such, for instance, are the systems of _Zeta Cancri_ and _Epsilon
Lyræ_. In the former system the closer components revolve rapidly
about their center of gravity in a period of about sixty years, while
the remote companion shows irregularities in its motion that indicate
that it is revolving about a dark body in a period of seventeen and
a half years, while the two together are revolving very slowly in a
period of six or seven centuries, about a common center of gravity
with the first pair in a retrograde direction.
The wider pair of _Epsilon Lyræ_ is a naked-eye double for it can
be seen as a double star by a keen eye, while even a three-inch
telescope will separate each of the components into a double star. So
extensive is this system that the periods of revolution of the closer
components occupy several centuries, one pair appearing to revolve
about twice as rapidly as the other, while the period of revolution
of the two pairs about a common center is probably a matter of
thousands of years. The gap that separates the two pairs may be so
great that light requires months to cross it.
These multiple systems are by no means exceptional. They are to be
found in profusion among the brilliant _Orion_ stars. They have been
referred to as "knots" of stars and it has been suggested that they
may have originated as local condensations in one vast nebulous
tract. A system of only two components appears to be the exception
rather than the rule, groups of several connected suns being more
numerous than single pairs.
In all of these double and multiple systems there exists the
possibility of minute satellites, such as our own earth, in
attendance upon some one component of the system. Such tiny bodies
shining only by reflected light from a nearby brilliant sun would be
hopelessly invisible in the most powerful telescope.
We can only assume that it is far more reasonable to believe in than
to disprove the existence of such satellites.
Our own solar system, then, represents neither in its mechanical nor
physical features, the only possibilities for the maintenance of
life; it can neither be considered a unique form, nor even the most
generally prevalent form in the universe.
XXX
ASTRONOMICAL DISTANCES
The grandeur of the scale upon which the visible universe is
fashioned lies almost beyond human comprehension. In measuring the
vast extent of our own solar system, which is but a single unit
in the system of the stars, we may have recourse to some earthly
standard of measurement, such as the mile. But when we desire to
express in terms of units that can be grasped by our imagination, the
distances of the stars that lie far, far beyond, we find that all
ordinary standards of measurement become utterly inadequate for our
purpose. In the measurement of celestial distances within the solar
system the unit employed is either the familiar mile or kilometer or
the "astronomical unit," which is the mean distance from the earth
to the sun (ninety-two million nine hundred thousand miles in round
numbers).
In the measurement of distances _beyond_ the solar system the unit
employed is either the _light-year_ or more recently the _parsec_,
which is rapidly replacing the light-year among astronomers. A
"light-year" is the distance that light, with its finite but almost
unimaginable velocity of one hundred and eighty-six thousand miles
_per second, travels in a year_. It is equal in round numbers to
sixty-three thousand times the distance from the earth to the sun or
approximately six thousand billions of miles. The parsec is equal
to three and twenty-six hundredths (3.26) light-years, and it is
approximately two hundred thousand times the distance from the earth
to the sun. It is "the distance of a star with the _parallax_ of
a second," a fact which its name, parsec, conveys to us. In other
words, at the distance of one parsec the distance from the earth to
the sun, "the astronomical unit," would subtend an angle equal to
one second of an arc. This angle is spoken of as the parallax of the
star. The larger the parallax, that is, the larger the angle the
astronomical unit or radius of the earth's orbit subtends, viewed
from the star, the nearer the star is to us. The fact that there is
no known star within one parsec, or three and twenty-six hundredths
light-years, of the sun shows the immensity of the scale of the
universe of stars.
Before considering the distances of the stars and the extent of the
sidereal system of which our sun and his satellites form a part, let
us undertake to express the distance of the sun, moon and planets
from the earth and the extent of the solar system in terms with which
we are familiar.
The nearest to the earth of all celestial bodies is its satellite,
the moon. So near is the moon that if we should make on some great
plain a model of the solar system in which the astronomical unit, the
distance from earth to sun, would be four hundred feet, the distance
between the earth and moon would be only one foot. On the same scale
the most distant planet Neptune would be two and one-quarter miles
away.
Granted that it were possible to escape the earth's gravitational
bonds and to travel by our swiftest means of conveyance, the
airplane, through interplanetary space, let us consider how long
it would take us to reach the moon, sun and planets if our speed
were maintained at a uniform rate of two hundred miles an hour. An
airplane traveling at this rate would circumnavigate the earth in a
little over five days and would reach the moon in seven weeks. A trip
to the sun, however, would take fifty-three years.
