DIVERGING SHADOW. In this cut, the opaque body is the larger, and the shadow projected from it diverges, or grows more broad as the distance from the planet increases. If the opaque body is smaller than the luminous one, the shadow converges to a point. CONVERGING SHADOW. Here the luminous body is the larger, and the shadow converges to a noint, and takes the form of a cone. The opaque body being smaller than the luminous one, the length of its shadow will be modified by its distance, as in the following: Here, also, the luminous body is the larger, and both precisely of the game size as in the cut preceding; but being placed nearer each other, the shadow is shown to be considerably shorter. 437. All the planets, both primaries and secondaries, cast shadows in a direction opposite the Sun (see cut on rext page). The form and length of these shadows depend upon the comparative magnitude of the Sun and planet, and their distance from each other. If the Sun and a planet were of the same size, the shadow of the planet would be in the form of a cylinder, whatever its distance. If the planet was larger than the Sun, the shadow would diverge, as we proceed from the planet off into space; and the nearer the Sun, the more divergent the shadow would be. But as the planets are all much smaller than the Sun, the shadows all converge to a point, and take the form of a cone; and the nearer to the Sun, the shorter their shadows. 437. Why have the largest and most distant planets the longest shadows? the primary planets eclipse each other? Do any of SHADOWS OF THE PLANETS. These principles are partly illustrated in the adjoining cut. The planets nearest the Sun have comparatively short shadows, while those more remote extend to a great distance. No primary, however, casts a shadow long enough to reach the next exterior planet. The magnitude of the Sun is such, that the shadow cast by each of the primary planets always converges to a point before it reaches any other planet; so that not one of the primary planets can eclipse another. The shadow of any planet which is accompanied by Satellites, may, on certain occasions, eclipse its satellites; but it is not long enough to eclipse any other body. The shadow of a satellite or Moon, may also, on certain occasions, fall on the primary, and eclipse it. 438. When the Sun is at his greatest distance from the Earth, and the Moon at her least distance, her shadow is sufficiently long to reach the Earth, and extend 19,000 miles beyond. When the Sun is at his least distance from the Earth, and the Moon at her greatest, her shadow will not reach the Earth's surface by 20,000 miles. So that when the Sun and Moon are at their mean distances, the cone of the Moon's shadow will terminate a little before it reaches the Earth's surface. In the former case, if a conjunction take place when the center of the Moon comes in a direct line between the centers of the Sun and Earth, the dark shadow of the Moon will fall centrally upon the Earth, and cover a circular area of 175 miles in diameter. To all places lying within this dark spot, the Sun will be totally eclipsed, as illustrated by the figure. 439. Eclipses of the Sun must always happen at New Moon, and those of the Moon at Full Moon. The reason of this is, that the Moon can never be between us and the Sun, to eclipse him, except at the time of her change, or New Moon; and she can never get into the Earth's shadow, to be eclipsed herself, except when she is in opposition to the Sun, and it is Full Moon. 440. If the Moon's orbit lay exactly in the plane of the ecliptic, she would eclipse the Sun at every change, and be eclipsed herself at every full; but as her orbit departs from the ecliptic over 5° (422), she may pass either above or below the Sun at 438. What is the length of the Moon's shadow when she is nearest the Earth and farthest from the Sun? What when nearest the Sun and farthest from the Earth? What when the Sun and Moon are at their mean distances? Moon do solar eclipses always occur? Lunar? Why? 439. At what time of the 440. Why not two solar and the time of her change, or above or below the Earth's shadow at the time of her full. NEW AND FULL MOONS WITHOUT ECLIPSES. Above the Earth's shadow. ECLIPTIC Shadow below the Earth. Below the Earth's shadow. Let the line joining the Earth and the Sun represent the plane of the ecliptic. Now as the orbit of the Moon departs from this plane about 5° 9', she may appear either above or below the Sun at New Moon, as represented in the figure, and her shadow may fall above the north pole or below the south. At such times, then, there can be no solar eclipse. On the right, the Moon is shown at her full, both above and below the Earth's shadow, in which case there can be no lunar eclipse. 441. As the Moon passes from one of her nodes to the other in 173 days, there is just this period between two successive eclipses of the Sun, or of the Moon. In whatever time of the year, then, we have eclipses at either node, we may be sure that in 173 days afterwards, we shall have eclipses at the other node. every As the Moon's nodes fall back, or retrograde in the ecliptic, at the rate of 19 year, they will complete a backward revolution entirely around the ecliptic to the same point again, in 18 years, 225 days; in which time there would always be a regular period of eclipses, if any complete number of lunations were finished without a remainder. But this never happens; for if both the Sun and Moon should start from a line of conjunction with either of the nodes in any point of the ecliptic, the Sun would perform 18 annual revolutions and 222° of another, while the Moon would perform 230 lunations, and 85° of another, before the node would come around to the same point of the ecliptic again; so that the Sun would then be 138° from the node, and the Moon 85° from the Sun. But after 223 lunations, or 18 years, 11 days, 7 hours, 42 minutes, and 81 seconds, the Sun, Moon, and Earth, will return so nearly in the same position with respect to each other, that there will be a regular return of the same eclipses for many ages. This grand period was discovered by the Chaldeans, and by them called Saros. If, therefore, to the mean time of any eclipse, either of the Sun or Moon, we add the Chaldean period of 18 years and 11 days, we shall have the return of the same eclipse. This mode of predicting eclipses will hold good for a thousand years. In this period there are usually 70 eclipses; 41 of the Sun and 29 of the Moon. 442. The diameter of the Earth's shadow, at the distance of the Moon, is nearly three times as large as the diameter of the Moon; and the length of the Earth's shadow is nearly four times as great as the distance of the Moon; exceeding it in the same ratio that the diameter of the Earth does the diameter of the Moon, which is as 3.663 to 1. 