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towards the center, is denominated Centripetal force; and the tendency of a revolving body to fly from the center in a tangent line, is called the Projectile or Centrifugal force. The joint action of these two central forces gives the planets a circular motion, and retains them in their orbits as they revolve, the primaries about the Sun, and the secondaries about their primaries. 565. 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.
LAWS OF PLANETARY MOTION.
566. Three very important laws, governing the movements of the planets, were discovered by Kepler, a German astronomer, in 1609. In honor of their discoverer, they are called Kepler's Laws. Kepler was a disciple of Tycho Brahe, a noted astronomer of Denmark, and was equally celebrated with his renowned tutor. His residence and observatory were at Wirtemburgh, in Ger
The first of these laws is, that the orbits of all the planets are elliptical, having the Sun in the common focus.
The point in a planet's orbit nearest the Sun is called the perihelion point, and the point most remote the aphelion point. Perihelion is from peri, about or near, and helios, the Sun; and aphelion, from apo, from, and helios, the Sun.
From this first law of Kepler, it results that the planets move with different velocities, in different parts of their orbits. From the aphelion to the perihelion points, the centripetal force combines with the centrifugal to accelerate the planet's motion; while from perihelion to aphelion points, the centripetal acts against the centrifugal force, and retards it.
The tendency to depart from the center? What does the joint action of these two forces produce? 565. What relation between the Sun's attraction and the centrifugal force of the planets? What effect has the distance of a planet from the Sun, upon his attractive force? How is this increased tendency counterbalanced? 566. What important laws when and by whom discovered? State the first? What are the aphelion and perihelion points? Derivation? What results from this first law?
From A to B in the diagram, the centrifugal force, represented by the line C, acts with the tendency to revolve, and the planet's motion is accelerated; but from B to A the same force, shown by the line D, acts against the tendency to advance, and the planet is retarded. Hence it comes to aphelion with its least velocity, and to perihelion with its greatest.
In the statement of velocities on page 45, the mean or average velocity is given.
567. The second law is, that the radius vector of a planet describes equal areas in equal times. The radius is an imaginary line joining the center of the Sun and the center of the planet, in any part of its orbit. Vector is from veho, to carry ; hence the radius vector is a radius carried round. By the statement that it describes equal areas in equal times, is meant that it sweeps over the same surface in an hour, when a planet is near the Sun, and moves swiftly, as, when furthest from the Sun, it moves most slowly.
The nearer a planet is to the Sun, the more rapid its motion. It follows, therefore, that if the orbit of a planet is an ellipse, with the Sun in one of the foci, its rate of motion will be unequal in different parts of its orbit-swiftest at perihelion, and slowest at aphelion. From perihelion to aphelion the centripetal more directly counteracts the centrifugal force, and the planet is retarded. On the other hand, from the aphelion to the perihelion point, the centripetal and centrifugal forces are united, or act in a similar direction. They consequently hasten the planet onward, and its rate of motion is constantly accelerated. Now suppose, when the planet is at a certain point near its perihelion, we draw a line from its center to the center of the Sun. This line is the radius vector. At the end of one day, for instance, after the planet has advanced considerably in its orbit, we draw another line in the same manner to the Sun's center, and estimate the area between the two lines. At another time, when the planet is near its aphelion, we note the space over which the radius vector travels in one day, and estimate its area. On comparison, it will be found, that notwithstanding the unequal velocity of the planet, and consequently of the radius vector, at the two ends of the ellipse, the area over which the radius vector has traveled is the same in both cases. The same principle obtains in every part of the planetary orbits, whatever may be their ellipticity or the mean distance of the planet from the Sun; hence the rule that the radius vector describes equal areas in equal times. In the preceding cut, the twelve triangles, numbered 1, 2, 8, &c., over each of which the radius vector sweeps in equal times, are equal.
568. The third law of Kepler is, that the squares of the periodic times of any two planets are proportioned to the cubes of their mean distances from the Sun.
Take, for example, the Earth and Mars, whose periods are 365-2564 and 686-9796 days, and whose distances from the Sun are in the proportion of 1 to 1.52369, and it will be found that (865.2564)2: (686.9796)2:: (1)3:(1.52869)3.
567. State the second law of Kepler? Explain it? 568. The third law? What illustration?
According to these laws, which are known to prevail throughout the solar system many of the facts of astronomy are deduced from other facts previously ascertained. They are, therefore, of great importance, and should be studied till they are, at least, thoroughly understood, if not committed to memory.
569. From the foregoing principles, it follows, that the force of gravity, and the centrifugal force, are mutual opposing powers -each continually acting 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 proportion 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 make 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 than 84 minutes), gravitation would be completely overpowered, and all fluids and loose substances near the equator would fly off from the surface.
