periodic times of Mercury and the earth are so adjusted to each other,
that Mercury performs nearly twenty-nine revolutions while the earth
performs seven. If, therefore, the two bodies meet at the node in any
given year, seven years afterwards they will meet nearly at the same
node, and a transit may take place, accordingly, at intervals of seven
years. But fifty-four revolutions of Mercury correspond still nearer to
thirteen revolutions of the earth; and therefore a transit is still more
probable after intervals of thirteen years. At intervals of thirty-three
years, transits of Mercury are exceedingly probable, because in that
time Mercury makes almost exactly one hundred and thirty-seven
revolutions. Intermediate transits, however, may occur at the other
node. Thus, transits of Mercury happened at the ascending node in 1815,
and 1822, at intervals of seven years; and at the descending node in
1832, which will return in 1845, after thirteen years.
Transits of Venus are events of very unfrequent occurrence. Eight
revolutions of the earth are completed in nearly the same time as
thirteen revolutions of Venus; and hence two transits of Venus may occur
after an interval of eight years, as was the case at the last return of
the phenomenon, one transit having occurred in 1761, and another in
1769. But if a transit does not happen after eight years, it will not
happen at the same node, until an interval of two hundred and
thirty-five years: but intermediate transits may occur at the other
node. The next transit of Venus will take place in 1874, being two
hundred and thirty-five years after the first that was ever _observed_,
which occurred in 1639. This was seen, for the first time by mortal
eyes, by two youthful English astronomers, Horrox and Crabtree. Horrox
was a young man of extraordinary promise, and indicated early talents
for practical astronomy, which augured the highest eminence; but he died
in the twenty-third year of his age. He was only twenty when the transit
appeared, and he had made the calculations and observations, by which he
was enabled to anticipate its arrival several years before. At the
approach of the desired time for observing the transit, he received the
sun's image through a telescope in a dark room upon a white piece of
paper, and after waiting many hours with great impatience, (as his
calculation did not lead him to a knowledge of the precise time of the
occurrence,) at last, on the twenty-fourth of November, 1639, old style,
at three and a quarter hours past twelve, just as he returned from
church, he had the pleasure to find a large round spot near the limb of
the sun's image. It moved slowly across the sun's disk, but had not
entirely left it when the sun set.
The great interest attached by astronomers to a transit of Venus arises
from its furnishing the most accurate means in our power of determining
the _sun's horizontal parallax_,--an element of great importance, since
it leads us to a knowledge of the distance of the earth from the sun,
which again affords the means of estimating the distances of all the
other planets, and possibly, of the fixed stars. Hence, in 1769, great
efforts were made throughout the civilized world, under the patronage of
different governments, to observe this phenomenon under circumstances
the most favorable for determining the parallax of the sun.
The common methods of finding the parallax of a heavenly body cannot be
relied on to a greater degree of accuracy than four seconds. In the case
of the moon, whose greatest parallax amounts to about one degree, this
deviation from absolute accuracy is not very material; but it amounts to
nearly half the entire parallax of the sun.
If the sun and Venus were equally distant from us, they would be equally
affected by parallax, as viewed by spectators in different parts of the
earth, and hence their _relative_ situation would not be altered by it;
but since Venus, at the inferior conjunction, is only about one third as
far off as the sun, her parallax is proportionally greater, and
therefore spectators at distant points will see Venus projected on
different parts of the solar disk, as the planet traverses the disk.
Astronomers avail themselves of this circumstance to ascertain the sun's
horizontal parallax, which they are enabled to do by comparing it with
that of Venus, in a manner which, without a knowledge of trigonometry,
you will not fully understand. In order to make the difference in the
apparent places of Venus on the sun's disk as great as possible, very
distant places are selected for observation. Thus, in the transits of
1761 and 1769, several of the European governments fitted out expensive
expeditions to parts of the earth remote from each other. For this
purpose, the celebrated Captain Cook, in 1769, went to the South Pacific
Ocean, and observed the transit at the island of Otaheite, while others
went to Lapland, for the same purpose, and others still, to many other
parts of the globe. Thus, suppose two observers took their stations on
opposite sides of the earth, as at A, and B, Fig. 57, page 242; at A,
the planet V would be seen on the sun's disk at _a_, while at B, it
would be seen at _b_.
