Part 8

116. _Lunar Craters._--The smaller saucer-shaped formations on the surface of the moon are called _craters_. They are of all sizes, from a mile to a hundred and fifty miles in diameter; and they are supposed to be of volcanic origin. A high telescopic power shows that these craters vary remarkably, not only in size, but also in structure and arrangement. Some are considerably elevated above the surrounding surface, others are basins hollowed out of that surface, and with low surrounding ramparts; some are like walled plains, while the majority have their lowest depression considerably below the surrounding surface; some are isolated upon the plains, others are thickly crowded together, overlapping and intruding upon each other; some have elevated peaks or cones in their centres, and some are without these central cones, while others, again, contain several minute craters instead; some have their ramparts whole and perfect, others have them broken or deformed, and many have them divided into terraces, especially on their inner sides.

A typical lunar crater is shown in Fig. 136.

It is not generally believed that any active volcanoes exist on the moon at the present time, though some observers have thought they discerned indications of such volcanoes.

117. _Copernicus._--This is one of the grandest of lunar craters (Fig. 137). Although its diameter (forty-six miles) is exceeded by others, yet, taken as a whole, it forms one of the most impressive and interesting objects of its class. Its situation, near the centre of the lunar disk, renders all its wonderful details conspicuous, as well as those of objects immediately surrounding it. Its vast rampart rises to upwards of twelve thousand feet above the level of the plateau, nearly in the centre of which stands a magnificent group of cones, three of which attain a height of more than twenty-four hundred feet.

Many ridges, or spurs, may be observed leading away from the outer banks of the great rampart. Around the crater, extending to a distance of more than a hundred miles on every side, there is a complex network of bright streaks, which diverge in all directions. These streaks do not appear in the figure, nor are they seen upon the moon, except at and near the full phase. They show conspicuously, however, by their united lustre on the full moon.

This crater is seen just to the south-west of the large dusky plain in the upper part of Fig. 132. This plain is _Mare Imbrium_, and the mountain-chain seen a little to the right of Copernicus is named the _Apennines_. Copernicus is also seen in Fig. 135, a little to the left of the same range.

Under circumstances specially favorable, myriads of comparatively minute but perfectly formed craters may be observed for more than seventy miles on all sides around Copernicus. The district on the south-east side is specially rich in these thickly scattered craters, which we have reason to suppose stand over or upon the bright streaks.

118. _Dark Chasms._--Dark cracks, or chasms, have been observed on various parts of the moon's surface. They sometimes occur singly, and sometimes in groups. They are often seen to radiate from some central cone, and they appear to be of volcanic origin. They have been called _canals_ and _rills_.

One of the most remarkable groups of these chasms is that to the west of the crater named _Triesneker_. The crater and the chasms are shown in Fig. 138. Several of these great cracks obviously diverge from a small crater near the west bank of the great one, and they subdivide as they extend from the apparent point of divergence, while they are crossed by others. These cracks, or chasms, are nearly a mile broad at the widest part, and, after extending full a hundred miles, taper away till they become invisible.

119. _Mountain-Ranges._--There are comparatively few mountain-ranges on the moon. The three most conspicuous are those which partially enclose Mare Imbrium; namely, the _Apennines_ on the south, and the _Caucasus_ and the _Alps_ on the east and north-east. The Apennines are the most extended of these, having a length of about four hundred and fifty miles. They rise gradually, from a comparatively level surface towards the south-west, in the form of innumerable small elevations, which increase in number and height towards the north-east, where they culminate in a range of peaks whose altitude and rugged aspect must form one of the most terribly grand and romantic scenes which imagination can conceive. The north-east face of the range terminates abruptly in an almost vertical precipice; while over the plain beneath, intensely black spire-like shadows are cast, some of which at sunrise extend full ninety miles, till they lose themselves in the general shading due to the curvature of the lunar surface. Many of the peaks rise to heights of from eighteen thousand to twenty thousand feet above the plain at their north-east base (Fig. 139).

