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a circular motion, and retains them in their orbits as they revolve, the primaries about the Sun, and the secondaries about their primaries.
The degree of the Sun's attractive power at each particular planet, whatever be its distance, is uniformly equal to the centrifugal force of the planet. The nearer any planet is to the Sun, the more strongly is it attracted by him; the farther any planet is from the Sun, the less is it attracted by him; therefore, those planets which are the nearer to the Sun must move the faster in their orbits, in order thereby to acquire centrifugal forces equal to the power of the Sun's attraction; and those which are the farther from the Sun must move the slower, in order that they may not have too great a degree of centrifugal force, for the weaker attraction of the Sun at those distances.
The discovery of these great truths, by Kepler and Newton, established the UNIVERSAL LAW OF PLANETARY MOTION; which may be stated as follows:
1. Every planet moves in its orbit with a velocity varying every instant, in consequence of two forces; one tending to the centre of the Sun, and the other in the direction of a tangent to its orbit, arising from the primitive impulse given at the time it was launched into space. The former is called its Centripetal, the latter, its Centrifugal force. Should the centrifugal force cease, the planet would fall to the Sun by its gravity; were the Sun not to attract it, it would fly off from its orbit in a straight line.
2. By the time a planet has reached its aphelion, or that point of its orbit which is farthest from the Sun, his attraction has overcome its velocity, and draws it towards him with such an accelerated motion, that it at last overcomes the Sun's attraction, and shoots past him; then gradually decreasing in velocity, it arrives at the perihelion, when the Sun's attraction again prevails.
3. However ponderous or light, large or small, near or remote, the planets may be, their motion is always such that imaginary lines joining their centres to the Sun, pass over equal areas in equal times: and this is true not only with respect to the areas described every hour by the same planet, but the agreement holds, with rigid exactness, between the areas described in the same time, by all the planets and comets belonging to the Solar System.
From the foregoing principles, it follows, that the force of gravity, and the centrifugal force, are mutual opposing powers-each continually acting
To what is the Sun's attractive power at each particular planet equal? Explain this more fully. By whom was the universal law of planetary motion established? Repeat the law.
against the other. Thus, the weight of bodies, on the Earth's equator, is diminished by the centrifugal force of her diurnal rotation, in the propor tion of one pound for every 290 pounds: that is, had the Earth no motion on her axis, all bodies on the equator would weigh one two hundred and eighty-ninth part more than they now do.
On the contrary, if her diurnal motion were accelerated, the centrifugal force would be proportionally increased, and the weight of bodies at the equator would be, in the same ratio, diminished. Should the Earth revolve upon its axis, with a velocity which would inake the day but 84 minutes long, instead of 24 hours, the centrifugal force would counterbalance that of gravity, and all bodies at the equator would then be absolutely destitute of weight; and if the centrifugal force were further augmented, (the Earth revolving in less time than 84 minutes,) gravitation would be completely overpowered, and all fluids and loose substances near the equator would fly off from the
The weight of bodies, either upon the Earth, or on any other planet having a motion around its axis, depends jointly upon the mass of the planet, and its diurnal velocity. A body weighing one pound upon the equator of the Earth, would weigh, if removed to the equator of the Sun, 27.9 lbs. Of Mercury, 1.03 lbs. Of Venus, 0.98 lbs. Of the Moon, & lb. Of Mars, Jupiter, 2.716 lbs. Of Saturn, 1.01 lbs.
PRECESSION OF THE EQUINOXES-OBLIQUITY OF THE ECLIPTIC.
Or all the motions which are going forward in the Solar System, there is none, which it is important to notice, more difficult to comprehend, or to explain, than the PRECESSION OF THE EQUINOXES, as it is termed.
The equinoxes, as we have learned, are the two opposite points in the Earth's orbit, where it crosses the equator. The first is in Aries; the other, in Libra. By the precession of the equinoxes is meant, that the intersection of the equator with the ecliptic is not always in the same point:in other words, that the Sun, in its apparent annual course, does not cross the equinoctial, Spring and Autumn, exactly in the same points, but every year a little behind those of the preceding year.
This annual falling back of the equinoctical points, is called by astronomers, with reference to the motion of the heavens, the Precession of the Equinoxes; but it would better accord with fact as well as the apprehension of the learner, to call it, as it is, the Recession of the Equinoxes: for the equinoctial points do actually recede upon the ecliptic, at the rate of about 501′′ of a degree every year. It is the name
How is the weight of bodies on the Earth's equator affected by its diurnal rotation? What would be the effect if the diurnal motion of the Earth were accelerated? What would be the consequence if the Earth revolved about its axis in 84 minutes, or in less time? What are the equinoxes? What is meant by the precession of the equinoxes 7 Why is it called precession of the equinoxes, and what would be a better term?
only, and not the position, of the equinoxes which remains permanent. Wherever the Sun crosses the equinoctial in the spring there is the vernal equinox; and wherever he crosses it in the autumn there is the autumnal equinox; and these points are constantly moving to the west.
To render this subject familiar, we will suppose two carriage roads, extending quite around the Earth: one, representing the equator, running due east and west; and the other, representing the ecliptic, running nearly in the same direction as the former, yet so as to cross it with a small angle, (say of 2310,) both at the point where we now stand, for instance, and in the nadir, exactly opposite; let there also be another road, to represent the prime meridian, running north and south, and crossing the first at right angles, in the common point of intersection, as in the annexed figure.
