Letters on Astronomy Part 13

The _dimensions_ of the planetary system are seen from this table to be vast, comprehending a circular s.p.a.ce thirty-six hundred millions of miles in diameter. A rail-way car, travelling constantly at the rate of twenty miles an hour, would require more than twenty thousand years to cross the orbit of Ura.n.u.s.

_Magnitudes._

Diam. in miles.

1. Mercury, 3140 2. Venus, 7700 3. Earth, 7912 4. Mars, 4200 5. Ceres, 160 6. Jupiter, 89,000 7. Saturn, 79,000 8. Ura.n.u.s, 35,000

We remark here a great diversity in regard to magnitude,--a diversity which does not appear to be subject to any definite law. While Venus, an inferior planet, is nine tenths as large as the earth, Mars, a superior planet, is only one seventh, while Jupiter is twelve hundred and eighty-one times as large. Although several of the planets, when nearest to us, appear brilliant and large, when compared with most of the fixed stars, yet the angle which they subtend is very small,--that of Venus, the greatest of all, never exceeding about one minute, which is less than one thirtieth the apparent diameter of the sun or moon. Jupiter, also, by his superior brightness, sometimes makes a striking figure among the stars; yet his greatest apparent diameter is less than one fortieth that of the sun.

_Periodic Times_.

Mercury revolves around the sun in nearly 3 months.

Venus, " " " " 7-1/2 "

Earth, " " " " 1 year.

Mars, " " " " 2 years.

Ceres, " " " " 4-2/3 "

Jupiter, " " " " 12 "

Saturn, " " " " 29 "

Ura.n.u.s, " " " " 84 "

From this view, it appears that the planets nearest the sun move most rapidly. Thus, Mercury performs nearly three hundred and fifty revolutions while Ura.n.u.s performs one. The apparent progress of the most distant planets around the sun is exceedingly slow. Ura.n.u.s advances only a little more than four degrees in a whole year; so that we find this planet occupying the same sign, and of course remaining nearly in the same part of the heavens, for several years in succession.

After this comparative view of the planets in general, let us now look at them individually; and first, of the inferior planets, Mercury and Venus.

MERCURY and VENUS, having their orbits so far within that of the earth, appear to us as attendants upon the sun. Mercury never appears further from the sun than twenty-nine degrees, and seldom so far; and Venus, never more than about forty-seven degrees. Both planets, therefore, appear either in the west soon after sunset, or in the east a little before sunrise. In high lat.i.tudes, where the twilight is long, Mercury can seldom be seen with the naked eye, and then only when its angular distance from the sun is greatest. Copernicus, the great Prussian astronomer, (who first distinctly established the order of the solar system, as at present received,) lamented, on his death-bed, that he had never been able to obtain a sight of Mercury; and Delambre, a distinguished astronomer of France, saw it but twice. In our lat.i.tude, however, we may see this planet for several evenings and mornings, if we will watch the time (as usually given in the almanac) when it is at its greatest elongations from the sun. It will not, however, remain long for our gaze, but will soon run back to the sun. The reason of this will be readily understood from the following diagram, Fig. 50. Let S represent the sun, E, the earth, and M, N, Mercury at its greatest elongations from the sun, and O Z P, a portion of the sky. Then, since we refer all distant bodies to the same concave sphere of the heavens, it is evident that we should see the sun at Z, and Mercury at O, when at its greatest eastern elongation, and at P, when at its greatest western elongation; and while pa.s.sing from M to N through Q, it would appear to describe the arc O P; and while pa.s.sing from N to M through R, it would appear to run back across the sun on the same arc. It is further evident that it would be visible only when at or near one of its greatest elongations; being at all other times so near the sun as to be lost in his light.

[Ill.u.s.tration Fig. 50.]

A planet is said to be in _conjunction_ with the sun when it is seen in the same part of the heavens with the sun. Mercury and Venus have each two conjunctions, the inferior and the superior conjunction. The _inferior conjunction_ is its position when in conjunction on the same side of the sun with the earth, as at Q, in the figure; the _superior conjunction_ is its position when on the side of the sun most distant from the earth, as at R.

