is inclined at a small angle, 7 degrees, to the common planes
of the planetary system, and Chamberlin holds this to be one of
the strong points in favor of the planetesimal hypothesis. He
reasons thus: the star which passed close to our Sun and drew
out the planetary materials in the form of spiral streams must
have moved in the plane of the spiral; that is, in the plane of
our planetary system. Some of the materials would be drawn out
from our Sun only a very short distance and then fall back upon
the Sun. Great tidal waves would be formed on opposite sides of
the Sun, and these would try to follow the disturbing body. The
effect of these waves and of the materials which fall back
would be to change the Sun's original rotation plane in the
direction of the disturbing body's orbital plane.
Now the chance for a disturbing star's passing around our Sun
in a plane making a large angle, say from 45 degrees to 90
degrees, with the Sun's equator, is much greater than for a
small angle 0 degrees to 45 degrees. The chances are greatest
that the angle will be 90 degrees. Only those disturbing stars
which approach our Sun PRECISELY in the plane of the Sun's
equator could move around the Sun in this plane. All those
approaching along any line parallel to the Sun's equatorial
plane, but lying outside of this plane, and all those whose
directions of approach make any angle whatever with the
equatorial plane, would find it impossible to move in that
plane. That the angle under this hypothesis is only 7 degrees
is surprising, though, as we are dealing with but a single
case, we can not say, I think, that this militates either for
or against the hypothesis. We are entitled to say only that
unless the approach was so close as to cause disturbances in
our Sun to relatively great depths, the angle referred to would
have only one chance in ten or fifteen or twenty to be as small
as 7 degrees. Any disturbance which succeeded in taking out of
the Sun only 1/7 of 1 per cent. of its mass could scarcely
succeed in shifting the axis of rotation of the remaining 99
6/7 per cent. very much, I think. If the angle were 30 degrees
or 50 degrees or 80 degrees, instead of 7 degrees, the case for
the planetesimal hypothesis would be somewhat stronger.
A remarkable fact concerning the Sun is that the equatorial
region rotates once around in a shorter time than the regions
in higher latitudes require. The rotation period of the Sun's
equator is about 24 days; the period at latitude 45 degrees is
28 days; and at 75 degrees, 33 days. The planetesimal
hypothesis attributes this equatorial acceleration to the
falling back into the Sun of the materials which had been
lifted out to a short distance by the disturbing body, and to
the forward-rushing tide raised in the equatorial regions by
the disturbing body. This may well have occurred. However, we
must remember that the same phenomenon exists certainly in
Jupiter and Saturn, and quite probably in Uranus and Neptune;
that is, in all the bodies in the system that are gaseous and
free to show the effect. It seems to be the result of a
principle which has operated throughout the solar system, not
requiring, at least not directly requiring, the passage of a
disturbing star. I think the most plausible explanation of this
curious phenomenon is that great quantities of materials
originally revolving around the Sun and around each of the
planets have gradually been drawn into these bodies, by
preference into their equatorial areas. Such masses of matter
moving in orbits very close to these bodies must have traveled
with speeds vastly higher than the surface speeds of the
bodies. To illustrate, the rotational velocity of a particle
now in the Sun's surface at the equator is approximately 2 km.
per second. A small body revolving around the Sun close to his
surface, rapidly enough to prevent its falling quickly upon the
Sun, must have a velocity of more than 400 km. per second. If,
now, this small body encounters some resistance it will fall
into the Sun, and as it is traveling more than 200 times as
rapidly as the solar materials into which it drops, it will
both generate heat and accelerate the rotational velocity of
the surrounding materials. In the same way the equatorial
accelerations in Jupiter and Saturn can receive simple
explanation. The point is not necessarily in opposition to the
planetesimal hypothesis; but whatever the explanation, it ought
to apply to the planet as well as to the Sun.
