RETROGRESSION. ] 



ASTRONOMY. 



943 



very unphOosophical, and as only fitted for the prejudices 

 of the age. 



STATIONS AND RETROGRADATIONS. The various pro- 

 gressive and retrograde motions of the planets, explained 

 by the cumbrous machinery of the Ptolemaic system, on 

 the supposition of the earth being stationary, follow 

 naturally from the circular motions of the planets them- 

 selves, combined with that of the earth, in the true 

 system of the universe, and, indeed, led the illustrious 

 Copernicus to his great discovery. The two inferior 

 planets, Mercury and Venus, move round the sun in 

 less time than the earth ; and if S be the sun (Fig. 61), 

 V, Venus at inferior conjunction, and T the earth, the 

 planet will pass through an arc V V of its orbit, in the 

 game time that the earth passes through the smaller arc 

 . ei. T T 7 of its orbit. The 



planet, therefore, has ap- 

 peared to move quicker 

 than the earth in the 

 direction of the arrow, 

 which is in a retrograde 

 direction. If, however, 

 , Venus be found at su- 

 | perior conjunction with 

 the sun, and it passes 

 from V* to V" in the 

 same time that the earth 

 moves from T to T, it 

 will appear to move in a 

 contrary sense to the 

 arrow, and, therefore, 

 direct. Between these two points, the planet will, of 

 course, be animated with different rates of motion, and, 

 at certain times, will appear quite stationary in the 

 heavens. If the earth were fixed at T, the planet would 

 appear stationary at the point of greatest elongation. 

 As it is, however, the planet and earth must be both 

 moving at the same rate, and in the same direction, in 

 order that the former may appear stationary. The dura- 

 tion of the retrograde movement of Venus is only three 

 weeks before and after the time of inferior conjunction. 

 The superior planets bear the same relation to the 

 earth as the hitter does to Venus and Mercury ; so that 

 when the earth is stationary for any of those planets, 

 the planets appear in the same manner to be stationary 

 to the earth. The progressive and retrograde motions 

 of the superior planets may, therefore, be explained in 

 nearly the same manner. If M be Mars in opposition 

 (Fig. 62), as the earth moves more rapidly in its orbit 



"Fir. 02. 



WM" 



than the planet, it will pass from T to T', whilst Mars 

 only moves from M to M' ; so that whilst it was first seen 

 in the direction T M, it will afterwards appear in the 

 direction T' M ; or, in other words, the planet will appear 

 to have fallen back in the manner indicated by the arrow, 

 or in retrograde direction. When the planet is in con- 



Fig. 6J. 



junction with the sun, or at M", whilst it passes from 

 M" to M"', the ear*H will have moved from T to T in 

 the contrary direction, so that the planet will appear to 

 move in a direct sense, or according to the order of the 

 signs. Thus all the superior planets are retrograde at 

 the tune of opposition, because their motion is slower 

 than that of the earth ; and at the time of conjunction 

 they are always direct, because moving in the contrary 

 direction. Between those points the planet will appear 

 as stationary at that part of its orbit, when the earth, 

 passing from T to T", will be so oblique in regard to 

 M M' that the lines T M and T' M' will be parallel ; and 

 as the distances of the stars are immense in comparison 

 with any of the planets, the lines T M and T' M' will be 

 directed to the same point of the heavens, and the planet 

 will appear exactly in the same position in respect to any 

 fixed point or star. 



To DETERMINE THE ELONGATION OF A PLANET WHEN 

 STATIONARY is a difficult problem, when the inclinations 

 and ellipticity of the orbit are taken into consideration ; 

 but as at the present time it is more a matter of curiosity 

 than interest, the orbit may be considered as circular 



without much error, 

 and situated in the 

 same place as the 

 ecliptic. Let S (Fig. 

 63) be the sun, T the 

 earth, and M the po- 

 sition of Mars near its 

 stationary point; then, 

 when the earth passes 

 from T to T', the 

 planet will move from 

 M to M', and the 

 lines M'T, M'T', may 

 be considered as pa- 

 rallel, as before ex- 

 plained. Consequently 

 M'T'S MTS = MrS 

 M T S=T S T'; and in the'same manner S Mr SM T' 

 = S r> T S M' T = M S M'. Whence it follows that the 

 angular variations at T and M are proportional to the 

 angles T S T' and M S M' ; or as the angular velocities 



3 Q 



are inversely as the periodic times, then S Ma : S T? ; 

 and putting a = S M, and S T= unity, the sines of the 

 angles M and T will be in the ratio of their opposite 

 sides, or as a : 1, and the contemporary variations of the 

 auylus will be as their tangents ; or, 



sin. T sin. M 4 , ' 



cos. S ' cos. M ' 



whence 



sin.T 



sin. M 



>/(! -sin."T)' V (1 sin. 2 M)" 



a 3 a j a 2 



And sin. 2 T 



a' 1 



and sin. T= 



For an inferior planet the M and M' may represent the 

 place of the earth, and T and T'the positions of Mercury 

 and Venus. Thus if the mean distances of the earth and 

 Venus be taken at 100,000 and 72,333, then sin. T = 

 '48264, the sine of 28 51', or at this angle of elongation 

 from the sun, the planet is stationary. 



To determine the time when a planet is stationary, the 

 time of conjunction or opposition must be known. If m 

 and n are the daily motions of the earth and planet, then 

 m n, or n. m is the daily variation at the angle T S M, 

 as it is a superior or inferior planet ; then, 



PHASES OF THE SUPERIOR PLANETS. None of the 

 superior planets show the same succession of phases as 

 Mercury and Venus ; and only one of them, Mars, is 

 near enough to the earth to show any appearance of de- 

 parture from a full disc, the illuminated hemisphere 



