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CAUSES OF THE PLANETARY MOTION.
in a given time, would, in an equal time, carry it from B to C, and from C to D. But if, at B, it fall into the attraction of S, the Sun, which should so balance the projectile force as to carry it to E, at the same time that it would, by its former motion, have arrived at C, the planet would now revolve in a circle, B E F. But should the attraction of S be more powerful in proportion to the projectile force, it might bring the planet to G instead of E, or, being stronger, might carry it nearer the line B S, in any given proportion. If carried to G, it would revolve in the ellipse B G H. Before it arrives at G, and for some distance after, the lines of motion, caused by the projectile and centripetal forces, form an acute angle. The two powers, then, augment the motion caused by each other; and, attraction increasing as the squares of the distances decrease, the motion of the planet would be accelerated all the way from B to H. At H, it would be nearer the centre of attraction than at B, by twice the eccentricity of its orbit, and, being much more powerfully attracted, would be drawn to S, were not the projectile force also increased. This would now be so augmented, that it would carry
the planet from H to I in the same time that attraction would bring it to S. It would then be found at L, and proceed to B, completing the revolution. In passing from F to B, the planet would be as much retarded in its motion by gravity, as accelerated in its motion from B to F.
Thus it appears “ that bodies will move in all kinds of ellipses, whether long or short, if the spaces they move in be void of resistance. Only those which move in the longer ellipses, have so much the less projectile force impressed upon them, in the higher parts of their
Gravity in one part of an orbit becomes projectile force in another. What is gravity at B is projectile force at M. It operates principally by oblique action. This is immensely increased all the way from B to M.
A double projectile force will always balance a (quadruple power of gravity. The projectile force is greater)
in proportion to the centripetal, as the orbit is larger in which the planet moves. In the annual revolution of the Earth, if an angle of one degree be taken at the centre, the projectile force is to the centripetal about as 103 to 1. The disproportion is still greater in the orbits of the superior planets; greatest in that of Herschel.
The solar attraction at Herschel is 3,240,000,000,000,000,000 times less than it is one mile from the Sun. To us it is inconceivable, that such a diminished attraction can have any perceptible effect at the Geor-).. gium Sidus. It must, however, be remembered, that the planets move without resistance in an empty void. That bodies, balanced as they are, can be moved by a very small force, cannot be doubted. Attraction with drawn, we know not but Archimedes could have(made good his assertion by the force of his hand. That bodies so immense, however, and so immensely distant from each other, should all revolve in perfect harmony, may well excite the admiration of limited mortals; must be infinitely easy td Almighty Power) that, at the creation, “ spake, and it was done."
How is matter in itself? If a body be put in motion by an impulse, how would it pass ? Of what is circular or elliptical motion the effect? In what figures do the planets move? How are they kept in their orbits? What does gravity in one part of an orbit become in another? What will a double projectile force balance ? Does the proportion of the projectile force increase as the orbit is larger? In what orbit is the proportion of the projectile force greatest ?. Can the solar attraction have any perceptible effect at Herschel? If attraction were withdrawn, what is it possible Archimedes could have done? What power keeps the orbits duly balanced ?
*“ Give me where I may stand, and I will move the Earth." This was applied by the celebrated Syracusan to the mechanical force of the lever, but may be true in respect to the movement of the planets in empty void.
Prospect of the Heavens, as seen from different Parts
of the Solar System.
SECTION I. Prospect at the Sun.
| At the centre only can a just view be had of the solar system. Stationed there, a spectator would see all the primary planets moving in harmonious order from west to east, He might take the periodical time of one, perhaps Mercury, by which to measure the revolutions of the rest.
From their periodical times) and / apparent diameters, he might form some conjecture of their distances and magnitude. As all do not move in the same orbits, their paths would appear to cross each other at very small angles. The orbits being elliptical, but the line from any planet to the spectator passing equal areas in equal times, the spaces measured by such planet in a given time, would (appear unequal. Some variation in the diameter of each planet would also be apparent.
The fixed stars would appear equally distant, and all at rest.
Where only can a just view be had of the solar system? Stationed at the Sun, how would a spectator see the primary planets move? By the periodical time of what planet might he measure the revolutions of the rest? From what could he form a conjecture of the distances and magnitude of the planets ? Would the spaces measured by a planet in a given time appear equal? How would the fixed stars appear ?
Section II. Prospect at Mercury. A different view would be presented at Mercury, A spectator at this planet being, by the whole diameter
of Mercury's orbit, nearer to the other planets at some times than at other times, their diameters would appear to vary inversely as their distances.) To such a spectator Venus and the Earth would appear superior planets.) Thèse, and all the planets farther distant, would have conjunctions and oppositions. Their motions would appear sometimes / direct, sometimes retrograde.) They would seem stationary at intervals. If Mercury have not a rotation on his axis, a succession of day and night would scarcely be suggested to such a spectator. He might, however, observe the diurnal rotation of the other planets.
Why would the diameter of the planets seem to vary at Mercury? In what proportion would they seem to vary? Would the other planets at Mercury appear to be superior, or inferior ? Would they appear to have conjunctions only, or conjunctions and oppositions? How would their motions appear ?
SECTION III. Prospect at the Earth.
The prospect at the Earth is best known to its inhabitants. The inferior planets have two conjunctions in every synodical revolution ; the superior planets have conjunctions and oppositions in succession. The planets seem to enlarge or diminish, as they are nearer or farther distant. The inferior planets, by the position of their illuminated sides, assume all the phases of the Moon. By the rotation of the Earth on its axis, the Sun, the planets, and the fixed stars, appear to have a diurnal revolution from east to west.
Where is the prospect of the solar system best known to the inhabitants of the Earth? What planets appear to have conjunctions: only, and what conjunctions and oppositions ? Why do the planets appear larger at some times than at others? Which of the planets: exhibit the phases of the Moon?
Section IV. Prospect at Jupiter. (
To beings like ourselves, with eyes unassisted by glasses, it can scarcely be known, at Jupiter, that there are inferior planets. The greatest elongation of the Earth would not exceed 11° 11'; that of Mars, 170 13'.) By means of equatorial telescopes, however, planets may be seen extremely near the Sun.
Can it be known at Jupiter that there are inferior planets ? At Jupiter what would be the greatest elongation of the Earth and Mars? By what means can planets be seen very near the Sun ?
Section V. Prospect at Herschel.
An inhabitant of this Earth, transported to Herschel, would almost lose sight of the solar system. To him the Earth could never appear more than 30 2' from the Sun; Mars, 4° 38'; Jupiter, 15° 48'. Of these, without the assistance of glasses, he would not be likely to have a view, nor to have any knowledge, unless he had been an astronomer in this world. This, however, may depend on circumstances, particularly the atmosphere of Herschel. : But Saturn, having his greatest elongation 30°, might often be seen exhibiting, his ring excepted, all the phases of the Moon. To such an inhabitant, however, Saturn might not be the only planet visible. We know not but there may be planets in the system still farther distant from the Sun, well known to the inhabitants of the Georgium Sidus; for Almighty Power is not bounded by our limited view,
If an inhabitant of this Earth were transported to Herschel, could he have a view of the solar system? To him, how far would the Earth and the other planets appear from the Sun? May it be that the inhabitants of Herschel see other planets unknown to us ?