only by the apparent motion of the fun, occafioned by the real motion of Venus. But as this is by no means the cafe, an apparent motion of the earth among the figns of the ecliptic will be produced. Thus, the earth viewed from N, will appear among the fixed stars at P; from в it will appear at R; from u at o, where it will be ftationary fo long as the orbit of Venus does not fenfibly differ from its tangent; from J it will be feen returned back to R with a retrograde motion; from м at P; from к at T; from v at Q, where it again becomes ftationary; and from a it will be again feen at T, its motion having again become direct: whence we may obferve, that When a fuperior planet viewed from an inferior s appears stationary, the inferior planet viewed at the fame time from the fuperior is alfo ftationary; and, When the inferior planet viewed from the fupe- T rior moves apparently retrograde, or contrary to the order of the figns, the fuperior planet has also an apparently retrograde motion. But fince the earth has an annual motion round u the fun in its orbit, (110, M) we are therefore to difcover what part of the apparent motion of Venus is produced by that caufe. It is plain, that if the earth were at rest, and Venus seen at u, its greatest elongation, it would again be feen in the fame pofition, after performing a complete revolution in its orbit. But while Venus is performing this revolution, the earth is carried from E towards w, and fo forth. I 2 V forth. Therefore Venus muft pafs between two fimilar elongations, not only a complete revolution, but likewise the whole angular space which the earth has performed in the fame time. Hence its periodical time may be found. For the time between two fimiliar pofitions is obferved to be 583 days. Now, dividing the earth's orbit into 365 equal parts or days, the angular velocity of Venus will be denoted by the angular space paffed over in the given time, namely, one revolution, or 365 days added to 583 days, equal to 948; and the earth's angular velocity will be 583. The periodical times of Venus and the earth will be reciprocally as their angular velocities; confequently, As the angular velocity of Venus 948 Is to the angular velocity of the earth 583 So is the periodical time of the earth 365 To the periodical time of Venus 224 2 W Were it not for the fixed ftars, it would be impoffible to difcover or obferve the annual rhotion of the earth. We fhould conclude, that each planet made a complete revolution between any two fimilar fituations with refpect to the fun, because the spaces of elongation are fimilarly defcribed, and are in quantity the fame, whether the earth be in motion or not. Thus, if the earth be fixed at. E, the fame apparent elongations will be made by Venus with any velocity whatsoever in its orbit, but they will occur more frequently the greater the velocity. If a motion be given to the earth earth in the orbit EW, Venus will approach from u to м, which is now in motion, with a velocity equal to the difference between its angular velocity and that of the earth: or if the earth's angular velocity be greateft, it will apparently recede from M, and describe its revolutions in the contrary direction to its real motion. Now, as all the apparent motion of Venus in elongation is known by its approach or recefs from the line s E, and fince any angular motion of SE can only change the relative velocity of Venus; and fince a change of velocity will not alter the elongations, except as to time, it is evident that we cannot determine whether ɛ be at rest or no, from the appearances of the planets which revolve about the fun. It is then from the apparent motion of the fun, with respect to the fixed ftars, that we conclude that the earth describes an orbit in about 365 days. E If the fuperior planet E be at reft, the retrograde x motion of the inferior planet u among the fixed ftars will be the fame as its motion in elongation, viz. the angle UE V. But if E move in the fame direction as u, but angularly flower, the arc described by the retrograde motion in the ecliptic will be less than that defcribed between the twooppofite elongations. The fame is true of the retrograde motion of the fuperior viewed from the inferior planet. For the motion of E towards w caufes an ap- Y parent motion of the fun towards D. And as the retrograde motion of u referred to the arc Ds is flowest near the elongations, it is plain that u will not become stationary in the ecliptic till its apparent motion in elongation from D towards s is equal to the fun's apparent motion in the contrary direction; that is to fay, till fome time after paffing the greatest elongation, fuppofe at d. After which its motion must become retrograde till it arrives at H, equidiftant from its greatest elongation on the other fide, where it will again become stationary, its apparent motion in elongation being equal and contrary to that of the fun in the ecliptic. Now, the angle HEd is less than the angle of retrograde motion in elongation CE D. And fince the angle 1 Eq is equal to HE D, it is alfo less than CED. But those angles IE q and H ED are the measures of the retrograde motions of the fuperior and inferior planets, when viewed from each other. Whence the propofition is evident. CHAP. IV. OF THE SUPERIOR PLANETS, AND OF THE TRUE FORM OF THE PLANETARY ORBITS. THE appearance of the earth when viewed from Venus being explained, it will be easy to apply that explanation to the apparent motions of the fuperior planets. Of the two inferior planets Venus ferved us as an instance; and of the three fuperior ones we shall select Jupiter, as being the most bright and confpicuous. The motions of this planet being accounted for, fimilar obfervations and fimilar reafoning will obviously folve those of the other pla nets, 1 nets, whose particular phenomena will not, therefore, require a more minute elucidation. That the planet Jupiter revolves in an orbit, which includes that of the earth, and refpects the fun as its center, was fhewn in the beginning of the laft chapter; and its apparent motions are observed to be fimilar to those which it was proved the earth would have when feen from Venus. It remains to difcover its periodical time and diftance from the fun. Let s (fig. 47) represent the fun, the earth, J Jupiter, the circle Ee a the earth's orbit, and the circle J Bj the orbit of Jupiter. Suppose Jupiter to be in oppofition to the fun. The earth revolving in its orbit will, in the space of 365. days, arrive again at E, but the opposition will not then happen, becaufe Jupiter in the mean time will have moved in its orbit towards j. The earth muft therefore pass through the arc Ee or 33 days before it overtakes it. Confequently, the angular velocity of Jupiter will be denoted by 33, and that of the earth by one whole revolution, (or 365) added to 33, equal to 3981. But as the periodical times are reciprocally as the angular velocities, it will be As the angular velocity of Jupiter So is the periodical time of the earth 33/ 398 365 days 4340 days. Smaller fractions being rejected, the periodical times are not here exact. I 4 The |