The appearance of Venus on the sun's disk being that of a well-defined
black spot, and the exactness with which the moment of external or
internal contact may be determined, are circumstances favorable to the
exactness of the result; and astronomers repose so much confidence in
the estimation of the sun's horizontal parallax, as derived from
observations on the transit of 1769, that this important element is
thought to be ascertained within one tenth of a second. The general
result of all these observations gives the sun's horizontal parallax
eight seconds and six tenths,--a result which shows at once that the sun
must be a great way off, since the semidiameter of the earth, a line
nearly four thousand miles in length, would appear at the sun under an
angle less than one four hundredth of a degree. During the transits of
Venus over the sun's disk, in 1761 and 1769, a sort of penumbral light
was observed around the planet, by several astronomers, which was
thought to indicate an _atmosphere_. This appearance was particularly
observable while the planet was coming on or going off the solar disk.
The total immersion and emersion were not instantaneous; but as two
drops of water, when about to separate, form a ligament between them, so
there was a dark shade stretched out between Venus and the sun; and when
the ligament broke, the planet seemed to have got about an eighth part
of her diameter from the limb of the sun. The various accounts of the
two transits abound with remarks like these, which indicate the
existence of an atmosphere about Venus of nearly the density and extent
of the earth's atmosphere. Similar proofs of the existence of an
atmosphere around this planet are derived from appearances of twilight.
[Illustration Fig. 57.]
The elder astronomers imagined that they had discovered a _satellite_
accompanying Venus in her transit. If Venus had in reality any
satellite, the fact would be obvious at her transits, as, in some of
them at least, it is probable that the satellite would be projected near
the primary on the sun's disk; but later astronomers have searched in
vain for any appearances of the kind, and the inference is, that former
astronomers were deceived by some optical illusion.
FOOTNOTE:
[12] You will recollect that the sun is said to be at the node, when the
places of the node and the sun are both projected, by a spectator on the
earth, upon the same part of the heavens.
LETTER XXI.
SUPERIOR PLANETS: MARS, JUPITER, SATURN, AND URANUS.
"With what an awful, world-revolving power,
Were first the unwieldy planets launched along
The illimitable void! There to remain
Amidst the flux of many thousand years,
That oft has swept the toiling race of men,
And all their labored monuments, away."--_Thomson._
MERCURY AND VENUS, as we have seen, are always observed near the sun,
and from this circumstance, as well as from the changes of magnitude and
form which they undergo, we know that they have their orbits within that
of the earth, and hence we call them _inferior_ planets. On the other
hand, Mars, Jupiter, Saturn, and Uranus, exhibit such appearances, at
different times, as show that they revolve around the sun at a greater
distance than the earth, and hence we denominate them _superior_
planets. We know that they never come between us and the sun, because
they never undergo those changes which Mercury and Venus, as well as the
moon, sustain, in consequence of their coming into such a position.
They, however, wander to the greatest angular distance from the sun,
being sometimes seen one hundred and eighty degrees from him, so as to
rise when the sun sets. All these different appearances must naturally
result from their orbits' being exterior to that of the earth, as will
be evident from the following representation. Let E, Fig. 58, page 244,
be the earth, and M, one of the superior planets, Mars, for example,
each body being seen in its path around the sun. At M, the planet would
be in opposition to the sun, like the moon at the full; at Q and Q´, it
would be seen ninety degrees off, or in quadrature; and at M´, in
conjunction. We know, however, that this must be a superior and not an
inferior conjunction, for the illuminated disk is still turned towards
us; whereas, if it came between us and the sun, like Mercury, or Venus,
in its inferior conjunction, its dark side would be presented to us.
[Illustration Fig. 58.]