The time which a planet occupies in making one entire circuit of the heavens, from any star, until it comes round to the same star again, is called its _sidereal revolution_. The period occupied by a planet between two successive conjunctions with the earth is called its _synodical revolution_. Both the planet and the earth being in motion, the time of the synodical revolution of Mercury or Venus exceeds that of the sidereal; for when the planet comes round to the place where it before overtook the earth, it does not find the earth at that point, but far in advance of it. Thus, let Mercury come into inferior conjunction with the earth at C, Fig. 51. In about eighty-eight days, the planet will come round to the same point again; but, mean-while, the earth has moved forward through the arc E E', and will continue to move while the planet is moving more rapidly to overtake her; the case being a.n.a.logous to that of the hour and minute hand of a clock.

[Ill.u.s.tration Fig. 51.]

The synodical period of Mercury is one hundred and sixteen days, and that of Venus five hundred and eighty-four days. The former is increased twenty-eight days, and the latter, three hundred and sixty days, by the motion of the earth; so that Venus, after being in conjunction with the earth, goes more than twice round the sun before she comes into conjunction again. For, since the earth is likewise in motion, and moves more than half as fast as Venus, by the time the latter has gone round and returned to the place where the two bodies were together, the earth is more than half way round, and continues moving, so that it will be a long time before Venus comes up with it.

The motion of an inferior planet is _direct_ in pa.s.sing through its superior conjunction, and _retrograde_ in pa.s.sing through its inferior conjunction. You will recollect that the motion of a heavenly body is said to be direct when it is in the order of the signs from west to east, and retrograde when it is contrary to the order of the signs, or from east to west. Now Venus, while going from B through D to A, (Fig.

51,) moves from west to east, and would appear to traverse the celestial vault B' S' A', from right to left; but in pa.s.sing from A through C to B, her course would be retrograde, returning on the same arc from left to right. If the earth were at rest, therefore, (and the sun, of course, at rest,) the inferior planets would appear to oscillate backwards and forwards across the sun. But it must be recollected that the earth is moving in the same direction with the planet, as respects the signs, but with a slower motion. This modifies the motions of the planet, accelerating it in the superior, and r.e.t.a.r.ding it in the inferior, conjunction. Thus, in Fig. 51, Venus, while moving through B D A, would seem to move in the heavens from B' to A', were the earth at rest; but, mean-while, the earth changes its position from E to E', on which account the planet is not seen at A', but at A'', being accelerated by the arc A' A'', in consequence of the earth's motion. On the other hand, when the planet is pa.s.sing through its inferior conjunction A C B, it appears to move backwards in the heavens from A' to B', if the earth is at rest, but from A' to B'', if the earth has in the mean time moved from E to E', being r.e.t.a.r.ded by the arc B' B''. Although the motions of the earth have the effect to accelerate the planet in the superior conjunction, and to r.e.t.a.r.d it in the inferior, yet, on account of the greater distance, the apparent motion of the planet is much slower in the superior than in the inferior conjunction, Venus being the whole breadth of her orbit, or one hundred and thirty-six millions of miles further from us when at her greatest, than when at her least, distance, as is evident from Fig. 51. When pa.s.sing from the superior to the inferior conjunction, or from the inferior to the superior, through the greatest elongations, the inferior planets are _stationary_. Thus, (Fig.

51,) when the planet is at A, the earth being at E, as the planet's motion is directly towards the spectator, he would constantly project it at the same point in the heavens, namely, A'; consequently, it would appear to stand still. Or, when at its greatest elongation on the other side, at B, as its motion would be directly from the spectator, it would be seen constantly at B'. If the earth were at rest, the stationary points would be at the greatest elongations, as at A and B; but the earth itself is moving nearly at right angles to the planet's motion, which makes the planet appear to move in the opposite direction. Its direct motion will therefore continue longer on the one side, and its retrograde motion longer on the other side, than would be the case, were it not for the motion of the earth. Mercury, whose greatest angular distance from the sun is nearly twenty-nine degrees, is stationary at an elongation of from fifteen to twenty degrees; and Venus, at about twenty-nine degrees, although her greatest elongation is about forty-seven degrees.

Mercury and Venus exhibit to the telescope _phases_ similar to those of the moon. When on the side of their inferior conjunction, as from B to C through D, Fig. 52, less than half their enlightened disk is turned towards us, and they appear horned, like the moon in her first and last quarters; and when on the side of the superior conjunction, as from C to B through A, more than half the enlightened disk is turned towards us, and they appear gibbous. At the moment of superior conjunction, the whole enlightened orb of the planet is turned towards the earth, and the appearance would be that of the full moon; but the planet is too near the sun to be commonly visible.

