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will be useful for the student to attend to the following observations; as by that means he will more readily understand the principles and terms that must be used in elucidating the subject.
Observation and analogy have now converted many propositions that were once doubtful, into established facts; such are the motions of the Earth and Moon. To common observation, both the Sun and the Moon appear to perform their revolutions about the Earth as a centre; but the science of Astronomy proves that this is true of the Moon only, while both that body and the Earth are carried together about the Sun. And as it is the different positions of these two bodies in their orbits with respect to each other and the great central luminary which give rise to the phenomena of eclipses, and their relative motions and distances from each other that regulate their duration, we shall endeavour to give as brief an explanation as possible of the principal circumstances of the motions, magnitude, and distances of each and first of
Before men were enlightened by science, they confounded realities with appearances; and, being able to see only a small portion of the Earth's surface at one time, they regarded the world they inhabited as an extended plain, placed in the middle of the universe; and about which the Sun, Moon, and stars, performed their diurnal revolutions. It is now, however, known that this is not the case, but that the Earth is nearly a spherical body, the mean radius of which is about 3956 English miles.
Astronomy not only furnishes the means of ascertaining the shape and magnitude of the Earth, as well as of the other bodies belonging to the solar system, but it also supplies the means of ascertaining its place in that system, and of calculating its motion. We have already explained one method by which astronomers determine the distance between the Earth and
the Sun, in our article on finding the parallax. See last month's Occurrences. This, however, is not the only one which is employed for that purpose. When the parallax of the Sun, or the angle that the semidiameter of the Earth would subtend to a spectator at the Sun, is known, the distance between these bodies may readily be found, as it forms one side of a right angled triangle, of which the parallax is one of the acute angles, and the radius of the Earth its opposite side. If, therefore, the horizontal parallax be denoted by p, the radius of the Earth by r, and the required distance by D, we shall have
Rad. 1: D:: sin p:r;
Now it has been stated, that the mean horizontal parallax is about 8".78, and by substituting this for p in the preceding formula, we shall obtain 23524 terrestrial semidiameters for the mean distance of the Earth from the Sun; which, multiplied by 3956, gives a little more than 93 millions of English miles.
The apparent diameter of a heavenly body is the number of degrees, minutes, &c. under which it appears to an observer; and this is ascertained by observation, and by means of the micrometer. It is found, that the apparent diameter of the Sun, as seen from the Earth, is 1922".7, or about 32'. The parallax of the Sun and his apparent diameter being known, it is easy to determine the magnitude of that luminary; for since the parallax is the angle at the Sun subtended by the radius of the Earth, and the apparent radius of the Sun is about 16′ or 960", we have
8".78: 960′′:: the terr. rad. : the solar rad.
and which is, therefore, =
109.34 nearly. Hence the solar diameter is more than one hundred and nine times that of the Earth.
A series of continued observations on the Sun soon produced the conviction, that, besides his apparent diurnal motion, he did not return precisely to the same point in the heavens each succeeding day; but that he appeared to traverse the whole twelve signs, and consequently to make the tour of the whole ecliptic, in the space of a year. Now as this apparent motion may be produced either by the real motion of the Sun or by that of the Earth in an opposite direction, and both reason and analogy decide for the latter, astronomers regard the Earth as revolving about the Sun once in 3654 days very nearly. This will be evident from an inspection of the following figure, in which if S represent the Sun, and E the Earth, it is obvious that when the latter is at E, the former will appear to be at S'; and that while the Earth moves from E to A, the Sun will appear to move through the opposite part of the orbit S'P, and, in the contrary direction, from S' to P.
If, therefore, an observer were situated at the surface of the Sun, he would perceive that the Earth had two distinct motions; the one about its axis in the space of every 24 hours, and the other about the Sun in a year. This annual motion, however, is not performed in a circle, but in an ellipse having the Sun in one of its foci; for the Sun's apparent diameter experiences periodic variations, and shows that his distance from the Earth also varies with the position of this latter body.
The point P (fig. 6), where the Earth is nearest the
Sun, and where the apparent diameter of that body is the greatest, is called the perigee; it is diametrically opposite the point A, which is the greatest distance, and is called apogee; the former is also sometimes called the perihelion, and the latter the aphelion: both these points together are denominated the apsides, and the line (AP in the preceding figure) which joins them the line of apsides. The Earth is in the first of these points near the winter solstice, and it arrives at the other near the summer solstice, and is then at its greatest distance from that vivifying luminary.
When the Earth is in apogee, the apparent solar diameter is 31'.516; and, when in perigee, 32'.593: though the difference is not very great, it shows that the ecliptic, through which the Earth travels in its annual course round the Sun, is an oval (as represented in the preceding figure, by the elliptic curve AGPH), in which the two lines AS and SP are the greatest and least distances; and as they are to each other in the same ratio as the apparent diameters of the Sun,
AS SP:: 32′.593 : 31'.516.
From this proportion it appears that the greatest distance exceeds the least by about a 30th part of itself.
The distance of the Sun from the Earth may now be stated to be, when he is
23075 terrestrial rad.
The greatest dimension AP of the entire orbit is therefore equal to 47048 of the Earth's semidia
Supposing the Earth always to have the same velocity in its orbit, it would describe equal portions of it in equal times: but as the line SE, which passes through the centres of the Earth and Sun,
and is denominated the Radius Vector, is subject to variation, if there be taken on the orbit two equal arcs supposed to be described in equal times, these two arcs, as seen from the Sun, will appear to be unequal; that will appear to be the greatest which is at the least distance. This actually happens; and the angular space which the Sun describes, decreases at the same time that the apparent diameter diminishes; that is, when the distance augments. And, by comparing the decrease of the radius vector with the augmentation of these angles, it will easily be seen that these last are greater than they ought to be, from the variation of distance alone.
The apparent diameter of the Sun, in perigee, is 32.593, and the arc which is apparently described in 24 hours is 61'.165; while in apogee, the diameter is 31'.516, and the apparent arc described in the same time is 57.192. Hence a spectator, placed at the Sun, would see the terraqueous globe describe an arc of about 61' in perigee, and only about 57' in its apogee, but with a motion in an opposite direction to the apparent motion of the Sun. If the inverse ratio of the distances, or that of the apparent diameters, 61.165
was equal to that of the arcs described, or
and this took place throughout
32.593 was equal to 31.516' the whole extent of the Earth's orbit, then it might be concluded that the motion of the Earth was uniform, and that inequality of distance alone caused the apparent change of velocity. But since these two fractions are not equal to each other, it must be admitted that the variation in the Earth's motion is real, and that it is accelerated when it approaches the Sun, and retarded when it recedes from it. The Earth, therefore, moves with the greatest velocity in perigee, and the least in apogee.
But the first of these fractions is equal to the