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 45© ASTRO N O M Y. As the planets approach nearer the fun, and recede of E/’s attraction, be projected as in the right line Z, farther him in every revolution,* there may be fome •with a force perpendicular to the attraction of U, then a difficultyfrom the reafon why the power of grawill go round U in the orbit IV, and accompany it in its vity, whenin itconceiving once gets the better of the projeCtile force, whole courfe round the body S. Here S may reprefent does not bring the planets nearer and nearer the fun in the fun, U the earth, and u the moon. revolution, till they fall upon and unite with him y If a planet at B gravitates, or is attracted toward the every why the pfojeCtile force, when it once gets the better fun fo as to fall from B to y in the time that the projec- orof gravity, does not carry the planets farther and farther tile force would have carried it from B to X; it will dethe fun, till it removes them quite out of the fphere fcribe the curve BY by the combined.action of thefe two from of his attraction, and caufes them to go on in ftraight forces, in the fame time that the projeCtile force fingly lines for ever afterward. But by confidering the effeCts would have carried it from B to X, or the gravitating of thefe powers, this difficulty will be removed. Suppower fingly have caufed it to defcend from B to j> ’, and a planet at B to be carried by the projeCtile force as thefe two forces being duly proportioned, and perpendi- pofe cular to one another, the planet obeying them both, will far as from B to b, in the time that gravity would have brought it down from 2? to 1 ; by thefe two forces it move in the circle BYTU. But if, whilft the projeCtile force carries the planet will deferibe the curve BC. When the planet comes to K, it will be but half as far from the fun S as from B to b, the fun’s attraction (which conftitutes the down planet’s gravitation) Ihould bring it down from B to i, it was at B; and therefore, by gravitating four times as the gravitating power would then be too ftrong for the ftrongly towards him, it would fall from 2f to Z in the projeCtile force, and would caufe the planet to deferibe fame length of time that it would have fallen from B to the curve BC. When the planet comes to C, the gra- 1 in the higher part of its orbit, thaf is, through four vitating power (which always increafes as the fquare of times as much fpace; but its projeCtile force is then fo the diftance from the fun S diminifhes) will be yet ftronger much increafed at K, as would carry it from K to k in for the projeCtile force; and by confpiring in fome de- the fame time; being double of what it was at B, and gree therewith, will accelerate the planet’s motion all the is therefore too ftrong for the gravitating power, either w'ay from C to K, caufing it to deferibe the arcs, BC, to draw the planet to the fun, or caufe it to go round CD, DE, EF, &c. all in equal times. Having its mo- him in the circle Klmn, &c. which would require its tion thus accelerated, it thereby gains fo much centrifu- failing from K to to, through a greater fpace than gragal force, or tendency to fly off at K in the line Kk, as vity can draw it, whilft the projeCHle force is fuch as overcomes the fun’s attraction; and the centrifugal force would carry it from A’to 2; and therefore the planet abeing too great to allow the planet to be brought nearer feends in its orbit KLMN, decreafing in its velocity,' for the fun, or even to move round him in the circle Klmn, the caufe already affigned. &e. it goes off, and afeends in the curve KLM.N, &c. The orbits of all the planets are ellipfes, very little its motion decreafing as gradually from K to B, as it in- different from circles; but the orbits of the comets are creafed from B to K, becaufe the fun’s attraction aCts very long ellipfes, and the lower focus'of them all is in now againft the planet’s projeCtile motion juft as much as the fun. If we fuppofe the mean diftance (br middle it aCted with it before. When the planet has got round between the greateft and leaft) of every planet and coto B, its projectile force is as much diminifhed from its met from the fun to be divided into 1000 equal parts, mean ftate about G or N, as it was augmented at K; the excentricities of their orbits, both in fuch parts and and fo, the fun’s attraction being more than fufficient to in Englilh miles, will be as follow. Mercury’s 210 keep the planet from going off at' B, it deferibes the parts, or 6,720,000 miles; Venus’s, 7 parts, or 413,000 fame orbit over again,, by virtue of the fame forces or miles; the earth’s, 17 parts, or 1,377,000 miles; powers. Mars’s, 93 parts, or 11,439,000 miles; Jupiter’s, 48 A double projeCtile force' will always balance a qua- parts, or 20,352.000 miles; Saturn’s, 55 parts, or druple power of gravity. Let the planet at B have 42,735,000 miles. Of the neareft of the three Toretwice as great an impulfe from thence towards X, as it mentioned comets, 1,458,000 miles; of the middlehad before; that is, in the fame length of time that it moft, 2,025,000,000 miles; and of the outermoft, was projected from B to b, as in the laft example, let it 6,600,000,000. now be projected from B to c, and it will require four By the laws of gravity and the projectile force, bodies times as much gravity to retain it in its orbit; that is,, it will move in all kinds of ellipfes,. whether long or (fiort, muft fall as far as from 5 to 4 in the time that the pro- if the fpaces they move in be void of refiftanc.e; only jeCtile force would carry it from 2? to c, otherwife it thofe which move in the longer ellipfes, have fo much could not deferibe the curve BD, as is evident by the fi- the lefs prbjeCtile force impreffed upon them in the higher gure. But in as much time as the planet moves from B parts of their orbits; and their velocities in coming to C in the higher part of its orbit, it moves from I to down towards the fun are fo prodigioufly increafed by his K, or from K to L, in the lower part thereof; becaufe, attraction, that their centrifugal forces in the lower parts from the joint aCtiod of thefe two forces* it muft always of their orbits are fo great, as to Overcome the fun’s atdeferibe equal areas in equal times, throughout its annual traction there, and caufe them to afeend again towards courfc. Thefe areas are reprefented by the triangles the higher parts of their orbits ; during which time, the BSC, CSD, DSE, ESF, 8tc. whofe contents are equal fun’s attraction aCting fo contrary to the motions of thofe to one another, quite round the figure. . booies, caufes them to move flower and flower, until their.