[Ill.u.s.tration Fig. 52.]

We should at first thought expect, that each of these planets would be largest and brightest near their inferior conjunction, being then so much nearer to us than at other times; but we must recollect that, when in this situation, only a small part of the enlightened disk is turned toward us. Still, the period of greatest brilliancy cannot be when most of the illuminated side is turned towards us, for then, being at the superior conjunction, its light will be diminished, both by its great distance, and by its being so near the sun as to be partially lost in the twilight. Hence, when Venus is a little within her place of greatest elongation, about forty degrees from the sun, although less than half her disk is enlightened, yet, being comparatively near to us, and shining at a considerable alt.i.tude after the evening or before the morning twilight, she then appears in greatest splendor, and presents an object admired for its beauty in all ages. Thus Milton,

"Fairest of stars, last in the train of night, If better thou belong not to the dawn, Sure pledge of day that crown'st the smiling morn With thy bright circlet."

Mercury and Venus both _revolve on their axes_ in nearly the same time with the earth. The diurnal period of Mercury is a little greater, and that of Venus a little less, than twenty-four hours. These revolutions have been determined by means of some spot or mark seen by the telescope, as the revolution of the sun on his axis is ascertained by means of his spots. Mercury owes most of its peculiarities to its proximity to the sun. Its light and heat, derived from the sun, are estimated to be neatly seven times as great as on the earth, and the apparent magnitude of the sun to a spectator on Mercury would be seven times greater than to us. Hence the sun would present to an inhabitant of that planet, with eyes like ours, an object of insufferable brightness; and all objects on the surface would be arrayed in a light more glorious than we can well imagine. (See Fig. 53.) The average heat on the greater portion of this planet would exceed that of boiling water, and therefore be incompatible with the existence both of an animal and a vegetable kingdom const.i.tuted like ours.

The motion of Mercury, in his revolution round the sun, is swifter than that of any other planet, being more than one hundred thousand miles every hour; whereas that of the earth is less than seventy thousand.

Eighteen hundred miles every minute,--crossing the Atlantic ocean in less than two minutes,--this is a velocity of which we can form but a very inadequate conception, although, as we shall see hereafter, it is far less than comets sometimes exhibit.

Venus is regarded as the most beautiful of the planets, and is well known as the _morning and evening star_. The most ancient nations, indeed, did not recognise the morning and evening star as one and the same body, but supposed they were different planets, and accordingly gave them different names, calling the morning star Lucifer, and the evening star Hesperus. At her period of greatest splendor, Venus casts a shadow, and is sometimes visible in broad daylight. Her light is then estimated as equal to that of twenty stars of the first magnitude. In the equatorial regions of the earth, where the twilight is short, and Venus, at her greatest elongation, appears very high above the horizon, her splendors are said to be far more conspicuous than in our lat.i.tude.

[Ill.u.s.tration Fig. 53. APPARENT MAGNITUDES OF THE SUN, AS SEEN FROM THE DIFFERENT PLANETS.]

[Ill.u.s.tration Figures 54, 55, 56. VENUS AND MARS.]

Every eight years, Venus forms her conjunction with the sun in the same part of the heavens. Whatever appearances, therefore, arise from her position with respect to the earth and the sun, they are repeated every eight years, in nearly the same form.

Thus, every eight years, Venus is remarkably conspicuous, so as to be visible in the day-time, being then most favorably situated, on several accounts; namely, being nearest the earth, and at the point in her orbit where she gives her greatest brilliancy, that is, a little within the place of greatest elongation. This is the period for obtaining fine telescopic views of Venus, when she is seen with spots on her disk. Thus two figures of the annexed diagram (Fig. 54) represent Venus as seen near her inferior conjunction, and at the period of maximum brilliancy.

The former situation is favorable for viewing her inequalities of surface, as indicated by the roughness of the line which separates the enlightened from the unenlightened part, (the _terminator_.) According to Schroeter, a German astronomer, Venus has mountains twenty-two miles high. Her mountains, however, are much more difficult to be seen than those of the moon.

The sun would appear, as seen from Venus, twice as large as on the earth, and its light and heat would be augmented in the same proportion.