570. 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, 1-6th of a-lb.; of Mars, lb.; of Jupiter, 2.716 lbs.; of Saturn, 1.01 lbs.
PROPER MOTION OF THE SUN IN SPACE.
X571. THOUGH We are accustomed to speak of the Sun as the fixed center of the Solar System, the idea of his fixedness is correct only so far as his relation to the bodies revolving around him are concerned. As the planets accompanied by their satellites revolve around the Sun, so he is found to be moving with all his retinue of worlds, in a vast orbit, around some distant and unknown center.
569. What results from these principles, as respects the weight of bodies on the Earth's surface? How increased or diminished? What illustrations given? 570. Upon what, then, does the weight of bodies upon the planets depend? What illustrations? 71. Is the Sun a fixed body? What motion in space? Who first advanced this idea?
This opinion was first advanced, we think, by Sir William Herschel; but the honor of actually determining this interesting fact, belongs to Struve, who ascertained not only the direction of the Sun and Solar System, but also their velocity. The point of tendency is towards the constellation Hercules, Right Ascension 259°, Declination 35°. The velocity of the Sun, &c., in space, is estimated at about 20,000 miles per hour, or nearly 8 miles per second;
572.(With this wonderful fact in view, we may no longer consider the Sun as fixed and stationary, but rather as a vast and luminous planet, sustaining the same relation to some central orb, that the primary planets sustain to him, or that the secondaries sustain to their primaries. Nor is it necessary that the stupendous mechanism of nature should be restricted even to these sublime proportions. The Sun's central body may also have its orbit, and its center of attraction and motion, and so on, till, as Dr. Dick observes, we come to the great center of all-to the THRONE OF GOD.
THE CENTRAL SUN.
573. In 1847, an article appeared in several European journals, announcing the probable discovery by Professor Mädler, of Dorpat, of the Sun's central orb; the inclination of his orbit to the plane of the ecliptic; and his periodic time!
By an extensive and laborious comparison of the quantities and directions of the proper motions of the stars in various parts of the heavens, combined with indications afforded by the parallaxes hitherto determined, and with the theory of universal gravitation,/Professor Mädler arrived at the conclusion that the Pleiades form the central group of our whole astral or sidereal system, including the Milky Way and all the brighter stars, but exclusive of the more distant nebulæ, and of the stars of which those nebulæ may be composed. And within this central group itself he has been led to fix on the star Alcyone, as occupying exactly or nearly the position of the center of gravity, and as entitled to be called the central Sun.
Assuming Bessel's parallax of the star 61 Cygni, long since remarkable for its larger proper motion, to be correctly determined, Mädler proceeds to form a first approximate estimate of the distance of this central body from the planetary or solar system; and arrives at the provisional conclusion, that Alcyone is about 34,000,000 times as far removed from us, or from our own Sun, as the latter luminary is from us. It would, therefore, according to this estimation, be at least a million times as distant as the new planet, of which the theoretical or deductive discovery has been so great and beautiful a triumph of modern astronomy, and so striking a confirmation of the law of Newton. The same approximate determination of distance conducts to the result, that the light of the central sun occupies more than five centuries in travelling thence to us.
Direction and velocity of the Sun and Solar System? 572. How, then, should we regard the Sun? What further speculation? Dr. Dick's observation? 573. What great discovery in 1847, and by whom? By what process? What conclusion first reached? What star afterward designated? Further description of the progress of the discovery? What conclusion respecting the passage of light from the central Sun to us?
574. The enormous orbit which our own Sun, with the Earth, and the other planets, is thus inferred to be describing about that distant center-not, indeed, under its influence alone, but by the combined attractions of all the stars which are nearer to it than we are, and which are estimated to amount to more than 117,000,000 of masses, each equal to the total mass of our own Solar Systemis supposed to require upwards of eighteen millions of years for
its complete description, at the rate of about eight geographical miles in every second of time. At this rate, the arc of its orbit, over which the Sun has traveled since the creation of the world, amounts to only about oth part of his orbit, or about 7 minutes-an arc so small, compared with the whole, as to be hardly distinguishable from a straight line.
The plane of this vast orbit of the Sun is judged to have an inclination of about 84 degrees to the ecliptic, or to the plane of the annual orbit of the Earth; and the longitude of the ascending node of the former orbit on the latter is concluded to be nearly 232 degrees.
PRECESSION OF THE EQUINOXES-OBLIQUITY OF THE
575. Of 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 what is called the
PRECESSION OF THE EQUINOXES.
The equinoxes, as we have learned, are the two opposite
574. Supposed period of the Sun's revolution? What portion of his orbit gone over since the creation of our race? Situation of his orbit with respect to the ecliptic? Longitude of ascending node? 575. Subject of this chapter? What are the equinoxes?