The superior planets do not exhibit to the telescope different phases,
but, with a single exception, they always present the side that is
turned towards the earth fully enlightened. This is owing to their great
distance from the earth; for were the spectator to stand upon the sun,
he would of course always have the illuminated side of each of the
planets turned towards him; but so distant are all the superior planets,
except Mars, that they are viewed by us very nearly, in the same manner
as they would be if we actually stood on the sun. Mars, however, is
sufficiently near to appear somewhat gibbous when at or near one of its
quadratures. Thus, when the planet is at Q, it is plain that, of the
hemisphere that is turned towards the earth, a small part is
unilluminated.
Mars is a small planet, his diameter being only about half that of the
earth, or four thousand two hundred miles. He also, at times, comes
nearer to the earth than any other planet, except Venus. His _mean_
distance from the sun is one hundred and forty-two millions of miles;
but his orbit is so elliptical, that his distance varies much in
different parts of his revolution. Mars is always very near the
ecliptic, never varying from it more than two degrees. He is
distinguished from all the planets by his deep red color, and fiery
aspect; but his brightness and apparent magnitude vary much, at
different times, being sometimes nearer to us than at others by the
whole diameter of the earth's orbit; that is, by about one hundred and
ninety millions of miles. When Mars is on the same side of the sun with
the earth, or at his opposition, he comes within forty-seven millions of
miles of the earth, and, rising about the time the sun sets, surprises
us by his magnitude and splendor; but when he passes to the other side
of the sun, to his superior conjunction, he dwindles to the appearance
of a small star, being then two hundred and thirty-seven millions of
miles from us. Thus, let M, Fig, 58, represent Mars in opposition, and
M´, in the superior conjunction, while E represents the earth. It is
obvious that, in the former situation, the planet must be nearer to the
earth than in the latter, by the whole diameter of the earth's orbit.
When viewed with a powerful telescope, the surface of Mars appears
diversified with numerous varieties of light and shade. The region
around the poles is marked by white spots, (see Fig. 56, page 237,)
which vary their appearances with the changes of seasons in the planet.
Hence Dr. Herschel conjectured that they were owing to ice and snow,
which alternately accumulate and melt away, according as it is Winter or
Summer, in that region. They are greatest and most conspicuous when that
part of the planet has just emerged from a long Winter, and they
gradually waste away, as they are exposed to the solar heat. Fig. 56,
represents the planet, as exhibited, under the most favorable
circumstances, to a powerful telescope, at the time when its gibbous
form is strikingly obvious. It has been common to ascribe the ruddy
light of Mars to an extensive and dense atmosphere, which was said to be
distinctly indicated by the gradual diminution of light observed in a
star, as it approaches very near to the planet, in undergoing an
occultation; but more recent observations afford no such evidence of an
atmosphere.
By observations on the spots, we learn that Mars revolves on his axis in
very nearly the same time with the earth, (twenty-four hours thirty-nine
minutes twenty-one seconds and three tenths,) and that the inclination
of his axis to that of his orbit is also nearly the same, being thirty
degrees eighteen minutes ten seconds and eight tenths. Hence the changes
of day and night must be nearly the same there as here, and the seasons
also very similar to ours. Since, however, the distance of Mars from the
sun is one hundred and forty-two while that of the earth is only
ninety-five millions of miles, the sun will appear more than twice as
small on that planet as on ours, (see Fig. 53, page 236,) and its light
and heat will be diminished in the same proportion. Only the equatorial
regions, therefore, will be suitable for the existence of animals and
vegetables.
The earth will be seen from Mars as an inferior planet, always near the
sun, presenting appearances similar, in many respects, to those which
Venus presents to us. It will be to that planet the evening and morning
star, sung by their poets (if poets they have) with a like enthusiasm.
The moon will attend the earth as a little star, being never seen
further from her side than about the diameter under which we view the
moon. To the telescope, the earth will exhibit phases similar to those
of Venus; and, finally, she will, at long intervals, make her transits
over the solar disk. Mean-while, Venus will stand to Mars in a relation
similar to that of Mercury [Illustration Figures 59, 60. JUPITER AND
SATURN.] to us, revealing herself only when at the periods of her
greatest elongation, and at all other times hiding herself within the
solar blaze. Mercury will never be visible to an inhabitant of Mars.
