Rotation of the Sun and Planets—Saturn’s Rings—Periods of the Rotation
of the Moon and other Satellites equal to the Periods of their
Revolutions—Form of Lunar Spheroid—Libration, Aspect, and Constitution
of the Moon—Rotation of Jupiter’s Satellites.
THE oblate form of several of the planets indicates rotatory motion.
This has been confirmed in most cases by tracing spots on their surface,
by which their poles and times of rotation have been determined. The
rotation of Mercury is unknown, on account of his proximity to the sun;
that of the new planets has not yet been ascertained. The sun revolves
in twenty-five days and ten hours about an axis which is directed
towards a point half-way between the pole-star and α of Lyra, the plane
of rotation being inclined by 7° 30ʹ, or a little more than seven
degrees, to the plane of the ecliptic: it may therefore be concluded
that the sun’s mass is a spheroid, flattened at the poles. From the
rotation of the sun, there was every reason to believe that he has a
progressive motion in space, a circumstance which is confirmed by
observation. But, in consequence of the reaction of the planets, he
describes a small irregular orbit about the centre of gravity of the
system, never deviating from his position by more than twice his own
diameter, or a little more than seven times the distance of the moon
from the earth. The sun and all his attendants rotate from west to east,
on axes that remain nearly parallel to themselves (N. 140) in every
point of their orbit, and with angular velocities that are sensibly
uniform (N. 141). Although the uniformity in the direction of their
rotation is a circumstance hitherto unaccounted for in the economy of
nature, yet, from the design and adaptation of every other part to the
perfection of the whole, a coincidence so remarkable cannot be
accidental. And, as the revolutions of the planets and satellites are
also from west to east, it is evident that both must have arisen from
the primitive cause which determined the planetary motions.[6] Indeed,
La Place has computed the probability to be as four millions to one that
all the motions of the planets, both of rotation and revolution, were at
once imparted by an original common cause, but of which we know neither
the nature nor the epoch.
The larger planets rotate in shorter periods than the smaller planets
and the earth. Their compression is consequently greater, and the action
of the sun and of their satellites occasions a nutation in their axes
and a precession of their equinoxes (N. 147) similar to that which
obtains in the terrestrial spheroid, from the attraction of the sun and
moon on the prominent matter at the equator. Jupiter revolves in less
than ten hours round an axis at right angles to certain dark belts or
bands, which always cross his equator. (See Plate 1.) This rapid
rotation occasions a very great compression in his form. His equatorial
axis exceeds his polar axis by 6000 miles, whereas the difference in the
axes of the earth is only about twenty-six and a half. It is an evident
consequence of Kepler’s law of the squares of the periodic times of the
planets being as the cubes of the major axes of their orbits, that the
heavenly bodies move slower the farther they are from the sun. In
comparing the periods of the revolutions of Jupiter and Saturn with the
times of their rotation, it appears that a year of Jupiter contains
nearly ten thousand of his days, and that of Saturn about thirty
thousand Saturnian days.
The appearance of Saturn is unparalleled in the system of the world. He
is a spheroid nearly 1000 times larger than the earth, surrounded by a
ring even brighter than himself, which always remains suspended in the
plane of his equator: and, viewed with a very good telescope, it is
found to consist of two concentric rings, divided by a dark band. The
exterior ring, as seen through Mr. Lassell’s great equatorial at Malta,
has a dark-striped band through the centre, and is altogether less
bright than the interior ring, one half of which is extremely brilliant;
while the interior half is shaded in rings like the seats in an
amphitheatre. Mr. Lassell made the remarkable discovery of a dark
transparent ring, whose edge coincides with the inner edge of the
interior ring, and which occupies about half the space between it and
Saturn. He compares it to a band of dark-coloured crape drawn across a
portion of the disc of the planet, and the part projected upon the blue
sky is also transparent. At the time these observations were made at
Malta, Captain Jacob discovered the transparent ring at Madras. It is
conjectured to be fluid; even the luminous rings cannot be very dense,
since the density of Saturn himself is known to be less than the eighth
part of that of the earth. A transit of the ring across a star might
reveal something concerning this wonderful object. The ball of Saturn is
striped by belts of different colours. At the time of these observations
the part above the ring was bright white; at his equator there was a
ruddy belt divided in two, above which were belts of a bluish green
alternately dark and light, while at the pole there was a circular space
of a pale colour. (See Plate 2.) The mean distance of the interior part
of the double ring from the surface of the planet is about 22,240 miles,
it is no less than 33,360 miles broad, but, by the estimation of Sir
John Herschel, its thickness does not much exceed 100 miles, so that it
appears like a plane. By the laws of mechanics, it is impossible that
this body can retain its position by the adhesion of its particles
alone. It must necessarily revolve with a velocity that will generate a
centrifugal force sufficient to balance the attraction of Saturn.
Observation confirms the truth of these principles, showing that the
rings rotate from west to east about the planet in ten hours and a half,
which is nearly the time a satellite would take to revolve about Saturn
at the same distance. Their plane is inclined to the ecliptic, at an
angle of 28° 10ʹ 44ʺ·5; in consequence of this obliquity of position,
they always appear elliptical to us, but with an excentricity so
variable as even to be occasionally like a straight line drawn across
the planet. In the beginning of October, 1832, the plane of the rings
passed through the centre of the earth; in that position they are only
visible with very superior instruments, and appear like a fine line
across the disc of Saturn. About the middle of December, in the same
year, the rings became invisible, with ordinary instruments, on account
of their plane passing through the sun. In the end of April, 1833, the
rings vanished a second time, and reappeared in June of that year.
