Part 7

Feb. 25: 1 h. 30 m. (for on the three previous nights the sky was overcast).—Three satellites appeared, two on the east, which were at a distance of 4´ apart, the same as the distance of the nearer satellite from Jupiter; on the west there was one satellite at a distance of 2´ from Jupiter. They were exactly in the same straight line in the direction of the ecliptic (Fig. 56).

Feb. 26: 0 h. 30 m.—A pair of satellites only were present, one on the east, distant 10´ from Jupiter; the other was on the west, at a distance of 6´ (Fig. 57). The eastern satellite was slightly smaller than the western. At the fifth hour three satellites were visible; for, besides the two already noticed, a third satellite was in view, on the west, near Jupiter, very small, which previously had been hidden behind Jupiter, and it was at a distance of 1´ from the planet (Fig. 58).

But the satellite on the east was seen to be further off than before, being at a distance of 11´ from Jupiter. On this night, for the first time, I determined to observe the motion of Jupiter and the adjacent planets (his satellites) along the zodiac, by reference to some fixed star; for there was a fixed star in view, eastwards of Jupiter, at a distance of 11´ from the satellite on the east, and a little to the south, in the following manner (Fig. 59).

Feb. 27: 1 h. 4 m.—The satellites appeared in the following configuration. The satellite furthest to the east was at a distance of 10´ from Jupiter; the next in order was near Jupiter, being at a distance of 0´ 30´´ from the planet. The next satellite was on the western side, at a distance of 2´ 30´´ from Jupiter; and the satellite further to the west was at a distance of 1´ from this. The two satellites near to Jupiter appeared small, especially the satellite on the east; but the satellites furthest off were very bright, particularly that on the west, and they made a straight line in the direction of the ecliptic exactly. The motion of the planets towards the east was plainly seen by reference to the aforesaid fixed star, for Jupiter and his attendant satellites were nearer to it, as may be seen in the accompanying figure (Fig. 60). At the fifth hour the satellite on the east, near to Jupiter, was 1´ from the planet.

Feb. 28: 1 h.—Only two satellites were visible, one on the east, at a distance of 9´ from Jupiter, and another on the west, at a distance of 2´; they were both rather bright, and in the same straight line with Jupiter, and a straight line drawn from the fixed star perpendicular to this straight line fell upon the satellite on the east, as in the figure (Fig. 61). At the fifth hour a third satellite was seen at a distance of 2´ from Jupiter, on the east, in the position shown in the figure (Fig. 62).

March 1: 0 h. 40 m.—Four satellites, all on the east of the planet, were seen; the satellite nearest to Jupiter was 2´ from the planet; the next 1´ from this; the third was 0´ 20´´ from the second, and was brighter than the others; and the satellite still further to the east was at a distance of 4´ from it, and was smaller than the others (Fig. 63). They made a straight line very nearly, only the satellite third from Jupiter was slightly above the line. The fixed star formed with Jupiter and the most easterly satellite an equilateral triangle, as in the figure.

March 2: 0 h. 40 m.—Three satellites were in attendance, two on the east and one on the west, in the configuration shown in the diagram (Fig. 64). The satellite furthest to the east was 7´ from Jupiter; from this satellite the next was distant 0´ 30´´, and the satellite on the west was separated from Jupiter by an interval of 2´. The satellites furthest off were brighter and larger than the remaining satellite, which appeared very small. The satellite furthest to the east seemed to be raised a little towards the north, out of the straight line drawn through the other satellites and Jupiter.

The fixed star already noticed was at a distance of 8´ from the western satellite, that is, from the perpendicular drawn from that satellite to the straight line drawn through all the system, as shown in the figure given.

These determinations of the motion of Jupiter and the adjacent planets (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.

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. 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.

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.

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, 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.

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.