Jupiter is distinguished from all the other planets by his great
_magnitude_. His diameter is eighty-nine thousand miles, and his volume
one thousand two hundred and eighty times that of the earth. His figure
is strikingly spheroidal, the equatorial being more than six thousand
miles longer than the polar diameter. Such a figure might naturally be
expected from the rapidity of his diurnal rotation, which is
accomplished in about ten hours. A place on the equator of Jupiter must
turn twenty-seven times as fast as on the terrestrial equator. The
distance of Jupiter from the sun is nearly four hundred and ninety
millions of miles, and his revolution around the sun occupies nearly
twelve years. Every thing appertaining to Jupiter is on a grand scale. A
world in itself, equal in dimensions to twelve hundred and eighty of
ours; the whole firmament rolling round it in the short space of ten
hours, a movement so rapid that the eye could probably perceive the
heavenly bodies to change their places every moment; its year dragging
out a length of more than four thousand days, and more than ten thousand
of its own days, while its nocturnal skies are lighted up with four
brilliant moons;--these are some of the peculiarities which characterize
this magnificent planet.
The view of Jupiter through a good telescope is one of the most splendid
and interesting spectacles in astronomy. The disk expands into a large
and bright orb, like the full moon; the spheroidal figure which theory
assigns to revolving spheres, especially to those which turn with great
velocity, is here palpably exhibited to the eye; across the disk,
arranged in parallel stripes, are discerned several dusky bands, called
_belts_; and four bright satellites, always in attendance, and ever
varying their positions, compose a splendid retinue. Indeed, astronomers
gaze with peculiar interest on Jupiter and his moons, as affording a
miniature representation of the whole solar system, repeating, on a
smaller scale, the same revolutions, and exemplifying more within the
compass of our observation, the same laws as regulate the entire
assemblage of sun and planets. Figure 59, facing page 247, gives a
correct view of Jupiter, as exhibited to a powerful telescope in a clear
evening. You will remark his flattened or spheroidal figure, the belts
which appear in parallel stripes across his disk, and the four
satellites, that are seen like little stars in a straight line with the
equator of the planet.
The _belts of Jupiter_ are variable in their number and dimensions. With
the smaller telescopes only one or two are seen, and those across the
equatorial regions; but with more powerful instruments, the number is
increased, covering a large part of the entire disk. Different opinions
have been entertained by astronomers respecting the cause of these
belts; but they have generally been regarded as clouds formed in the
atmosphere of the planet, agitated by winds, as is indicated by their
frequent changes, and made to assume the form of belts parallel to the
equator, like currents that circulate around our globe. Sir John
Herschel supposes that the belts are not ranges of clouds, but portions
of the planet itself, brought into view by the removal of clouds and
mists, that exist in the atmosphere of the planet, through which are
openings made by currents circulating around Jupiter.
The _satellites of Jupiter_ may be seen with a telescope of very
moderate powers. Even a common spyglass will enable us to discern them.
Indeed, one or two of them have been occasionally seen with the naked
eye. In the largest telescopes they severally appear as bright as
Sirius. With such an instrument, the view of Jupiter, with his moons and
belts, is truly a magnificent spectacle. As the orbits of the satellites
do not deviate far from the plane of the ecliptic, and but little from
the equator of the planet, they are usually seen in nearly a straight
line with each other, extending across the central part of the disk.
(See Fig. 59, facing page 247.)
Jupiter and his satellites exhibit in miniature all the phenomena of the
solar system. The satellites perform, around their primary, revolutions
very analogous to those which the planets perform around the sun,
having, in like manner, motions alternately direct, stationary, and
retrograde. They are all, with one exception, a little larger than the
moon; and the second satellite, which is the smallest, is nearly as
large as the moon, being two thousand and sixty-eight miles in diameter.