Similar phenomena will occur as often as Saturn has the same longitude
with either node of his rings. Each side of these rings has alternately
fifteen years of sunshine and fifteen years of darkness.
It is a singular result of theory, that the rings could not maintain
their stability of rotation if they were everywhere of uniform
thickness; for the smallest disturbance would destroy the equilibrium,
which would become more and more deranged, till, at last, they would be
precipitated on the surface of the planet. The rings of Saturn must
therefore be irregular solids, of unequal breadth in different parts of
the circumference, so that their centres of gravity do not coincide with
the centres of their figures. Professor Struve has also discovered that
the centre of the rings is not concentric with the centre of Saturn. The
interval between the outer edge of the globe of the planet and the outer
edge of the rings on one side is 11ʺ·272, and, on the other side, the
interval is 11ʺ·390, consequently there is an excentricity of the globe
in the rings of 0ʺ·215. If the rings obeyed different forces, they would
not remain in the same plane, but the powerful attraction of Saturn
always maintains them and his satellites in the plane of his equator.
The rings, by their mutual action, and that of the sun and satellites,
must oscillate about the centre of Saturn, and produce phenomena of
light and shadow whose periods extend to many years. According to M.
Bessel the mass of Saturn’s ring is equal to the 1/118 part of that of
the planet.
The periods of rotation of the moon and the other satellites are equal
to the times of their revolutions, consequently these bodies always turn
the same face to their primaries. However, as the mean motion of the
moon is subject to a secular inequality, which will ultimately amount to
many circumferences (N. 108), if the rotation of the moon were perfectly
uniform and not affected by the same inequalities, it would cease
exactly to counterbalance the motion of revolution; and the moon, in the
course of ages, would successively and gradually discover every point of
her surface to the earth. But theory proves that this never can happen;
for the rotation of the moon, though it does not partake of the periodic
inequalities of her revolution, is affected by the same secular
variations, so that her motions of rotation and revolution round the
earth will always balance each other, and remain equal. This
circumstance arises from the form of the lunar spheroid, which has three
principal axes of different lengths at right angles to each other.
The moon is flattened at her poles from her centrifugal force, therefore
her polar axis is the least. The other two are in the plane of her
equator, but that directed towards the earth is the greatest (N. 142).
The attraction of the earth, as if it had drawn out that part of the
moon’s equator, constantly brings the greatest axis, and consequently
the same hemisphere, towards us, which makes her rotation participate in
the secular variations of her mean motion of revolution. Even if the
angular velocities of rotation and revolution had not been nicely
balanced in the beginning of the moon’s motion, the attraction of the
earth would have recalled the greatest axis to the direction of the line
joining the centres of the moon and earth; so that it would have
vibrated on each side of that line in the same manner as a pendulum
oscillates on each side of the vertical from the influence of
gravitation. No such libration is perceptible; and, as the smallest
disturbance would make it evident, it is clear that, if the moon has
ever been touched by a comet, the mass of the latter must have been
extremely small. If it had been only the hundred thousandth part of that
of the earth, it would have rendered the libration sensible. According
to analysis, a similar libration exists in the motions of Jupiter’s
satellites, which still remains insensible to observation, and yet the
comet of 1770 passed twice through the midst of them.
The moon, it is true, is liable to librations depending upon the
position of the spectator. At her rising, part of the western edge of
her disc is visible, which is invisible at her setting, and the contrary
takes place with regard to her eastern edge. There are also librations
arising from the relative positions of the earth and moon in their
respective orbits; but, as they are only optical appearances, one
hemisphere will be eternally concealed from the earth. For the same
reason the earth, which must be so splendid an object to one lunar
hemisphere, will be for ever veiled from the other. On account of these
circumstances, the remoter hemisphere of the moon has its day a
fortnight long, and a night of the same duration, not even enlightened
by a moon, while the favoured side is illuminated by the reflection of
the earth during its long night. A planet exhibiting a surface thirteen
times larger than that of the moon, with all the varieties of clouds,
land, and water, coming successively into view, must be a splendid
object to a lunar traveller in a journey to his antipodes. The great
height of the lunar mountains probably has a considerable influence on
the phenomena of her motion, the more so as her compression is small,
and her mass considerable. In the curve passing through the poles, and
that diameter of the moon which always points to the earth, nature has
furnished a permanent meridian, to which the different spots on her
surface have been referred, and their positions are determined with as
much accuracy as those of many of the most remarkable places on the
surface of our globe. According to the observations of Professor Secchi
at Rome, the mountains of the moon are mostly volcanic and of three
kinds. The first and oldest have their borders obliterated, so that they
look like deep wells; the second, which are of an intermediate class,
have elevated, and, for the most part, regular unbroken edges, with the
ground around them raised to a prodigious extent in proportion to the
size of the volcano, with generally an insulated rock in the centre of
the crater. The third, and most recent class, are very small, and seem
to be the last effort of the expiring volcanic force, which is probably
now extinct.
The distance and minuteness of Jupiter’s satellites render it extremely
difficult to ascertain their rotation. It was, however, accomplished by
Sir William Herschel from their relative brightness. He observed that
they alternately exceed each other in brilliancy, and, by comparing the
maxima and minima of their illumination with their positions relatively
to the sun and to their primary, he found that, like the moon, the time
of their rotation is equal to the period of their revolution about
Jupiter. Miraldi was led to the same conclusion with regard to the
fourth satellite, from the motion of a spot on its surface.