After traveling for fourteen and a fraction years we would pass
the orbit of Venus and eighteen years later the orbit of Mercury.
If we preferred to travel outward from the earth in the direction
of Mars and the outer planets instead of toward the sun, more than
twenty-seven years would elapse before we would reach the orbit of
Mars. An airplane journey to Jupiter would be a matter of more than
two hundred years, to Saturn four hundred and fifty years, to Uranus
nearly one thousand years, and to Neptune, about one thousand five
hundred years. To cross the solar system on the diameter of Neptune's
orbit in an airplane, traveling day and night without stopping at the
rate of 200 miles per hour would take more than three thousand years.
The sun's attraction reaches far beyond Neptune's orbit, however.
There are comets belonging to the solar system compelled by the sun's
attraction to accompany him on his travels through space that return
periodically to the immediate vicinity of the sun from regions far
beyond the orbit of Neptune and there is also the possibility that
one or more undiscovered planets may travel around the sun in orbits
far exterior to Neptune's orbit.
Measured in terms of familiar units, such as are employed for the
measurement of distances on our own planet, the extent of the solar
system is tremendously great. Viewed from Neptune, the sun is so
far away that it presents no appreciable disk. It is in this sense
star-like to the Neptunians, but at the distance of Neptune the stars
appear no more brilliant and no nearer than they do to us.
To Neptune the sun, though star-like in form, supplies a very
appreciable quantity of light and heat (one nine-hundredth of the
amount the earth receives) while the amount of light and heat that
Neptune receives from the nearest stars is entirely inappreciable.
When our airplane reaches Neptune after a journey of one thousand
five hundred years, it is, as it were, just clearing the ground
for its flight to the stars. To cover the intervening space to
the nearest star, traveled by light in four and a third years, an
airplane would need _fourteen and a half million years_. In that time
the solar system itself would be in some far distant part of the
universe, since it is speeding onward through space at the rate of
twelve miles a second or about four astronomical units a year.
Changing now our unit of measurement that we may express interstellar
distances in comprehensible numbers, we prepare to travel from the
earth to the stars with the velocity of light.
With this velocity, one hundred and eighty-six thousand miles per
second, we circumnavigate our globe in one-seventh of a second, reach
the moon in one and a fourth seconds and the sun in eight minutes.
In a little over four hours we pass the orbit of Neptune and are
started on our journey to the stars, penetrating further and further
into interstellar space. For a year we travel and reach not a single
star though we are speeding ever onward with the velocity of light.
We have now covered the distance of one light-year, which means that
the waves of light from the sun we have left behind must travel for a
year before they reach us. We continue our journey and find ourselves
next at a distance of one parsec from the sun. We have traveled a
distance of approximately three and a quarter light-years, and were
it possible to see the earth as well as the sun at this distance,
the two would appear to be but one second of arc apart, a distance
that requires the most careful adjustment and manipulation of the
telescope to measure accurately. We are still one light-year distant
from Alpha Centauri, the nearest of the bright stars. A few of the
stars will now appear somewhat brighter than they appeared to us on
earth, but the majority of the stars appear just as we see them here
and the forms of the constellations remain practically unchanged
in appearance, for we are only beginning our journey through the
sidereal universe and our position in it has only shifted by a very
slight amount. If we should continue our journey to the immediate
vicinity of Alpha Centauri, we would find that it is not like our
own sun, a single star, but is a binary star consisting of two suns
in revolution around their common center of gravity. The distance
of this binary system from the solar system has been measured
with considerable accuracy and is known to be four and a third
light-years. Though there may be a few faint stars or non-luminous
stars nearer to us than Alpha Centauri, this star has long held the
distinction of being the nearest of the stars. As the sun continues
his journey through the universe the two stars, Alpha Centauri and
our sun, will finally draw away from each other after many ages have
passed and some other sun of space will be our nearest star. The
distances that separate the stars from each other probably average as
great as the distance from the sun to Alpha Centauri. Within a sphere
whose center is at the earth and whose radius is five parsecs, or
about sixteen light-years, there are only about twenty known stars.
There is, therefore, small chance of collision among bodies that are
so small in proportion to the tremendous intervals of space that
separate them from each other. There is ample room for the individual
stars to pursue their journey through space without interfering with
each other's motion so long as they are as widely scattered as they
appear to be in this portion of the universe. The fact that our own
sun has continued its journey through the universe for some hundreds
of millions of years without any catastrophe such as would result
from closely approaching or colliding with another sun of space shows
how enormous is the scale upon which our sidereal system is fashioned.