—————————+———————————+———————————————+——————————————— FIG. | DATE. | EAST. | WEST. —————————+———————————+———————————————+——————————————— 1 | Jan. 7 | | | • • ◯ • —————————+———————————+——————————————————————————————— 2 | 8 | | | ◯ • • • —————————+———————————+——————————————————————————————— 3 | 10 | | | • • ◯ —————————+———————————+——————————————————————————————— 4 | 11 | | | • • ◯ —————————+———————————+——————————————————————————————— 5 | 12 | | | • •◯ • —————————+———————————+—————————-————————————————————— 6 | 13 | | | • ◯ • ⠁ • —————————+———————————+——————————————————————————————— 7 | 15 | • | | ◯ • • • —————————+———————————+——————————————————————————————— 8 | 15 | | | ◯ • • • —————————+———————————+——————————————————————————————— 9 | 16 | | | • ◯ • • —————————+———————————+——————————————————————————————— 10 | 17 | | | • ◯ • —————————+———————————+——————————————————————————————— 11 | Jan. 17 | • • | | • ◯ —————————+———————————+——————————————————————————————— 12 | 18 | | | • ◯ • —————————+———————————+——————————————————————————————— 13 | 19 | | | • ◯ • • —————————+———————————+——————————————————————————————— 14 | 19 | | | • • ◯ • • —————————+———————————+——————————————————————————————— 15 | 20 | | | • ◯ • • —————————+———————————+——————————————————————————————— 16 | 20 | | | • ◯ • • —————————+———————————+——————————————————————————————— 17 | 20 | • ◯ • • | | • —————————+———————————+——————————————————————————————— 18 | 21 | | | • • ◯ • —————————+———————————+——————————————————————————————— 19 | 22 | • ◯• • | | • —————————+———————————+——————————————————————————————— 20 | 22 | | | • ◯ • • • —————————+———————————+——————————————————————————————— 21 | 23 | | | • • ◯ • —————————+———————————+——————————————————————————————— 22 | 23 | | | • ◯ —————————+———————————+——————————————————————————————— 23 | 24 | • • ◯ | | • —————————+———————————+——————————————————————————————— 24 | 25 | | | • • ◯ —————————+———————————+——————————————————————————————— 25 | 26 | | | • • ◯ • —————————+———————————+——————————————————————————————— 26 | 26 | • | | • • ◯ • —————————+———————————+——————————————————————————————— 27 | 27 | | | • ◯ —————————+———————————+——————————————————————————————— 28 | 30 | • | | • ◯ • —————————+———————————+——————————————————————————————— 29 | 31 | • | | • ◯ • —————————+———————————+——————————————————————————————— 30 | Jan. 31 | • | | • ◯ • —————————+———————————+——————————————————————————————— 31 | Feb. 1 | | | • • ◯ • —————————+———————————+——————————————————————————————— 32 | 2 | | | • ◯ • • —————————+———————————+——————————————————————————————— 33 | 2 | | | • • ◯ • • —————————+———————————+——————————————————————————————— 34 | 3 | | | • ◯ • • —————————+———————————+——————————————————————————————— 35 | 4 | | | • • ◯ • • —————————+———————————+——————————————————————————————— 36 | 4 | | | • • ◯ • • —————————+———————————+——————————————————————————————— 37 | 6 | | | • ◯ • —————————+———————————+——————————————————————————————— 38 | 7 | | | • • ◯ —————————+———————————+——————————————————————————————— 39 | 8 | | | • • • ◯ —————————+———————————+——————————————————————————————— 40 | 9 | | | • • ◯ • —————————+———————————+——————————————————————————————— 41 | 10 | | | • • ◯ —————————+———————————+——————————————————————————————— 42 | 11 | | | • • ◯ • —————————+———————————+——————————————————————————————— 43 | 11 | • | | • • ◯ • —————————+———————————+——————————————————————————————— 44 | 11 | | | • • • ◯ • —————————+———————————+——————————————————————————————— 45 | 12 | | | • • ◯ • • —————————+———————————+——————————————————————————————— 46 | 13 | | | • • ◯ • • —————————+———————————+——————————————————————————————— 47 | 15 | | | • • • ◯ —————————+———————————+——————————————————————————————— 48 | 15 | | | • • ◯ —————————+———————————+——————————————————————————————— 49 | Feb. 15 | | | • • ◯ • —————————+———————————+——————————————————————————————— 50 | 16 | | | • ◯ • • —————————+———————————+——————————————————————————————— 51 | 17 | | | • ◯ • —————————+———————————+——————————————————————————————— 52 | 18 | | | • ◯ • • —————————+———————————+——————————————————————————————— 53 | 18 | | | • • ◯ • • —————————+———————————+——————————————————————————————— 54 | 19 | | | ◯ • • —————————+———————————+——————————————————————————————— 55 | 21 | | | • ◯ • • —————————+———————————+——————————————————————————————— 56 | 25 | | | • • ◯ • —————————+———————————+——————————————————————————————— 57 | 26 | | | • ◯ • —————————+———————————+——————————————————————————————— 58 | 26 | | | • ◯ • • —————————+———————————+——————————————————————————————— 59 | 26 | • ◯ • • | | ⨀ Star. —————————+———————————+——————————————————————————————— 60 | 27 | • • ◯ • • | | Star ⨀ —————————+———————————+——————————————————————————————— 61 | 28 | • ◯ • | | Star ⨀ —————————+———————————+——————————————————————————————— 62 | 28 | | | • • ◯ • —————————+———————————+——————————————————————————————— 63 | Mar. 1 | • | | • • • ◯ | | Star ⨀ —————————+———————————+——————————————————————————————— 64 | 2 | • | | • ◯ • | | Star ⨀ —————————+———————————+———————————————————————————————

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.

“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, 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?”

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.

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.