(See Fig. 53.) In many respects, however, the phenomena of this planet are similar to those of our own; and the general likeness between Venus and the earth, in regard to dimensions, revolutions, and seasons, is greater than exists between any other two bodies of the system.

I will only add to the present Letter a few words on the _transits_ of the inferior planets.

The transit of Mercury or Venus is its pa.s.sage across the sun's disk, as the moon pa.s.ses over it in a solar eclipse. The planet is seen projected on the sun's disk in a small, black, round spot, moving slowly over the face of the sun. As the transit takes place only when the planet is in inferior conjunction, at which time her motion is retrograde, it is always from left to right; and, on account of its motion being r.e.t.a.r.ded by the motion of the earth, (as was explained by Fig. 51, page 232,) it remains sometimes a long time on the solar disk. Mercury, when it makes its transit across the sun's centre, may remain on the sun from five to seven hours.

You may ask, why we do not observe this appearance every time one of the inferior planets comes into inferior conjunction, for then, of course, it pa.s.ses between us and the sun. It must, indeed, at this time, cross the meridian at the same time with the sun; but, because its...o...b..t is inclined to that of the sun, it may cross it (and generally does) a little above or a little below the sun. It is only when the conjunction takes place at or very near the point where the two orbits cross one another, that is, near the _node_, that a transit can occur. Thus, if the orbit of Mercury, N M R, Fig. 50, (page 231,) were in the same plane with the earth's...o...b..t, (and of course with the sun's apparent orbit,) then, when the planet was at Q, in its inferior conjunction, the earth being at E, it would always be projected on the sun's disk at Z, on the concave sphere of the heavens, and a transit would happen at every inferior conjunction. But now let us take hold of the point R, and lift the circle which represents the orbit of Mercury upwards seven degrees, letting it turn upon the diameter _d b_; then, we may easily see that a spectator at E would project the planet higher in the heavens than the sun; and such would always be the case, except when the conjunction takes place at the node. Then the point of intersection of the two orbits being in one and the same plane, both bodies would be referred to the same point on the celestial sphere. As the sun, in his apparent revolution around the earth every year, pa.s.ses through every point in the ecliptic, of course he must every year be at each of the points where the orbit of Mercury or Venus crosses the ecliptic, that is, at each of the nodes of one of these planets;[12] and as these nodes are on opposite sides of the ecliptic, consequently, the sun will pa.s.s through them at opposite seasons of the year, as in January and July, February and August. Now, should Mercury or Venus happen to come between us and the sun, just as the sun is pa.s.sing one of the planet's nodes, a transit would happen. Hence the transits of Mercury take place in May and November, and those of Venus, in June and December.

Transits of Mercury occur more frequently than those of Venus. The periodic times of Mercury and the earth are so adjusted to each other, that Mercury performs nearly twenty-nine revolutions while the earth performs seven. If, therefore, the two bodies meet at the node in any given year, seven years afterwards they will meet nearly at the same node, and a transit may take place, accordingly, at intervals of seven years. But fifty-four revolutions of Mercury correspond still nearer to thirteen revolutions of the earth; and therefore a transit is still more probable after intervals of thirteen years. At intervals of thirty-three years, transits of Mercury are exceedingly probable, because in that time Mercury makes almost exactly one hundred and thirty-seven revolutions. Intermediate transits, however, may occur at the other node. Thus, transits of Mercury happened at the ascending node in 1815, and 1822, at intervals of seven years; and at the descending node in 1832, which will return in 1845, after thirteen years.

Transits of Venus are events of very unfrequent occurrence. Eight revolutions of the earth are completed in nearly the same time as thirteen revolutions of Venus; and hence two transits of Venus may occur after an interval of eight years, as was the case at the last return of the phenomenon, one transit having occurred in 1761, and another in 1769. But if a transit does not happen after eight years, it will not happen at the same node, until an interval of two hundred and thirty-five years: but intermediate transits may occur at the other node. The next transit of Venus will take place in 1874, being two hundred and thirty-five years after the first that was ever _observed_, which occurred in 1639. This was seen, for the first time by mortal eyes, by two youthful English astronomers, Horrox and Crabtree. Horrox was a young man of extraordinary promise, and indicated early talents for practical astronomy, which augured the highest eminence; but he died in the twenty-third year of his age. He was only twenty when the transit appeared, and he had made the calculations and observations, by which he was enabled to antic.i.p.ate its arrival several years before. At the approach of the desired time for observing the transit, he received the sun's image through a telescope in a dark room upon a white piece of paper, and after waiting many hours with great impatience, (as his calculation did not lead him to a knowledge of the precise time of the occurrence,) at last, on the twenty-fourth of November, 1639, old style, at three and a quarter hours past twelve, just as he returned from church, he had the pleasure to find a large round spot near the limb of the sun's image. It moved slowly across the sun's disk, but had not entirely left it when the sun set.

