(his satellites) by reference to a fixed star, I have thought well
to present to the notice of astronomers, in order that any one may
be able to understand from them that the movements of these planets
(Jupiter’s satellites) both in longitude and in latitude agree exactly
with the motions [of Jupiter] which are extracted from tables.
These are my observations upon the four Medicean planets, recently
discovered for the first time by me; and although it is not yet
permitted me to deduce by calculation from these observations the
orbits of these bodies, yet I may be allowed to make some statements,
based upon them, well worthy of attention.
[Sidenote: Deductions from the previous observations concerning the
orbits and periods of Jupiter’s satellites.]
And, in the first place, since they are sometimes behind, sometimes
before Jupiter, at like distances, and withdraw from this planet
towards the east and towards the west only within very narrow limits of
divergence, and since they accompany this planet alike when its motion
is retrograde and direct, it can be a matter of doubt to no one that
they perform their revolutions about this planet, while at the same
time they all accomplish together orbits of twelve years’ length about
the centre of the world. Moreover, they revolve in unequal circles,
which is evidently the conclusion to be drawn from the fact that I
have never been permitted to see two satellites in conjunction when
their distance from Jupiter was great, whereas near Jupiter two, three,
and sometimes all (four), have been found closely packed together.
Moreover, it may be detected that the revolutions of the satellites
which describe the smallest circles round Jupiter are the most rapid,
for the satellites nearest to Jupiter are often to be seen in the east,
when the day before they have appeared in the west, and contrariwise.
Also the satellite moving in the greatest orbit seems to me, after
carefully weighing the occasions of its returning to positions
previously noticed, to have a periodic time of half a month.[17]
Besides, we have a notable and splendid argument to remove the scruples
of those who can tolerate the revolution of the planets round the Sun
in the Copernican system, yet are so disturbed by the motion of one
Moon about the Earth, while both accomplish an orbit of a year’s length
about the Sun, that they consider that this theory of the constitution
of the universe must be upset as impossible; for now we have not one
planet only revolving about another, while both traverse a vast orbit
about the Sun, but our sense of sight presents to us four satellites
circling about Jupiter, like the Moon about the Earth, while the whole
system travels over a mighty orbit about the Sun in the space of twelve
years.
[17] In the edition of Galileo’s works published at Florence,
1854, there are given the tables of the hourly movements of the
satellites of Jupiter, from which Galileo determined their periods
of revolution. In the beginning of his treatise on floating bodies,
_Discorso intorno i Galleggianti_, 1611-12, Galileo gives the times
of rotation as approximately, (i.) 1 d. 18-1/2 h.; (ii.) 3 d.
13-1/3 h.; (iii.) 7 d. 4 h.; (iv.) 16 d. 18 h.; he also published
configurations of the satellites calculated for March, April,
and a part of May 1613. The periodic times of the satellites, as
corrected by later observers, are, (i.) 1 d. 18 h. 28 m.; (ii.) 3
d. 13 h. 15 m.; (iii.) 7 d. 3 h. 43 m.; (iv.) 16 d. 16 h. 32 m.
[Sidenote: Explanation of the variations in brightness of Jupiter’s
satellites.]
Lastly, I must not pass over the consideration of the reason why it
happens that the Medicean stars, in performing very small revolutions
about Jupiter, seem sometimes more than twice as large as at other
times. We can by no means look for the explanation in the mists of the
Earth’s atmosphere, for they appear increased or diminished, while the
discs of Jupiter and neighbouring fixed stars are seen quite unaltered.
That they approach and recede from the Earth at the points of their
revolutions nearest to and furthest from the Earth to such an extent
as to account for so great changes seems altogether untenable, for a
strict circular motion can by no means show those phenomena; and an
elliptical motion (which in this case would be nearly rectilinear)
seems to be both untenable and by no means in harmony with the
phenomena observed. But I gladly publish the explanation which has
occurred to me upon this subject, and submit it to the judgment and
criticism of all true philosophers. It is certain that when atmospheric
mists intervene the Sun and Moon appear larger, but the fixed stars and
planets less than they really are; hence the former luminaries, when
near the horizon, are larger than at other times, but stars appear
smaller, and are frequently scarcely visible; also they are still more
diminished if those mists are bathed in light; so stars appear very
small by day and in the twilight, but the Moon does not appear so,
as I have previously remarked. Moreover, it is certain that not only
the Earth, but also the Moon, has its own vaporous sphere enveloping
it, for the reasons which I have previously mentioned, and especially
for those which shall be stated more fully in my _System_; and we may
consistently decide that the same is true with regard to the rest of
the planets; so that it seems to be by no means an untenable opinion
to place round Jupiter also an atmosphere denser than the rest of the
ether,[18] about which, like the Moon about the sphere of the elements,
the Medicean planets (Jupiter’s satellites) revolve; and that by the
intervention of this atmosphere they appear smaller when they are in
apogee; but when in perigee, through the absence or attenuation of
that atmosphere, they appear larger. Want of time prevents my going
further into these matters; my readers may expect further remarks upon
these subjects in a short time.
