274
ASTRONOMY.
between the foci of the earth. If the eye were in the plane of theecliptic beyond the orbits in the line of the nodes, (which supposethe same in all the orbits,') the planets would seem to move back-ward and forward in straight lines, sometimes appearing as a blackspot crossing tbe sun’s disk, at other times being hid behind him,(Plate XXII. Fig. 2.) But because the line of the nodes is dif-ferent in all the orbits, if the eye be in one of these lines, two ofthe planets will appear to move in straight lines, the others inellipses, as from A to B, C, D, &c. Fig. 3. so that they are notseen to transit the sun’s disk; hence it is, that the transits of Venus and Mercury never happen but when they are near the nodes atthe inferior conjunction.
(62.) The 4th Fig. shews the proportional magnitudes of the pri-mary planets, Fig. 5 presents a view of the proportional magni-tude of the Sun ’s apparent disk seen from the planets markedby their characters in the figure : the same figure shews also theproportion of light and heat at each planet.
(63.) In Fig. 1, the Moon ’s orbit is drawn to exceed its dueproportion forty times; a I> is the line of the nodes which has aretrograde motion; this line and a line parallel to it through theSun will meet the heavens apparently in the same point becauseof the great distance of the stars; in the figure a I> is parallel to theline of the nodes in the orbit of Mars ; when this is a real casetheir nodes are in the same point of the heavens.
(64.) To a spectator placed in a fixed point at or near the cen-tre of the sun, all the planets would appear to describe circles in theheavens : these circles, apparently described among the fi xed stars,are called the heliocentric circles of the planets. The comets also,though moving in the most eccentric orbits, would appear to de-scribe circle;, among the stars; for the planes of their orbits ex-tended to the heavens would mark a great circle of which the evewould be the centre; only, as the real motion is in an ellipsis, thebody would appear to move much more slowly in some part ofthe circle than another, and to differ excessively in magnitude.
(65.) To an inhabitant of any planet, however, the sun appearsto go round in his own heliocentric circle, or to describe in theheavens that same curve, which the planet would appear to do ifseen from the sun. Thus in Plate XXU. fig. 8. when the earth is atc, if we draw a line from a through the sun at S, the point G, inthe sphere of the heavens where the line terminates, is the placewhere the sun then appears to an inhabitant of the earth. In amonth’s time the earth will go from a to b: draw a line thenthrough the sun, and its extremity at II will point out his apparentplace at that time. In like manner, if we draw lines from theearth in twelve several situations in which it is represented for thetwelve months of the year, the sun will appear to have performeda revolution in order from G to II, I, &c.: and so it would ap-pear to a spectator placed in Venus or any other planet.
(66.) The heliocentric circle of the earth is called the Ecliptic ;because eclipses of the sun or moon can only happen when thelatter is in or near it. By some ancient writers, it has been calledthe circle of the sun, or the oblique circle, because it cuts theequator at oblique angles. A belt taken in the concave sphere ofthe heavens about ten degrees on each side of the ecliptic, is calledthe Zodiac , from zwoy, an animal, because the constellations of theZodiac are chiefly represented by the figures of animals. ' Althoughthe sun apparently goes round the earth annually in this circle, wecannot determine his place by mere inspection, as we can do thatof any other of the heavenly bodies: for the fixed stars are the onlymarks by which we can determine the place of any of the celestialbodies ; and the superior brightness of the sun renders them totallyinvisible, except in the tune of a great eclipse, when his light isfor a time totally ob.cured. But though v.e cannot know theplace of tlie sun 'directly, it is easily found from a knowledge ofthose fixed stars which are opposite to him. Thus, in Plate XXII.fig. 8. suppose it the time of the year in which the earth is atg, if wekuow that the point G is then diametrically opposite to the sun,we know that A, its opposite, is the sun’s place, and consequently,by finding the places throughout the vear diametrically oppositeto the sun, as GIllKLMABCDEF, 'we may be assured that inthese times the sun’s place was in the points ABC DFFG11IKLM.The point in the heavens diametrically opposite to the sun maybe known every night at twelve o’clock when the stars are visi-ble ; for the star which has an elevation above the horizon, at I hattime equal to the sun’s depress ion below it, is directly opposite to him.