443. The number of eclipses than two, nor more than seven. in any one year, cannot be less In the former case, they will two lunar eclipses every lunar month? 441. How often may eclipses occur at opposite nodes? What cycle of eclipses described? Number of eclipses in this cycle? 442. What is the diameter of the Earth's shadow at the distance of the Moon? 443. What number of eclipses may occur in any one year? If but two, what will they be? both be of the Sun; and in the latter, there will be five of the Sun, and two of the Moon-those of the Moon will be total. There are sometimes six; but the usual number is four: two of "the Sun, and two of the Moon. The cause of this variety is thus accounted for. Although the Sun usually passes by both nodes only once in a year, he may pass the same node again a little before the end of the year. In consequence of the retrograde motion of the Moon's nodes, he will come to either of them 178 days after passing the other. He may, therefore, return to the same node in about 346 days, having thus passed one node twice, and the other once, making each time, at each, an eclipse of both the Sun and the Moon, or six in all. And since 12 lunations, or 354 days from the first eclipse, in the beginning of the year, leave room for another New Moon before the close of the year, and since this New Moon may fall within the ecliptic limit, it is possible for the Sun to be eclipsed again. Thus there may be seven eclipses in the same year. 444. Eclipses of the Sun always come on from the west, and pass over eastward ; while eclipses of the Moon come on from the east, and pass over westward. This is a necessary result of the eastward motion of the Moon in her orbit. LUNAR ECLIPSE. In the right hand cut, the Moon is seen revolving eastward, throwing her shadow upon the Earth, and hiding the western limb of the Sun. In some instances, however, when the eclipse is very slight, it may first appear on the northern or southern imb of the Sun-that is, the upper or lower side; but even then its direction must be from west to east. It will also be obvious from this figure, that the shadow of the Moon upon the Earth must also traverse her surface from west to east; consequently the eclipse will be visible earlier in the west than in the east. On the left, the Moon is seen striking into the Earth's shadow from the west, and having her eastern limb first obscured. By holding the book up south of him, the student will see at once why the revolution of the Moon eastward must cause a solar eclipse to proceed from west to east, and a lunar eclipse from east to west. To locate objects and motions correctly, the student should generally imagine himself looking to the south, as we are situated north of the equinoctial. The student should bear in mind that nearly all the cuts in the book are drawn to represent a view from northern latitude upon the Earth. Hence, by holding the book up south of him, the cuts will generally afford an accurate illustration both of the positions and motions of the bodies represented. SOLAR ECLIPSE. 860.000 MILES 445. The time which elapses between two successive changes of the Moon is called a Lunation, which, at a mean rate, is about If seven? What is the usual number? Can you explain the cause of this variety? 444. What is the direction of a solar eclipse? A lunar? Why this difference? 445. What is a lunation? What would be the effect if the solar and lunar months were equal? What result from the existing inequality? 294 days. If 12 lunar months were exactly equal to the 12 solar months, the Moon's nodes would always occupy the same points in the ecliptic, and all eclipses would happen in the same months of the year, as is the case with the transits of Mercury and Venus but, in 12 lunations, or lunar months, there are only 354 days; and in this time the Moon has passed through both her nodes, but has not quite accomplished her revolution around the Sun; the consequence is, that the Moon's nodes fall back in the ecliptic at the rate of about 19° annually; so that the eclipses happen sooner every year by about 19 days. 446. Eclipses can never take place, except when the Moon is near the ecliptic; or, in other words, at or near one of her nodes. At all other times, she passes above or below the Sun, and also above or below the Earth's shadow. It is not necessary that she should be exactly at her node, in order that an eclipse occur. If she is within 17° of her node, at the time of her change, she will eclipse the Sun; and if within 12° of her node at her full, she will strike into the Earth's shadow, and be more or less eclipsed. These distances are called, respectively, the solar and lunar ecliptic limits. This subject may be understood by consulting the following figure. THE MOON CHANGING AT DIFFERENT DISTANCES FROM HER NODES. E H E Let the line E E represent the ecliptic, and the line 0 0 the plane of the Moon's orbit. The light globes are the Sun, and the dark ones the Moon, which may be imagined as much nearer the student; hence their apparent diameter is the same. Let the point A represent the node of the Moon's orbit. Now if the change occur when the Moon is at B, she will pass below the Sun. If when at C, she will just touch his lower limb. At C, she will eclipse him a little, and so on to A; at which point, if the change occurs, the eclipse would be central, and probably total. If the Moon was at G, H, I, or J, in her orbit, when the change occurred, she would eclipse the upper or northern limb of the Sun, according to her distance from her node at the time; but if she was at K, she would pass above the Sun, and would not eclipse him at all. The points C and J will represent the Solar Ecliptic Limits. The mean ecliptic limit for the Sun is 16° on each side of the node; the mean ecliptic limit for the Moon is 10% on each side of the node. In the former case, then, there are 33 degrees about each node, making, in all, 66° out of 360°, in which eclipses of the Sun may happen; in the latter case there are 21° about each node, making, in all, 42° out of 360° in which eclipses of the Moon usually occur. The proportion of the solar to the lunar eclipses, therefore, is as 66 to 42, or as 11 to 7. Yet, there are more visible clipses of the Moon, at any given place, than of the Sun; because a lunar eclipse is risible to a whole hemisphere, a solar eclipse only to a small portion of it. 447. All parts of a planet's shadow are not alike dense. The 446. Where must the Moon be, with respect to the ecliptic and her nodes, in order to an eclipse? What meant by ecliptic limits? Name the distance of each, respectively, 447. What is the umbra of the Earth or Moon? The from the node. Illustrate. |