Fig. 140 represents an ideal lunar landscape near the base of such a lunar range. Owing to the absence of an atmosphere, the stars will be visible in full daylight.

120. _The Valley of the Alps._--The range of the _Alps_ is shown in Fig. 141. The great crater at the north end of this range is named _Plato_. It is seventy miles in diameter.

The most remarkable feature of the Alps is the valley near the centre of the range. It is more than seventy-five miles long, and about six miles wide at the broadest part. When examined under favorable circumstances, with a high magnifying power, it is seen to be a vast flat-bottomed valley, bordered by gigantic mountains, some of which attain heights of ten thousand feet or more.

121. _Isolated Peaks._--There are comparatively few isolated peaks to be found on the surface of the moon. One of the most remarkable of these is that known as _Pico_, and shown in Fig. 142. Its height exceeds eight thousand feet, and it is about three times as long at the base as it is broad. The summit is cleft into three peaks, as is shown by the three-peaked shadow it casts on the plain.

122. _Bright Rays._--About the time of full moon, with a telescope of moderate power, a number of bright lines may be seen radiating from several of the lunar craters, extending often to the distance of hundreds of miles. These streaks do not arise from any perceptible difference of level of the surface, they have no very definite outline, and they do not present any sloping sides to catch more sunlight, and thus shine brighter, than the general surface. Indeed, one great peculiarity of them is, that they come out most forcibly when the sun is shining perpendicularly upon them: hence they are best seen when the moon is at full, and they are not visible at all at those regions upon which the sun is rising or setting. They are not diverted by elevations in their path, but traverse in their course craters, mountains, and plains alike, giving a slight additional brightness to all objects over which they pass, but producing no other effect upon them. "They look as if, after the whole surface of the moon had assumed its final configuration, a vast brush charged with a whitish pigment had been drawn over the globe in straight lines, radiating from a central point, leaving its trail upon every thing it touched, but obscuring nothing."

The three most conspicuous craters from which these lines radiate are _Tycho_, _Copernicus_, and _Kepler_. Tycho is seen at the bottom of Figs. 143 and 130. Kepler is a little to the left of Copernicus in the same figures.

It has been thought that these bright streaks are chasms which have been filled with molten lava, which, on cooling, would afford a smooth reflecting surface on the top.

123. _Tycho._--This crater is fifty-four miles in diameter, and about sixteen thousand feet deep, from the highest ridge of the rampart to the surface of the plateau, whence rises a central cone five thousand feet high. It is one of the most conspicuous of all the lunar craters; not so much on account of its dimensions as from its being the centre from whence diverge those remarkable bright streaks, many of which may be traced over a thousand miles of the moon's surface (Fig. 143). Tycho appears to be an instance of a vast disruptive action which rent the solid crust of the moon into radiating fissures, which were subsequently filled with molten matter, whose superior luminosity marks the course of the cracks in all directions from the crater as their common centre. So numerous are these bright streaks when examined by the aid of the telescope, and they give to this region of the moon's surface such increased luminosity, that, when viewed as a whole, the locality can be distinctly seen at full moon by the unassisted eye, as a bright patch of light on the southern portion of the disk.

III. INFERIOR AND SUPERIOR PLANETS.

Inferior Planets.

124. _The Inferior Planets._--The _inferior planets_ are those which lie between the earth and the sun, and whose orbits are included by that of the earth. They are _Mercury_ and _Venus_.

125. _Aspects of an Inferior Planet._--The four chief _aspects_ of an inferior planet as seen from the earth are shown in Fig. 144, in which _S_ represents the sun, _P_ the planet, and _E_ the earth.

When the planet is between the earth and the sun, as at _P_, it is said to be in _inferior conjunction_.

When it is in the same direction as the sun, but beyond it, as at _P''_, it is said to be in _superior conjunction_.

When the planet is at such a point in its orbit that a line drawn from the earth to it would be tangent to the orbit, as at _P'_ and _P'''_, it is said to be at its _greatest elongation_.