Stars that are ten, fifty or even one hundred light-years from the
earth are our nearest neighbors in space. They are the stars that
show a slight displacement in the heavens or measurable parallax,
viewed from opposite sides of the earth's orbit. There are probably a
thousand stars among the hundreds of millions of stars within reach
of the greatest telescopes whose distances have been determined
in light-years by direct measurement of their displacement in the
heavens resulting from the change of position of the earth in its
orbit. The most distant of the stars are apparently immovable in
the heavens showing neither the effect of the sun's motion or their
own motion through space. Methods for finding the distances of many
far remote stars and star-clusters have been devised, however, and
some comparatively recent investigations have given results for the
distances of these objects indicating that the diameter of the system
of stars to which our sun belongs is approximately three hundred
thousand light-years. It is difficult to grasp the full significance
of this fact. It means that hundreds of millions of the suns of space
throng the visible universe at distances from us and from each other
running into hundreds, thousands and even hundreds of thousands of
light-years. The light waves from some tiny object that we view
today in one of our great reflectors may have started on their
journey through space over one hundred thousand years ago when men of
the Old Stone Age inhabited our planet earth!
Astronomers have found as a result of their investigations that the
sidereal system to which our solar system belongs is in the form of
a flattened spheroid with its longest axis in the plane of the Milky
Way. The extent of this star system composed of hundreds of millions
of individual suns in addition to nebulæ and clusters is probably
something like three hundred thousand light-years along its longest
axis, while globular star clusters lying above and below its central
plane are estimated to be at distances from it ranging from ten
thousand to two hundred thousand light-years. This entire organized
system is our sidereal universe. Space beyond is unexplored. The
globular star clusters are among the most distant celestial objects
so far discovered. The spiral nebulæ may be entirely within the
limits of this system or they may be even more distant than the
globular clusters for their distances are not known as yet.
There is a possibility that our sidereal universe, vast as it is
known to be, may be but a unit in some still greater unit and that
other similar systems lie beyond the reach of existing telescopes at
unimaginable distances.
The mind of man is overwhelmed by the thought of sidereal systems
as vast as our own lying far beyond his ken. Whether or not such
external systems do exist and are with our own sidereal system units
in some still vaster creation we cannot know.
So vast, indeed, is this one visible universe of ours that the
mind of man, accustomed to earthly standards, cannot comprehend
its magnitude or the infinitesimal size of our whole solar system
compared to it.
XXXI
SOME ASTRONOMICAL FACTS WORTH REMEMBERING
Kepler's Three Laws of Planetary Motion:
I. The planets move in ellipses with the sun at one focus.
II. The radius vector of a planet (line adjoining sun and planet)
sweeps over equal areas in equal times.
III. The square of the time of revolution (the year) of each planet
is proportional to the cube of its mean distance from the sun.
* * * * *
Sir Isaac Newton discovered that the law of gravitation extends to
the stars. That is, every mass in the universe attracts every other
mass with an attraction directly proportional to the product of the
masses and inversely proportional to the square of the distances
between them.
* * * * *
Ocean tides are caused by the difference between the attraction of
the sun and moon for the main body of the earth and their attraction
for different particles of the earth's surface. The tide-raising
force of the disturbing body is proportional to its mass and
inversely proportional to the cube of its distance. The tides
produced by the sun are, therefore, only two-fifths as great as the
tides produced by the moon.
* * * * *
The celestial sphere is an imaginary sphere of infinite radius,
with the earth at its center, upon which the celestial bodies are
considered to be projected for convenience in determining their
positions with respect to fixed points of reference in the heavens.
The north and south poles of the heavens are the points on the
celestial sphere directly above the north and south poles of the
earth.
The celestial equator is the great circle in which the plane of the
earth's equator intersects the celestial sphere. It passes through
the east and west points of the horizon and through the zenith--or
point directly overhead--at the earth's equator.
The ecliptic is the great circle in which the plane of the earth's
orbit intersects the celestial sphere. The celestial equator and the
ecliptic are inclined to each other at an angle of 23-1/2°, which is
called the obliquity of the ecliptic. The two points in which the
celestial equator and the ecliptic intersect are called respectively
the vernal equinox and the autumnal equinox.