Let a carriage now start from this point of intersection, not in the road leading
directly east, but along that of the ecliptic, which leaves the former a little to the north, and let a person be placed to watch when the carriage coines around again, after having inade the circuit of the Earth, and see whether the carriage will cross the equinoctial road again precisely in the same track as when it left the goal. Though the person stood exactly in the former track, he need not fear being run over, for the carriage will cross the road 100 rods west of him, that is, 100 rods west of the meridian on which he stood. It is to be observed, that 100 rods on the equator is equal to 501 seconds of a degree.
If the carriage still continue to go around the Earth, it will, on completing its second circuit, cross the equinoctial path 200 rods west of the meridian whence it first set out; on the third circuit, 300 rods west; on the fourth circuit, 400 rods, and so on, continually. After 713 circuits, the point of intersection would be one degree west of its place at the commencement of the route. At this rate it would be easy to determine how many complete circuits the carriage must perforin before this continual falling back of the intersecting point would have retreated over every degree of the orbit, until it reached again the point from whence it first departed. The application of this illustration will be manifest, when we consider, further, that,
The Sun revolves from one equinox to the same equinox again, in 365d. 5h. 48′ 47′′.81. This constitutes the natural, or tropical year, because, in this period, one revolution of the seasons is exactly completed. But it is, mean
The equinoctial points are continually moving; how, then, is their position define 1. Give, at length, a familiar illustration by which this subject may be understood. Suppose the carriage continues its circuit around the earth, where would it cross the equinoctial the 2d, 3d, and 4th times, &c.? After how many circuits would this falling back of the equinoctial points amount to one degree on the ecliptic? In what time does the Sun revolve from one equinox to the same equinox again? What is this period called?
while, to be borne in mind, that the equinox itself, during this period, has not kept its position among the stars, but has deserted its place, and fallen back a little way to meet the Sun; whereby the Sun has arrived at the equinox before he has arrived at the same position among the stars from which he departed the year before; and consequently, must perform as much more than barely a tropical revolution, to reach that point again.
To pass over this interval, which completes the Sun's sidereal revolution, takes (20'.22′′.94) about 22 minutes and 23 seconds longer. By adding 22 minutes and 23 seconds to the time of a tropical revolution, we obtain 365d. 6h. 9m. 103s. for the length of a sidereal revolution; or the time in which the Sun revolves from one fixed star to the same star again.
As the Sun describes the whole ecliptic, or 360°, in a tropical year, he moves over 59′ 8′′ of a degree every day, at a mean rate, which is equal to 501" of a degree in 20 minutes and 23 seconds of time; consequently he will arrive at the same equinox or solstice when he is 504′′ of a degree short of the same star or fixed poin in the heavens, from which he set out the year before. So that, with respect to the fixed stars, the Sun and equinoctial points fall back, as it were, 1o in 713 years. This will make the stars appear to have gone forward 1°, with respect to the signs in the ecliptic, in that time: for it must be observed, that the same signs always keep in the same points of the ecliptic, without regard to the place of the constellations. Hence it becomes necessary to have new plates engraed for celestial globes and maps, at least once in 50 years, in order to exhibit truly the altered position of the stars. At the present rate of motion, the recession of the equinoxes, as it should be called, or the precession of the stars, amounts to 30°, or one whole sign, in 2140 years.
Why is it so called? Does the equinox remain stationary during this period? What results from this? How long does it take the Sun to pass over the interval through which the equinox has thus retreated? What is the length of a sidereal revolution, and how is it determined? What portion of the ecliptic does the Sun describe, at a mean rate, every day? What portion does it describe in 20 minutes and 23 seconds? If the Sun and equinoctial points fall back in the ecliptic 50 1-4" of a degree every year, how many years before this regression will amount to a degree? How will this affect the appearance of the stars What practical inconvenience results from this fact? In what period of time does the precession of the stars amount to 30°, or one whole sign?
To explain this by a figure; Suppose the Sun to have been in conjunction with a fixed star at S, in the first degree of Taurus, (the second sign of the ecliptic,) 340 years before the birth of our Saviour, or about the 17th year of Alexander the Great; then having made 2140 revolutions through the ecliptic, he would be found again at the end of so many sidereal years at S; but at the end of so many Julian years, he would be found at J, and at the end of so many tropica! years, which would bring it down to the beginning of the present century, he would be found at T, in the first degree of Aries, which has receded from S to T in that time by the precession of the equinoctial points Aries and Libra. The arc S T would be equal to the amount of the precession (for precession we must still call it) of the equinox in 2140 years, at the rate of 50." 23572 of a degree, or 20 minutes and 23 seconds of time annually, as above stated.
From the constant retrogradation of the equinoctial points, and with them of all the signs of the ecliptic, it follows that the longitude of the stars must continually increase. The tame cause affects also their right ascension and declination. Hence, those stars which, in the infancy of astronomy were in the sign Aries, we now find in Taurus; and those which were in Taurus, we now find in Gemini, and so on. Hence likewise it is, that the star which rose or set at any particular time of the year, in the time of Hesiod, Eudoxus, Virgil, Pliny, and others, by no means answers at this time to their descriptions.
Explain this by a diagram. How does the retrogradation of the equinoctial points affect the longitude of the stars? Does the same cause extend to their right ascension and declination also? How is this rendered apparent ?