126. _Apparent Motion of an Inferior Planet._--When the planet is at _P_, if it could be seen at all, it would appear in the heavens at _A_. As it moves from _P_ to _P'_, it will appear to move in the heavens from _A_ to _B_. Then, as it moves from _P'_ to _P''_, it will appear to move back again from _B_ to _A_. While it moves from _P''_ to _P'''_, it will appear to move from _A_ to _C_; and, while moving from _P'''_ to _P_, it will appear to move back again from _C_ to _A_. Thus the planet will appear to oscillate to and fro across the sun from _B_ to _C_, never getting farther from the sun than _B_ on the west, or _C_ on the east: hence, when at these points, it is said to be at its _greatest western_ and _eastern elongations_. This oscillating motion of an inferior planet across the sun, combined with the sun's motion among the stars, causes the planet to describe a path among the stars similar to that shown in Fig. 145.

127. _Phases of an Inferior Planet._--An inferior planet, when viewed with a telescope, is found to present a succession of phases similar to those of the moon. The reason of this is evident from Fig. 146. As an inferior planet passes around the sun, it presents sometimes more and sometimes less of its bright hemisphere to the earth. When the earth is at _T_, and Venus at superior conjunction, the planet turns the whole of its bright hemisphere towards the earth, and appears _full_; it then becomes _gibbous_, _half_, and _crescent_. When it comes into _inferior conjunction_, it turns its dark hemisphere towards the earth: it then becomes _crescent_, _half_, _gibbous_, and _full_ again.

128. _The Sidereal and Synodical Periods of an Inferior Planet._--The time it takes a planet to make a complete revolution around the sun is called the _sidereal period_ of the planet; and the time it takes it to pass from one aspect around to the same aspect again, its _synodical period_.

The synodical period of an inferior planet is longer than its sidereal period. This will be evident from an examination of Fig. 147. _S_ is the position of the sun, _E_ that of the earth, and _P_ that of the planet at inferior conjunction. Before the planet can be in inferior conjunction again, it must pass entirely around its orbit, and overtake the earth, which has in the mean time passed on in its orbit to _E'_.

While the earth is passing from _E_ to _E'_, the planet passes entirely around its orbit, and from _P_ to _P'_ in addition. Now the arc _PP'_ is just equal to the arc _EE'_: hence the planet has to pass over the same arc that the earth does, and 360° more. In other words, the planet has to gain 360° on the earth.

The synodical period of the planet is found by direct observation.

129. _The Length of the Sidereal Period._--The length of the sidereal period of an inferior planet may be found by the following computation:--

Let _a_ denote the synodical period of the planet, Let _b_ denote the sidereal period of the earth, Let _x_ denote the sidereal period of the planet. Then _360°/b_ = the daily motion of the earth, And _360°/x_ = the daily motion of the planet, And _360°/x - 360°/b_ = the daily gain of the planet: Also _360°/a_ = the daily gain of the planet: Hence _360°/x - 360°/b = 360°/a_. Dividing by 360°, we have _1/x - 1/b = 1/a_; Clearing of fractions, we have _ab - ax = bx_: Transposing and collecting, we have _(a + b)x = ab_:

Therefore _x = ab/a+b_.

130. _The Relative Distance of an Inferior Planet._--By the _relative distance_ of a planet, we mean its distance from the sun compared with the earth's distance from the sun. The relative distance of an inferior planet may be found by the following method:--

Let _V_, in Fig. 148, represent the position of Venus at its greatest elongation from the sun, _S_ the position of the sun, and _E_ that of the earth. The line _EV_ will evidently be tangent to a circle described about the sun with a radius equal to the distance of Venus from the sun at the time of this greatest elongation. Draw the radius _SV_ and the line _SE_. Since _SV_ is a radius, the angle at _V_ is a right angle. The angle at _E_ is known by measurement, and the angle at _S_ is equal to 90°- the angle _E_. In the right-angled triangle _EVS_, we then know the three angles, and we wish to find the ratio of the side _SV_ to the side _SE_.