[18] Modern astronomers agree in assigning an atmosphere to
Jupiter, but consider it not extensive enough to affect the
brightness of the satellites.—(WEBB, _Celestial Objects for Common
Telescopes_.) Their absolute magnitudes are different, and their
surfaces have been observed to be obscured by spots, which may
account for the variations of their brightness. These spots, like
the lunar spots, are probably due to variations of reflective
power at different parts of their surfaces, for as they always
turn the same face to Jupiter, they present different portions of
their surfaces to us periodically, and it has been ascertained
by observation that “these fluctuations in their brightness are
periodical, depending on their position with respect to the
Sun.”—(HERSCHEL, _Outlines of Astronomy_; ARAGO, _Astronomie
Populaire_, 1854.)
_Original Configurations of Jupiter’s Satellites observed by Galileo in
the months of January, February, and March 1610, and published with the
1st edition of his book_ Sidereus Nuncius, _Venice, 1610._
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FIG. | DATE. | EAST. | WEST.
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1 | Jan. 7 |
| | • • ◯ •
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2 | 8 |
| | ◯ • • •
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3 | 10 |
| | • • ◯
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4 | 11 |
| | • • ◯
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5 | 12 |
| | • •◯ •
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6 | 13 |
| | • ◯ • ⠁ •
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7 | 15 | •
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8 | 15 |
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9 | 16 |
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10 | 17 |
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11 | Jan. 17 | • •
| | • ◯
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12 | 18 |
| | • ◯ •
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13 | 19 |
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14 | 19 |
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15 | 20 |
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16 | 20 |
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17 | 20 | • ◯ • •
| | •
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18 | 21 |
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19 | 22 | • ◯• •
| | •
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20 | 22 |
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21 | 23 |
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22 | 23 |
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23 | 24 | • • ◯
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24 | 25 |
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25 | 26 |
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26 | 26 | •
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27 | 27 |
| | • ◯
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28 | 30 | •
| | • ◯ •
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29 | 31 | •
| | • ◯ •
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30 | Jan. 31 | •
| | • ◯ •
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31 | Feb. 1 |
| | • • ◯ •
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32 | 2 |
| | • ◯ • •
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33 | 2 |
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34 | 3 |
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35 | 4 |
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36 | 4 |
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37 | 6 |
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38 | 7 |
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39 | 8 |
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40 | 9 |
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41 | 10 |
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42 | 11 |
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43 | 11 | •
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44 | 11 |
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45 | 12 |
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46 | 13 |
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47 | 15 |
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48 | 15 |
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49 | Feb. 15 |
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50 | 16 |
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51 | 17 |
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52 | 18 |
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53 | 18 |
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54 | 19 |
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55 | 21 |
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56 | 25 |
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57 | 26 |
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58 | 26 |
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59 | 26 | • ◯ • •
| | ⨀ Star.
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60 | 27 | • • ◯ • •
| | Star ⨀
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61 | 28 | • ◯ •
| | Star ⨀
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62 | 28 |
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63 | Mar. 1 | •
| | • • • ◯
| | Star ⨀
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64 | 2 | •
| | • ◯ •
| | Star ⨀
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A PART OF THE PREFACE TO
KEPLER’S DIOPTRICS
FORMING
_A CONTINUATION OF GALILEO’S
SIDEREAL MESSENGER._
In the preface to Kepler’s _Dioptrics_ there are introduced letters
of Galileo about the new and astonishing discoveries which he
had made in the heavens by the aid of the telescope since the
publication of his work, _The Sidereal Messenger_. The portion
of the preface which refers to Galileo, containing these letters
and Kepler’s remarks upon them, is added here, as continuing the
original account of Galileo’s astronomical discoveries.
_Extract from the Preface of Kepler’s Dioptrics. Augsburg, 1611._
[Sidenote: Kepler remarks on the importance of the application of the
telescope to astronomical investigations as indicated by Galileo’s
discoveries, published in his _Sidereal Messenger_.]