If the spiral nebulae have been formed in accordance with
Chamberlin and Moulton's hypothesis, the secondary nuclei in
them must revolve in a great variety of elliptic orbits. The
orbits would intersect, and in the course of long ages the
separate masses would collide and combine and the number of
separate masses would constantly grow smaller. Moulton has
shown that IN GENERAL the combining of two masses whose orbits
intersect causes the combined mass to move in an orbit more
nearly circular than the average orbit of the separate masses,
and in general in orbit planes more nearly coincident with the
general plane of the system. Accordingly, the major planets
should move in orbits more nearly circular and more nearly in
the plane of the system than do the asteroids; and so they do.
If the asteroids should combine to form one planet the orbit of
this planet should be much less eccentric than the average of
all the present asteroid eccentricities, and the deviation of
its orbit plane should be less than the average deviation of
the present planes. We can not doubt that this would be the
case. Mercury and Mars, the smallest planets, should have,
according to this principle, the largest eccentricities and
orbital inclinations of any of the major planets. This is true
of the eccentricities, but Mars's orbit plane, contrarily, has
a small inclination. Venus and the Earth, next in size, should
have the next largest inclinations and eccentricities, but they
do not; Venus's eccentricity is the smallest of all. The
Earth's orbital inclination and eccentricity are both small.
Jupiter and Saturn, Uranus and Neptune, should have the
smallest orbital inclinations; their average inclination is
about the same as for Venus and the Earth. They should likewise
have the smallest eccentricities. Neptune, the smallest of the
four, has an orbit nearly circular; Jupiter, Saturn and Uranus
have eccentricities more than 4 times those of Venus and the
Earth. Considering the four large planets as one group and the
four small planets as another group, we find that the
inclinations of the orbits of the two groups, per unit mass,
are about equal; but the average eccentricity of the orbits of
the large planets, per unit mass, is 21 times that of the
orbits of the small planets.[1] The evidence, except as to the
asteroids and Mercury, is not favorable to the planetesimal
hypothesis, unless we make special assumptions as to the
distribution of materials in the spiral nebulae.
[2] The average eccentricity of the orbits of the four inner
planets (per unit mass) is 0.0221, and of the four outer
planets is 0.0489.
The fact that the disturbing body drew 225 times as much matter
a great distance to form the four large planets as it drew out
a short distance to form the four small planets and the
asteroids seems difficult of explanation on the planetesimal
hypothesis. However, this distribution of matter is at present
a difficulty in any of the hypotheses. The planetesimal
hypothesis explains well all west to east rotations of the
planets on their axes, but to make Uranus rotate nearly at
right angles to the plane of the system, and Neptune in a plane
inclined 135 degrees to the plane of the system, is a
difficulty in any of the hypotheses, unless special assumptions
are made to fit each case.
The authors succeed well, I think, in showing that the
satellites should prefer to revolve around their planets in the
direction of the planetary revolution and rotation, especially
for close satellites, and, on the basis of special assumptions,
in the reverse direction for satellites at a greater distance.
They show that the chances favor small eccentricities for
satellites revolving about their planets in the west to east,
or direct sense, and large eccentricities for satellites moving
in retrograde directions. The inner satellite of Mars and the
rings of Saturn make no special difficulty under the
planetesimal hypothesis.
The evidence of the comets, as bona fide members of the solar
system which approach the Sun almost, and perhaps quite,
indifferently from all directions, is that the volume of space
occupied by the parent structure of the system was of enormous
dimensions, both at right angles to the present principal plane
of the system and in that plane. We are accustomed to think of
the spiral nebulae as thin relatively to their major diameters.
To this extent the planetesimal hypothesis does not furnish a
good explanation of the origin of comets, unless we assume that
a small amount of matter was widely scattered in all directions
around the parent spiral; and this conception leads to some
apparent difficulties. The origin of the comets is difficult to
explain under any of the hypotheses.
RESUME OF HYPOTHESES
Kant's hypothesis had the great defect of trying to prove too
much. It started from matter AT REST, and came to grief in
trying to give a motion of rotation to the entire mass through
the operation of internal forces alone--an impossibility.