They are all very small compared with the primary, the largest being
only one twenty-sixth part of the primary. The outermost satellite
extends to the distance from the planet of fourteen times his diameter.
The whole system, therefore, occupies a region of space more than one
million miles in breadth. Rapidity of motion, as well as greatness of
dimensions, is characteristic of the system of Jupiter. I have already
mentioned that the planet itself has a motion on its own axis much
swifter than that of the earth, and the motions of the satellites are
also much more rapid than that of the moon. The innermost, which is a
little further off than the moon is from the earth, goes round its
primary in about a day and three quarters; and the outermost occupies
less than seventeen days.
The orbits of the satellites are nearly or quite circular, and deviate
but little from the plane of the planet's equator, and of course are but
slightly inclined to the plane of his orbit. They are therefore in a
similar situation with respect to Jupiter, as the moon would be with
respect to the earth, if her orbit nearly coincided with the ecliptic,
in which case, she would undergo an eclipse at every opposition. The
eclipses of Jupiter's satellites, in their general circumstances, are
perfectly analogous to those of the moon, but in their details they
differ in several particulars. Owing to the much greater distance of
Jupiter from the sun, and its greater magnitude, the cone of its shadow
is much longer and larger than that of the earth. On this account, as
well as on account of the little inclination of their orbit to that of
the primary, the three inner satellites of Jupiter pass through his
shadow, and are totally eclipsed, at every revolution. The fourth
satellite, owing to the greater inclination of its orbit, sometimes,
though rarely, escapes eclipse, and sometimes merely grazes the limits
of the shadow, or suffers a partial eclipse. These eclipses, moreover,
are not seen, as is the case with those of the moon, from the centre of
their motion, but from a remote station, and one whose situation with
respect to the line of the shadow is variable. This makes no difference
in the _times_ of the eclipses, but it makes a very great one in their
visibility, and in their apparent situations with respect to the planet
at the moment of their entering or quitting the shadow.
[Illustration Fig. 61.]
The eclipses of Jupiter's satellites present some curious phenomena,
which you will easily understand by studying the following diagram. Let
A, B, C, D, Fig. 61, represent the earth in different parts of its
orbit; J, Jupiter, in his orbit, surrounded by his four satellites, the
orbits of which are marked 1, 2, 3, 4. At _a_, the first satellite
enters the shadow of the planet, emerges from it at _b_, and advances to
its greatest elongation at _c_. The other satellites traverse the shadow
in a similar manner. The apparent place, with respect to the planet, at
which these eclipses will be seen to occur, will be altered by the
position the earth happens at that moment to have in its orbit; but
their appearances for any given night, as exhibited at Greenwich, are
calculated and accurately laid down in the Nautical Almanac.
When one of the satellites is passing between Jupiter and the sun, it
casts its shadow on the primary, as the moon casts its shadow on the
earth in a solar eclipse. We see with the telescope the shadow
traversing the disk. Sometimes, the satellite itself is seen projected
on the disk; but, being illuminated as well as the primary, it is not so
easily distinguished as Venus or Mercury, when seen on the sun's disk in
one of their transits, since these bodies have their dark sides turned
towards us; but the satellite is illuminated by the sun, as well as the
primary, and therefore is not easily distinguishable from it.
The eclipses of Jupiter's satellites have been studied with great
attention by astronomers, on account of their affording one of the
easiest methods of determining the _longitude_. On this subject, Sir
John Herschel remarks: "The discovery of Jupiter's satellites by
Galileo, which was one of the first fruits of the invention of the
telescope, forms one of the most memorable epochs in the history of
astronomy. The first astronomical solution of the problem of 'the
longitude,'--the most important problem for the interests of mankind
that has ever been brought under the dominion of strict scientific
principles,--dates immediately from this discovery. The final and
conclusive establishment of the Copernican system of astronomy may also
be considered as referable to the discovery and study of this exquisite
miniature system, in which the laws of the planetary motions, as
ascertained by Kepler, and especially that which connects their periods
and distances, were speedily traced, and found to be satisfactorily
maintained."