“_The Sidereal Messenger_” of Galileo has been for a long time in
everybody’s hands, also my “_Discussion_, such as it is, _with this
Messenger_,” and my _Brief Narrative_ in confirmation of Galileo’s
_Sidereal Messenger_, so any reader may briefly weigh the chief
points of that _Messenger_ and see the nature and the value of the
discoveries made by the aid of the telescope, the theory of which I
am intending to demonstrate in this treatise. Actual sight testified
that there is a certain bright heavenly body which we call the Moon.
It was demonstrated from the laws of optics that this body is round;
also Astronomy, by some arguments founded upon optics, had built
up the conclusion that its distance from the earth is about sixty
semi-diameters of the earth. Various spots showed themselves in that
body; and the result was a dubious opinion among a few philosophers,
derived from Hecatæus’ account of the stories about the island of the
Hyperboreans,[19] that the reflected images of mountains and valleys,
sea and land, were seen there; but now the telescope places all these
matters before our eyes in such a way that he must be an intellectual
coward who, while enjoying such a view, still thinks that the matter
is open to doubt. Nothing is more certain than that the southern
parts of the moon teem with mountains, very many in number, and vast
in size; and that the northern parts, inasmuch as they are lower,
receive in most extensive lakes the water flowing down from the south.
The conclusions which previously Pena published as disclosed by the
aid of optics, started indeed from certain slight supports, rather
than foundations, afforded by actual sight, but were proved by long
arguments depending one upon another, so that they might be assigned
to human reason rather than to sight; but now our very eyes, as if a
new door of heaven had been opened, are led to the view of matters once
hidden from them. But if it should please any one to exhaust the force
of reasoning upon these new observations, who does not see how far the
contemplation of nature will extend her boundaries, when we ask, “What
is the use of the tracts of mountains and valleys, and the very wide
expanse of seas in the moon?” and “May not some creature less noble
than man be imagined such as might inhabit those tracts?”
[19] Diodorus Siculus, ii. 47.
With no less certainty also do we decide by the use of this instrument
even that famous question, which, coeval with philosophy itself, is
disputed to this day by the noblest intellects—I mean, whether the
earth can move (as the theory of the Planets greatly requires) without
the overthrow of all bodies that have weight, or the confusion of the
motion of the elements? For if the earth were banished from the centre
of the universe, some fear lest the water should leave the orb of the
earth and flow to the centre of the universe; and yet we see that in
the moon, as well as in the earth, there is a quantity of moisture
occupying the sunken hollows of that globe; and although this orb
revolves actually in the ether, and outside the centres not merely
of the universe, but even of our earth, yet the mass of water in the
moon is not at all hindered from cleaving invariably to the orb of the
moon, and tending to the centre of the body to which it belongs. So,
by this instance of the phenomena of the moon, the science of optics
amends the received theory of mechanics, and confirms on this point
my introduction to my _Commentaries upon the Motions of the Planet
Mars_.[20]
[20] Kepler says in his introduction to his _Commentaries upon
the Motions of the Planet Mars_, that the theory of gravitation
depends on certain axioms, one of which is that “heavy bodies do
not tend to the centre of the universe, supposing the earth to be
placed there, because that point is the centre of the universe,
but because it is the centre of the earth. So, wherever the earth
be set, or whithersoever it be transported, heavy bodies have a
continual tendency to it.” Kepler’s object in this work was to
correct the methods for determining the apparent places of the
planets according to the three theories then current—the Ptolemaic,
the Copernican, and that of Tycho Brahe.
In 1593 the observed place of the planet Mars differed by nearly
5° from the place calculated for it. Kepler accordingly studied
the motions of this planet, and “by most laborious demonstrations
and discussions of many observations,” arrived at the conclusions
known as Kepler’s first and second laws; according to which the
Copernican system of eccentrics and epicycles was replaced by an
ellipse whose centre and eccentricity were the same as the centre
and eccentricity of the eccentric in the older method, and the Sun
therefore was in one of the foci. Also the motion of the planet in
its orbit was such that equal areas were described about the Sun by
the radius vector of the planet in equal times.—KEPLER, _Astronomia
Nova_ αἰτιολογητός (Prague), 1609.
The followers of the Samian philosophy (for I may use this epithet to
designate the philosophy originated by the Samians, Pythagoras and
Aristarchus) have a strong argument against the apparent immobility
of the earth provided in the phenomena of the moon. For we are taught
by optics that if any one of us was in the moon, to him the moon, his
abode, would seem quite immovable, but our earth and sun and all the
rest of the heavenly bodies movable; for the conclusions of sight are
thus related.
Pena has noticed how astronomers, using the principles of optics, have
by most laborious reasoning removed the Milky Way from the elementary
universe, where Aristotle had placed it, into the highest region of the
ether; but now, by the aid of the telescope lately invented, the very
eyes of astronomers are conducted straight to a thorough survey of the
substance of the Milky Way; and whoever enjoys this sight is compelled
to confess that the Milky Way is nothing else but a mass of extremely
small stars.