Kant's idea of nuclei or centers of gravitational attraction,
scattered here and there throughout the chaotic mass, which
grew into the planets and their satellites, is very valuable.
Laplace's hypothesis had the great advantage of starting with
an extended mass already in rotation, but it violated fatally
the law of constancy of moment of momentum. We should expect
this hypothesis to create a solar system free from
irregularities, very much as if it were the product of an
instrument-maker's precision lathe. The solar system as it
exists is a combination of regularities and many surprising
irregularities.
Chamberlin and Moulton's hypothesis has the advantage of a
parent mass in rotation, practically in a common plane, and
with the materials distributed at distances from the nucleus as
nearly in harmony with the known distribution of matter in the
solar system as we care to have them, except perhaps as to the
comets. In effect it retains all the advantageous qualities of
Kant's proposals. It seems to have the flexibility required in
meeting the irregularities that we see in our system.
CONCERNING THE ORIGIN OF SPIRAL NEBULAE
I think it is very doubtful whether the spiral nebulae have in
general been formed by the close approaches of pairs of stars,
as the authors have postulated for the assumed solar spiral.[2]
The distribution of the spirals seems to me to negative the
idea. To witness the close approach of two stars we must look
in the direction where the stars are. To the best of
present-day knowledge the stars are in a spheroid whose longer
axes are coincident with the plane of the Milky Way. If this is
so, the close approach of pairs of stars should occur
preeminently in the Milky Way, and we should find the spirals
prevailingly in and near the Milky Way. This is precisely where
we do not find them. In fact, they seem to abhor the Milky Way.
The new stars, which are credibly explained as the products of
collisions of stars with nebulae, are found preeminently in the
Milky Way and almost negligibly in the regions outside of the
Milky Way. Again, the spirals are believed to be, on the whole,
of enormous size. They are too far away to let us measure their
distances by the usual methods, and they move too slowly on the
surface of the sphere to have let us determine their proper
motions. Slipher's recent work with a spectrograph seems to
show that the dozen spirals observed by him are moving with
high speeds of approach and recession; from 300 km. per second
approach in the case of the Andromeda nebula to 1,100 km. per
second recession in the case of several objects. If the spirals
are moving at random their speeds at right angles to the line
of sight must be even greater than their speeds of approach and
recession. Unless they are very distant bodies their proper
motions should be detected by observations extending over only
a few years. My colleague Curtis has this year compared recent
photographs of some 25 spirals with photographs of the same
object made by Keeler fifteen years ago. They reveal no
appreciable proper motions, or rotations. In this same interval
Neptune has revolved more than 30 degrees. Slipher has recently
measured the rotational speed of one "spindle" nebula, believed
to be a spiral. He finds it to be enormously rapid; no motions
in the solar system approach it in magnitude. The evidence is
to the effect that the spirals are in general very far away;[3]
perhaps on or beyond the confines of our stellar system, but
not certainly so. Accordingly, we are led to believe that the
spirals studied thus far have diameters 20 times or 100 times,
or in some cases several thousand times, the diameter of our
solar system. It is difficult to avoid the conclusion that in
general they are immensely more massive than is our solar
system. The spiral which has been assumed as the forerunner of
our system must have been of diminutive size as compared with
the larger and brighter spirals which we see to-day.
[2] It would seem that all rotating nebulae should in reality
possess some of the attributes of spiral motion. Whether the
spiral structure should be visible or invisible to a
terrestrial observer would depend upon the sizes and distances
of the nebulae, upon the distribution of materials composing
them, and perhaps upon other factors. See developed the
hypothesis that spiral nebulae owe their origin to the
collision of two nebulae. Collisions of this kind could readily
occur because of the enormous dimensions of the nebulae, and
motions of rotation and consequently spiral structure might
readily result therefrom. The abnormally high speeds of the
spiral nebulae are apparently a very strong objection to the
hypothesis.
[3] Bohlin found a parallax of 0"17 for the Andromeda Nebula,
and Lampland thinks that Nebula N.G.G. 4594 has a proper motion
of approximately 0"05 per annum.