The ratio of these lines may be found by trigonometrical computation as follows:--

_VS : ES = sin SEV : 1._

Substitute the value of the sine of SEV, and we have

_VS : ES = .723 : 1._

Hence the relative distances of Venus and of the earth from the sun are .723 and 1.

Superior Planets.

131. _The Superior Planets._--The _superior planets_ are those which lie beyond the earth. They are _Mars_, the _Asteroids_, _Jupiter_, _Saturn_, _Uranus_, and _Neptune_.

132. _Apparent Motion of a Superior Planet._--In order to deduce the apparent motion of a superior planet from the real motions of the earth and planet, let _S_ (Fig. 149) be the place of the sun; 1, 2, 3, etc., the orbit of the earth; _a_, _b_, _c_, etc., the orbit of Mars; and _CGL_ a part of the starry firmament. Let the orbit of the earth be divided into twelve equal parts, each described in one month; and let _ab_, _bc_, _cd_, etc., be the spaces described by Mars in the same time. Suppose the earth to be at the point 1 when Mars is at the point _a_, Mars will then appear in the heavens in the direction of 1 _a_. When the earth is at 3, and Mars at _c_, he will appear in the heavens at _C_. When the earth arrives at 4, Mars will arrive at _d_, and will appear in the heavens at _D_. While the earth moves from 4 to 5 and from 5 to 6, Mars will appear to have advanced among the stars from _D_ to _E_ and from _E_ to _F_, in the direction from west to east. During the motion of the earth from 6 to 7 and from 7 to 8, Mars will appear to go backward from _F_ to _G_ and from _G_ to _H_, in the direction from east to west. During the motion of the earth from 8 to 9 and from 9 to 10, Mars will appear to advance from _H_ to _I_ and from _I_ to _K_, in the direction from west to east, and the motion will continue in the same direction until near the succeeding opposition.

The apparent motion of a superior planet projected on the heavens is thus seen to be similar to that of an inferior planet, except that, in the latter case, the retrogression takes place near inferior conjunction, and in the former it takes place near opposition.

133. _Aspects of a Superior Planet._--The four aspects of a superior planet are shown in Fig. 150, in which _S_ is the position of the sun, _E_ that of the earth, and _P_ that of the planet.

When the planet is on the opposite side of the earth to the sun, as at _P_, it is said to be in _opposition_. The sun and the planet will then appear in opposite parts of the heavens, the sun appearing at _C_, and the planet at _A_.

When the planet is on the opposite side of the sun to the earth, as at _P''_, it is said to be in _superior conjunction_. It will then appear in the same part of the heavens as the sun, both appearing at _C_.

When the planet is at _P'_ and _P'''_, so that a line drawn from the earth through the planet will make a right angle with a line drawn from the earth to the sun, it is said to be in _quadrature_. At _P'_ it is in its western quadrature, and at _P'''_ in its eastern quadrature.

134. _Phases of a Superior Planet._--Mars is the only one of the superior planets that has appreciable phases. At quadrature, as will appear from Fig. 151, Mars does not present quite the same side to the earth as to the sun: hence, near these parts of its orbit, the planet appears slightly gibbous. Elsewhere in its orbit, the planet appears full.

All the other superior planets are so far away from the sun and earth, that the sides which they turn towards the sun and the earth in every part of their orbit are so nearly the same, that no change in the form of their disks can be detected.

135. _The Synodical Period of a Superior Planet._--During a synodical period of a superior planet the earth must gain one revolution, or 360°, on the planet, as will be evident from an examination of Fig. 152, in which _S_ represents the sun, _E_ the earth, and _P_ the planet at opposition. Before the planet can be in opposition again, the earth must make a complete revolution, and overtake the planet, which has in the mean time passed on from _P_ to _P'_.

In the case of most of the superior planets the synodical period is shorter than the sidereal period; but in the case of Mars it is longer, since Mars makes more than a complete revolution before the earth overtakes it.

The synodical period of a superior planet is found by direct observation.