Again, up to this time the nature of nebulous stars had been entirely
unknown; but if the telescope be directed to one of such nebulous
balls, as Ptolemy calls them, it again shows, as in the case of the
Milky Way, three or four very bright stars clustered very close
together.
Again, who without this instrument would have believed that the number
of the fixed stars was ten times, or perhaps twenty times, more than
that which is given in Ptolemy’s description of the fixed stars? And
whence, pray, should we seek for conclusive evidence about the end or
boundary of this visible universe, proving that it is actually the
sphere of the fixed stars, and that there is nothing beyond, except
from this very discovery by the telescope of this multitude of fixed
stars, which is, as it were, the vaulting of the mobile universe?
Again, how greatly an astronomer would go wrong in determining the
magnitude of the fixed stars, except he should survey the stars all
over again with a telescope, also may be seen in Galileo’s treatise,
and we will also hereafter produce in proof a letter from a German
astronomer.
But no words can express my admiration of that chapter of the _Sidereal
Messenger_ where the story is told of the discovery, by the aid of
a very highly finished telescope, of another world, as it were, in
the planet Jupiter. The mind of the philosopher almost reels as he
considers that there is a vast orb, which is equal in mass to fourteen
orbs like the earth (unless on this point the telescope of Galileo
shall shortly reveal something more exact than the measurements of
Tycho Brahe) round which circle four moons, not unlike this moon of
ours; the slowest revolving in the space of fourteen of our days, as
Galileo has published; the next to this, by far the brightest of the
four, in the space of eight days, as I detected in last April and May;
the other two in still shorter periods. And here the reasoning of my
_Commentaries about the Planet Mars_, applied to a similar case,
induces me to conclude also that the actual orb of Jupiter rotates with
very great rapidity, most certainly faster than once in the space of
one of our days; so that this rotation of the mighty orb upon its own
axis is accompanied wherever it goes by the perpetual circuits of those
four moons. Moreover, this sun of ours, the common source of heat and
light for this terrestrial world as well as for that world of Jupiter,
which we consider to be of the angular magnitude of 30´ at most, there
scarcely subtends more than 6´ or 7´, and is found again in the same
position among the fixed stars, having completed the zodiac in the
interval, after a period of twelve of our years.[21] Accordingly, the
creatures which live on that orb of Jupiter, while they contemplate the
very swift courses of those four moons among the fixed stars, while
they behold them and the sun rising and setting day by day, would swear
by Jupiter-in-stone, like the Romans (for I have lately returned from
those parts), that their orb of Jupiter remains immovable in one spot,
and that the fixed stars and the sun, which are the bodies really at
rest, no less than those four moons of theirs, revolve round that abode
of theirs with manifold variety of motions. And from this instance
now, much more than before from the instance of the moon, any follower
of the Samian philosophy will learn what reply may be made to any one
objecting to the theory of the motion of the earth as absurd, and
alleging the evidence of our sight. O telescope, instrument of much
knowledge, more precious than any sceptre! Is not he who holds thee in
his hand made king and lord of the works of God? Truly
“All that is overhead, the mighty orbs
With all their motions, thou dost subjugate
To man’s intelligence.”
If there is any one in some degree friendly to Copernicus and the
lights of the Samian philosophy, who finds this difficulty only, that
he doubts how it can happen, supposing the earth to perform again and
again her course among the planets through the ethereal plains, that
the moon should keep so constantly by her side, like an inseparable
companion, and at the same time fly round and round the actual orb
of the earth, just like a faithful dog which goes round and round
his master on some journey, now running in front, now deviating to
this side or that, in ever-varying mazes, let him look at the planet
Jupiter, which, as this telescope shows, certainly carries in its train
not one such companion only, like the earth, as Copernicus showed, but
actually four, that never leave it, though all the time hastening each
in its own orbit.
[21] The degree of accuracy attained by Kepler and Galileo with
their imperfect instruments will be appreciated by comparing
these statements with the determinations of later astronomers.
Jupiter is about 1300 times the size of the Earth. Its diameter is
about 87,000 miles; time of rotation, 9 h. 55 m. 21 sec.; time of
revolution, 4333 days nearly. The angular diameter of the sun, seen
from Jupiter, is between 6´ and 7´. The times of revolution of the
four satellites are, as already given: (i.) 1 d. 18 h. 28 m., (ii.)
3 d. 13 h. 15 m., (iii.) 7 d. 3 h. 43 m., (iv.) 16 d. 16 h. 32 m.