We are sadly in need of information concerning the constitution
of the spiral nebulae. Their spectra appear to be prevailingly
of the solar type, except that a very small proportion contain
some bright lines in addition to the continuous spectrum. So
far as their spectra are concerned, they may be great clusters
of stars, or they may consist each of a central star sending
its light out upon surrounding dark materials and thus
rendering these materials visible to us. The first alternative
is unsatisfactory, for all parts of spirals have hazy borders,
as if the structure is nebulous or consists of irregular groups
of small masses; and the second alternative is unsatisfactory,
for in many spirals the most outlying masses seem to be as
bright as masses of the same areas situated only one half as
far from the center, whereas in general the inner area should
be at least four times as bright as the outer area. All
astronomers are ready to confess that we do not know much about
the conditions existing in spiral nebulae.
THE EARTH-MOON SYSTEM
Our Earth and Moon form a unique combination in that they are
more nearly of the same size than are any other planet and its
satellites in our system. It required a 26-inch telescope on
the Earth to discover the tiny moons of Mars; but an astronomer
on Mars does not need any telescope to see the Earth and Moon
as a double planet--the only double planet in the solar system.
According to the Kantian school of hypotheses the Earth and
Moon owe their unique character to the accident that two
centers of condensation--two nuclei--not very unequal in mass,
were formed close to each other and were endowed with or
acquired motions such that they revolved around each other.
They drew in the surrounding materials; one of the two bodies
got somewhat the advantage of the other in gravitational
attraction; it succeeded in building itself up more than the
other nucleus did; and the Earth and the Moon were the result.
According to the Laplacean hypothesis, on the contrary, the
Earth and Moon were originally one body, gaseous and in
rotation. This ball of gas radiated heat, diminished in size,
rotated more and more rapidly, and finally abandoned a ring of
nebulosity, which later broke up and eventually condensed into
one mass called the Moon. The central mass composed the Earth.
It is a curious fact that Venus, which is only a shade smaller
than the Earth, should not have divided into two bodies
comparable with the Earth and Moon. Have the tides on Venus
produced by the Sun always been strong enough to keep the
rotation and revolution periods equal, as they are thought to
be now, and thus to have given no opportunity for a rapidly
rotating Venus to divide into two masses?
A third hypothesis of the Moon's origin is due principally to
Darwin. He and Poincare have shown that a great rotating mass
of fluid matter, such as the Earth-Moon could be assumed to
have been, by cooling, contracting and increasing rotation
speed, would, under certain conditions thought to be
reasonable, become unstable and eventually divide into two
bodies revolving around their common center of mass, at first
with their surfaces nearly in contact. Here would begin to act
a tide-raising force which must have played, according to
Darwin's deductions, a most important part in the further
history of the Earth and Moon. The Earth would produce enormous
tides in the Moon, and the Moon much smaller tides in the
Earth. Both bodies would contract in size, through loss of
heat, and would try to rotate more and more rapidly. The two
rotating bodies would try to carry the matter in the tidal
waves around with the rest of the materials in the bodies, but
the pull of each body upon the wave materials in the other
would tend to slow down the speed of rotation. The tidal
resistance to rotation would be slight if the bodies at any
time were attenuated gaseous masses, for the friction within
the surface strata would be slight. Nevertheless, there would
eventually be a gradual slowing down of the Moon's rotation, a
gradual slowing down of the Earth's rotation, and a slow
increase in the distance between the two bodies. In other
words, the Moon's day, the Earth's day and our month would
gradually increase in length. Carried to its logical
conclusion, the Moon would eventually turn the same face to the
Earth, the Earth would eventually turn the same face to the
Moon, and the Earth's day and the Moon's day would equal the
month in length. The central idea in this logic is as old as
Kant: in 1754 he published an important paper in which he said
that tidal interactions between Earth and Moon had caused the
Moon to keep the same face turned toward us, that the Earth's
day was being very slowly lengthened, and that our planet would
eventually turn the same face to the Moon. Laplace, a
half-century later, proposed the action of such a force in
connection with the explanation of lunar phenomena, and
Helmholtz, just 100 years after Kant's paper was published,
lent his support to this principle; but Sir George Darwin has
been the great contributor to the subject. His popular volume,
"The Tides," devotes several chapters to the effects of tidal
friction upon the motions of two bodies in mutual revolution.