(67.) Aline passing through the centre of the sun perpendicu-
lar to the plane of the earth’s orbit will meet the heavens in apoint called the pole of the ecliptic ; if the line pass through Diecentre of Die earth it will be seen to meet the heavens in the samepoint because of the great distance of the stars. Circles drawnthrough the pole of the ecliptic cutting the ecliptic at right anglesare called circles of latitude. An arc of one of these circles con-tained between the ecliptic and any star or point in the heavensis the latitude of that jroint, or star. The latitude of any planetis either heliocentric or geocentric. r I he heliocentric latitudeis its latitude as seen from Die sun, the geocentric its latitudeas seen from the earth.
(68.) The place of a planet being known, its heliocentric la-titude is thus found : suppose a great circle passing Uirough thepole of the ecliptic and the planet V ; then will be formed a right-angled spherical triangle, in which are given the arc V N, the dis-tance of the node, and the angle at N, being the inclination of theorbit, to lind the latitude or perpendicular arc from V to theecliptic ; hence as rad. : sine of V N, so is sine of the inclinationto sine of the heliocentric latitude.
Example. Required the true heliocentric latitude of Venus , onthe 25th of May, 1813, at 30 minutes 54 seconds past nine in themorning, equal time at Greenwich; this planet being at thistime within I 1° 17'00".7 nf Imr fivippnflinnr on/1
tion of her orbit to the ecliptic 3° 23'35".
Is to the Sine of 2 from node, ll'M7'29'',7 . 6,291817
So is the Sine of the inclination of orbit of $ to eclip-tic, 3° 23'35" . 8,772213
To the Sine of the heliocentric latitude of 5
3 r 9' 5 °V 4 . 8,064030
Mo know whether Die heliocentric latitude of a planet benorth or south, the following rules must be attended to: IVlienthe planet’s distance from the ascending node, according to tin:order of the signs, is less than 3 signs, the latitude is nortli-ascend-ing ; if greater than 3, and less than 6 signs, the latitude is north-descending; if greater than 6, and less than 9 signs, the latitude is■south-ascending, but if greater than 9 signs, the latitude is south-de-scending. I11 our example the planet is 1 IS. 18°42'30",3 from herascending node, and consequently her latitude is south-descending.
(69.) M’lie arc of the ecliptic contained between the point wherethecircle of latitude cuts it, and the first point’of Aries, is called thelongitude of all those points, through which the circle of latitudepasses: the longitude is usually reckoned in signs and decrees, &c.and is expressed by saying, it is in such a degree and minute of asign, thus, long. % Si U 15° 10' may express that the long, ofMercury ’s ascending node is 15° 10'of M’aurus, or one sign 15°10, and bin. D,t £3 /)’ 12° 53' 30", that the descending node ofHerscliel is in 12° 53' 30" of Capricorn, or in 9S. 12° 53' 30".The place of a phenomenon in the heavens, is usually denotedby its latitude and longitude. M'lie longitude is also either helio-centric or geocentric, according as it expresses the place of theobject as seen from the sun or irom the earth.
(70) M'lie heliocentric latitude of a planet is greater than thegeocentric, when the planet is nearer to the sun than to the earth,but less when the earth is nearer to the planet, than the planet isto the sun..Let S, (fig. 8, Plate XXIII.) represent the sun, M' andC two situations of the earth, V a plain t having ascended fromthe node N ; from V let fall V E perpendicular to the plane ofthe ecliptic, join SE, C E, M" E, and S V, CV, M'V ; then theangle V S E is the heliocentric latitude, and V M’ E is the geocen-tric, when the earth is at M’, and V.C E, when it is at C ; w henceit appears that the heliocentric latitude is always the same whenthe planet is in the same point of its orbit, hut the geocentric isdifferent on account of the different situations of the earth in re-spect ot the planet ; because V E subtends an angle which is thesame with the latitude, it is evident that the latitude will begreater when the distance from the planet is less, and vice versa.Since Mercury is always nearer to the sun than to the earth, hisheliocentric latitude is always greater than bis geocentric, buttliat of Venus is sometimes greater and sometimes less; (bv trig.)S V : VE : : rad. : sine VS E ; and M' V :V E :: rad. : sine ofV M' E ;and since Dip means are the same in both, M'V : S V :: sine ofVSI5 : sine of VM’ E, that is, As the distance of the planet fromthe earth is to its distance from the sun, so is the sine of the he-liocentric latitude to the sine of the geocentric latitude.
( 71 .)