The great interest attached by astronomers to a transit of Venus arises from its furnishing the most accurate means in our power of determining the _sun's horizontal parallax_,--an element of great importance, since it leads us to a knowledge of the distance of the earth from the sun, which again affords the means of estimating the distances of all the other planets, and possibly, of the fixed stars. Hence, in 1769, great efforts were made throughout the civilized world, under the patronage of different governments, to observe this phenomenon under circ.u.mstances the most favorable for determining the parallax of the sun.

The common methods of finding the parallax of a heavenly body cannot be relied on to a greater degree of accuracy than four seconds. In the case of the moon, whose greatest parallax amounts to about one degree, this deviation from absolute accuracy is not very material; but it amounts to nearly half the entire parallax of the sun.

If the sun and Venus were equally distant from us, they would be equally affected by parallax, as viewed by spectators in different parts of the earth, and hence their _relative_ situation would not be altered by it; but since Venus, at the inferior conjunction, is only about one third as far off as the sun, her parallax is proportionally greater, and therefore spectators at distant points will see Venus projected on different parts of the solar disk, as the planet traverses the disk.

Astronomers avail themselves of this circ.u.mstance to ascertain the sun's horizontal parallax, which they are enabled to do by comparing it with that of Venus, in a manner which, without a knowledge of trigonometry, you will not fully understand. In order to make the difference in the apparent places of Venus on the sun's disk as great as possible, very distant places are selected for observation. Thus, in the transits of 1761 and 1769, several of the European governments fitted out expensive expeditions to parts of the earth remote from each other. For this purpose, the celebrated Captain Cook, in 1769, went to the South Pacific Ocean, and observed the transit at the island of Otaheite, while others went to Lapland, for the same purpose, and others still, to many other parts of the globe. Thus, suppose two observers took their stations on opposite sides of the earth, as at A, and B, Fig. 57, page 242; at A, the planet V would be seen on the sun's disk at _a_, while at B, it would be seen at _b_.

The appearance of Venus on the sun's disk being that of a well-defined black spot, and the exactness with which the moment of external or internal contact may be determined, are circ.u.mstances favorable to the exactness of the result; and astronomers repose so much confidence in the estimation of the sun's horizontal parallax, as derived from observations on the transit of 1769, that this important element is thought to be ascertained within one tenth of a second. The general result of all these observations gives the sun's horizontal parallax eight seconds and six tenths,--a result which shows at once that the sun must be a great way off, since the semidiameter of the earth, a line nearly four thousand miles in length, would appear at the sun under an angle less than one four hundredth of a degree. During the transits of Venus over the sun's disk, in 1761 and 1769, a sort of penumbral light was observed around the planet, by several astronomers, which was thought to indicate an _atmosphere_. This appearance was particularly observable while the planet was coming on or going off the solar disk.

The total immersion and emersion were not instantaneous; but as two drops of water, when about to separate, form a ligament between them, so there was a dark shade stretched out between Venus and the sun; and when the ligament broke, the planet seemed to have got about an eighth part of her diameter from the limb of the sun. The various accounts of the two transits abound with remarks like these, which indicate the existence of an atmosphere about Venus of nearly the density and extent of the earth's atmosphere. Similar proofs of the existence of an atmosphere around this planet are derived from appearances of twilight.

[Ill.u.s.tration Fig. 57.]

The elder astronomers imagined that they had discovered a _satellite_ accompanying Venus in her transit. If Venus had in reality any satellite, the fact would be obvious at her transits, as, in some of them at least, it is probable that the satellite would be projected near the primary on the sun's disk; but later astronomers have searched in vain for any appearances of the kind, and the inference is, that former astronomers were deceived by some optical illusion.

FOOTNOTE:

[12] You will recollect that the sun is said to be at the node, when the places of the node and the sun are both projected, by a spectator on the earth, upon the same part of the heavens.

LETTER XXI.