We must pass over the difficult and complicated intermediate
steps to Darwin's conclusions concerning the Earth and Moon,
which are substantially as follows: the Earth and Moon were
originally much closer together than they now are: after a very
long period of time, amounting to hundreds of millions of
years, the Moon will revolve around the Earth in 55 days
instead of in 27 days as at present; and the Moon and Earth
will then present the same faces constantly to each other. The
estimated period of time required, and the final length of day
and month, 55 days, are of course not insisted upon as accurate
by Darwin.
These tidal forces were unavoidably active, it matters not if
the Earth and Moon were originally one body, as Laplace and
Darwin have postulated, or originally two bodies, growing up
from two nuclei, in accordance with the Kantian school. Whether
these forces have been sufficiently strong to have brought the
Earth and Moon to their present relation, or will eventually
equalize the Moon's day, the Earth's day, and the month, is a
vastly more difficult question. Moulton's researches have cast
serious doubt upon this conclusion. All such investigations are
enormously difficult, and many questionable assumptions must be
made if we seek to go back to the Moon's origin, or forward to
its ultimate destiny.
Tidal waves, in order to be effective in reducing the
rotational speed of a planet, must be accompanied by internal
friction; and this requires that the planet be to some extent
inelastic. It was the view of Darwin and others that the
viscous state of the Earth and Moon permitted wave friction to
come into play. Michelson has recently proved that the Earth
has a high degree of elasticity. It deforms in response to
tidal forces, but quickly recovers from the action of these
forces. It therefore seems that the rate of tidal evolution of
the Earth-Moon system at present and in the future must be
extremely slow, and possibly almost negligible. What the
conditions within the Earth and Moon were in the distant past
is uncertain, but these bodies probably passed through viscous
stages which endured through enormously long periods of time.
No one seriously doubts that Jupiter, Saturn, Uranus and
Neptune are now largely gaseous, and that they will evolve,
through various degrees of viscosity, into the solid and
comparatively elastic state. It is natural to assume that the
Earth has already passed through an analogous experience.
The Moon turns always the same hemisphere toward the Earth.
Observations of Venus and Mercury are prevailingly to the
effect that those planets always turn the same hemispheres
toward the Sun. Many, and perhaps all, of the satellites of
Jupiter and Saturn seem to turn the same hemispheres always
toward their respective planets. This widely prevailing
phenomenon is no doubt due to a widely prevailing cause, which
astronomers have all but unanimously attributed to tidal
action.
BINARY STAR SYSTEMS
That an original mass actually divided to form the Earth and
Moon, according to the Laplacian or the Darwin-Poincare
principle, seems to be extremely doubtful, especially on
account of their diminutive sizes, and I greatly prefer to
think that the Earth and Moon were built up from two nuclei;
but that very much greater masses, masses larger on the average
than our Sun, composing highly attenuated stars, have divided
each into two masses to form many or most of our double stars,
I firmly believe. The two component stars would in such a case
at first revolve around each other with their surfaces almost
or quite in contact. Tidal forces would very gradually cause
the bodies to move in orbits of larger and larger size, with
correspondingly longer periods of revolutions, and the orbits
would become constantly more eccentric. While these processes
were under way the component bodies would be radiating heat and
growing smaller, and their spectra would be changing into the
more advanced types. We can not hope to watch such changes as
they occur, but we can, I think, find abundant illustrations of
these processes in the double stars. I have given reasons for
believing that one star in every two and one half, as a minimum
proportion, is not the single star which it appears to be to
the eye or in the telescope, but is a system of two or more
suns in mutual revolution. The formation of double stars,
therefore, is not a sporadic process: it is one of the
straightforward results of the evolutionary process.