The vernal equinox is an important point of reference on the
celestial sphere.
As the position of a point on the earth's surface is determined
by its longitude and latitude so the position of an object on the
celestial sphere--star, sun, planet--is determined by its Right
Ascension and Declination.
The Declination of a celestial object is its distance north or
south of the celestial equator, measured in degrees, minutes and
seconds of arc, on a great circle of the celestial sphere passing
through the object and north and south poles of the heavens. These
great circles are called hour circles and they correspond to the
meridians or circles of longitude on the earth's surface. The
declination of an object in the heavens corresponds to the latitude
of a point on the earth's surface. The Right Ascension of a point
on the celestial sphere corresponds to the longitude of a point on
the earth's surface. It is measured--as longitude is measured--in
degrees, minutes and seconds of arc or in hours, minutes and seconds
of time--eastward along the celestial equator from the hour circle
passing through the vernal equinox to the foot of the hour circle
passing through the object. The hour circle passing through the
vernal equinox is the zero meridian for the celestial sphere just as
the meridian of Greenwich is the zero meridian on the earth's surface.
* * * * *
The mean distance of the earth from the sun is 92,900,000 miles and
is called the astronomical unit.
The sun with its satellites advances through the universe at the rate
of 4 astronomical units in a year or approximately one million miles
a day.
The parallax of a star is the angle at the star subtended by the
radius of the earth's orbit, 92,900,000 miles, or the astronomical
unit. It is, in other words, the angular distance between the earth
and sun as viewed from the star. The larger the parallax the nearer
the star. The largest known stellar parallax is that of Alpha
Centauri and its value is 0".75.
The light-year is the distance that light travels in one year. It
is equal to about 63,000 astronomical units or nearly six trillion
(6,000,000,000,000) miles. The velocity of light is 186,000 miles per
second.
The parsec is equal to 3.26 light-years. It is the distance of a star
that has a parallax of one second of arc.
The apparent magnitude of a star is its apparent brightness estimated
on a scale in which a difference of one magnitude corresponds to a
difference in brightness of 2.51, or the fifth root of one hundred.
A difference of five magnitudes corresponds to a difference one one
hundredfold in brightness, of ten magnitudes to ten thousandfold
in brightness. In exact measurements on this scale magnitudes are
estimated to tenths.
Stars that are one magnitude brighter than stars of the standard
first magnitude are of the zero magnitude and stars still brighter
are of negative magnitudes.
Sirius is a star of the -1.6 magnitude. Jupiter at opposition is of
-2.0 magnitude and Venus at greatest brilliancy of -4.0 magnitude.
The sun on this scale of comparative brightness is of the -26.7
apparent magnitude. The faintest stars visible in the most powerful
telescope in the world--the 101-inch Mt. Wilson Hooker telescope--are
of the twentieth magnitude.
The _absolute_ magnitude of a star is its apparent magnitude at
the standard distance of ten parsecs or 32.6 light years. The
absolute magnitude of the sun is five. That is, the sun would be a
fifth-magnitude star at the standard distance of 32.6 light-years.
The absolute magnitudes of stars indicate how bright they would be
relatively if they were all at the same standard distance. Apparent
magnitudes indicate how bright the stars appear to be at their true
distances.
* * * * *
The mean distance of the moon from the earth is approximately 240,000
miles or sixty times the earth's radius.
The sun is four hundred times farther away than the moon and its
diameter is about four hundred times greater than the moon's diameter.
The nearest star is about 275,000 times more distant than the sun,
and the most distant known object, the globular star cluster, N.G.C.
7106, is about fourteen billion times more distant than the sun.
The earth is a spheroid flattened at the poles and its polar diameter
is about twenty-seven miles shorter than its equatorial diameter. An
object weighs less at the poles than at the equator.
The earth's interior is as rigid as steel and probably consists of a
core of magnetic iron surrounded by an outer stony shell.
Eclipses of the sun occur when the moon passes between the earth and
sun. They can only occur at the time of new moon. There must be at
least two solar eclipses every year separated by an interval of six
months and there may be as many as five solar eclipses in a year.
Eclipses of the moon occur when the earth comes between the sun and
moon, and the moon passes into the earth's shadow. Eclipses of the
moon can only occur at full moon. There may or may not be eclipses of
the moon every year. The greatest number of eclipses than can occur
in any one year, solar and lunar combined, is seven and the least
number is two and in that case they are both solar eclipses.