136. _The Sidereal Period of a Superior Planet._--The sidereal period of a superior planet is found by a method of computation similar to that for finding the sidereal period of an inferior planet:--

Let _a_ denote the synodical period of the planet, Let _b_ denote the sidereal period of the earth, Let _x_ denote the sidereal period of the planet. Then will _360°/b_ = daily motion of the earth, And _360°/x_ = daily motion of the planet; Also _360°/b - 360°/x_ = daily gain of the earth. But _360°/a_ = daily gain of the earth: Hence _360°/b - 360°/x = 360°/a_

_1/b - 1/x = 1/a_

_ax - ab = bx_

_(a-b)x = ab_

_x = ab/(a-b)_.

137. _The Relative Distance of a Superior Planet._--Let _S_, _e_, and _m_, in Fig. 153, represent the relative positions of the sun, the earth, and Mars, when the latter planet is in opposition. Let _E_ and _M_ represent the relative positions of the earth and Mars the day after opposition. At the first observation Mars will be seen in the direction _emA_, and at the second observation in the direction _EMA_.

But the fixed stars are so distant, that if a line, _eA_, were drawn to a fixed star at the first observation, and a line, _EB_, drawn from the earth to the same fixed star at the second observation, these two lines would be sensibly parallel; that is, the fixed star would be seen in the direction of the line _eA_ at the first observation, and in the direction of the line _EB_, parallel to _eA_, at the second observation. But if Mars were seen in the direction of the fixed star at the first observation, it would appear back, or west, of that star at the second observation by the angular distance _BEA_; that is, the planet would have retrograded that angular distance. Now, this retrogression of Mars during one day, at the time of opposition, can be measured directly by observation. This measurement gives us the value of the angle _BEA_; but we know the rate at which both the earth and Mars are moving in their orbits, and from this we can easily find the angular distance passed over by each in one day. This gives us the angles _ESA_ and _MSA_. We can now find the relative length of the lines _MS_ and _ES_ (which represent the distances of Mars and of the earth from the sun), both by construction and by trigonometrical computation.

Since _EB_ and _eA_ are parallel, the angle _EAS_ is equal to _BEA_.

_SEA = 180° - (ESA + EAS)_ _ESM = ESA - MSA_ _EMS = 180° - (SEA + ESM)_.

We have then

_MS : ES = sin SEA : sin EMS._

Substituting the values of the sines, and reducing the ratio to its lowest terms, we have

_MS : ES = 1.524 : 1._

Thus we find that the relative distances of Mars and the earth from the sun are 1.524 and 1. By the simple observation of its greatest elongation, we are able to determine the relative distances of an inferior planet and the earth from the sun; and, by the equally simple observation of the daily retrogression of a superior planet, we can find the relative distances of such a planet and the earth from the sun.

IV. THE SUN.

I. MAGNITUDE AND DISTANCE OF THE SUN.

138. _The Volume of the Sun._--The apparent diameter of the sun is about 32', being a little greater than that of the moon. The real diameter of the sun is 866,400 miles, or about a hundred and nine times that of the earth.

As the diameter of the moon's orbit is only about 480,000 miles, or some sixty times the diameter of the earth, it follows that the diameter of the sun is nearly double that of the moon's orbit: hence, were the centre of the sun placed at the centre of the earth, the sun would completely fill the moon's orbit, and reach nearly as far beyond it in every direction as it is from the earth to the moon. The circumference of the sun as compared with the moon's orbit is shown in Fig. 154.

The volume of the sun is 1,305,000 times that of the earth.

139. _The Mass of the Sun._--The sun is much less dense than the earth. The mass of the sun is only 330,000 times that of the earth, and its density only about a fourth that of the earth.

To find the mass of the sun, we first ascertain the distance the earth would draw the moon towards itself in a given time, were the moon at the distance of the sun, and then form the proportion: as the distance the earth would draw the moon towards itself is to the distance that the sun draws the earth towards itself in the same time, so is the mass of the earth to the mass of the sun.