Letters on Astronomy / in which the Elements of the Science are Familiarly Explained in Connection with Biographical Sketches of the Most Eminent Astronomers

by Denison Olmsted

Let us now inquire into the revolutions of the moon around the earth, and the various changes she undergoes every month, called her phases, which depend on the different positions she assumes, with respect to the earth and the sun, in the course of her revolution.

The moon revolves about the earth from west to east. Her apparent orbit, as traced out on the face of the sky, is a great circle; but this fact would not certainly prove that the orbit is really a circle, since, if it were an ellipse, or even a more irregular curve, the projection of it on the face of the sky would be a circle, as explained to you before. (See page 148.) The moon is comparatively so near to the earth, that her apparent movements are very rapid, so that, by attentively watching her progress in a clear night, we may see her move from star to star, changing her place perceptibly, every few hours. The interval during which she goes through the entire circuit of the heavens, from any star until she comes round to the same star again, is called a sidereal month, and consists of about twenty-seven and one fourth days. The time which intervenes between one new moon and another is called a synodical month, and consists of nearly twenty-nine and a half days. A new moon occurs when the sun and moon meet in the same part of the heavens; but the sun as well as the moon is apparently travelling eastward, and nearly at the rate of one degree a day, and consequently, during the twenty-seven days while the moon has been going round the earth, the sun has been going forward about the same number of degrees in the same direction. Hence, when the moon comes round to the part of the heavens where she passed the sun last, she does not find him there, but must go on more than two days, before she comes up with him again.

The moon does not pursue precisely the same track around the earth as the sun does, in his apparent annual motion, though she never deviates far from that track. The inclination of her orbit to the ecliptic is only about five degrees, and of course the moon is never seen further from the ecliptic than about that distance, and she is commonly much nearer to the ecliptic than five degrees. We may therefore see nearly what is the situation of the ecliptic in our evening sky at any particular time of year, just by watching the path which the moon pursues, from night to night, from new to full moon.

The two points where the moon's orbit crosses the ecliptic are called her nodes. They are the intersections of the lunar and solar orbits, as the equinoxes are the intersections of the equinoctial and ecliptic, and, like the latter, are one hundred and eighty degrees apart.

The changes of the moon, commonly called her phases, arise from different portions of her illuminated side being turned towards the earth at different times. When the moon is first seen after the setting sun, her form is that of a bright crescent, on the side of the disk next to the sun, while the other portions of the disk shine with a feeble light, reflected to the moon from the earth. Every night, we observe the moon to be further and further eastward of the sun, until, when she has reached an elongation from the sun of ninety degrees, half her visible disk is enlightened, and she is said to be in her first quarter. The terminator, or line which separates the illuminated from the dark part of the moon, is convex towards the sun from the new to the first quarter, and the moon is said to be horned. The extremities of the crescent are called cusps. At the first quarter, the terminator becomes a straight line, coinciding with the diameter of the disk; but after passing this point, the terminator becomes concave towards the sun, bounding that side of the moon by an elliptical curve, when the moon is said to be gibbous. When the moon arrives at the distance of one hundred and eighty degrees from the sun, the entire circle is illuminated, and the moon is full. She is then in opposition to the sun, rising about the time the sun sets. For a week after the full, the moon appears gibbous again, until, having arrived within ninety degrees of the sun, she resumes the same form as at the first quarter, being then at her third quarter. From this time until new moon, she exhibits again the form of a crescent before the rising sun, until, approaching her conjunction with the sun, her narrow thread of light is lost in the solar blaze; and finally, at the moment of passing the sun, the dark side is wholly turned towards us, and for some time we lose sight of the moon.

By inspecting Fig. 38, (where T represents the earth, A, B, C, &c., the moon in her orbit, and a, b, c, &c., her phases, as seen in the heavens,) we shall easily see how all these changes occur.

Fig. 38.

You have doubtless observed, that the moon appears much further in the south at one time than at another, when of the same age. This is owing to the fact that the ecliptic, and of course the moon's path, which is always very near it, is differently situated with respect to the horizon, at a given time of night, at different seasons of the year. This you will see at once, by turning to an artificial globe, and observing how the ecliptic stands with respect to the horizon, at different periods of the revolution. Thus, if we place the two equinoctial points in the eastern and western horizon, Libra being in the west, it will represent the position of the ecliptic at sunset in the month of September, when the sun is crossing the equator; and at that season of the year, the moon's path through our evening sky, one evening after another, from new to full, will be nearly along the same route, crossing the meridian nearly at right angles. But if we place the Winter solstice, or first degree of Capricorn, in the western horizon, and the first degree of Cancer in the eastern, then the position of the ecliptic will be very oblique to the meridian, the Winter solstice being very far in the southwest, and the Summer solstice very far in the northeast; and the course of the moon from new to full will be nearly along this track. Keeping these things in mind, we may easily see why the moon runs sometimes high and sometimes low. Recollect, also, that the new moon is always in the same part of the heavens with the sun, and that the full moon is in the opposite part of the heavens from the sun. Now, when the sun is at the Winter solstice, it sets far in the southwest, and accordingly the new moon runs very low; but the full moon, being in the opposite tropic, which rises far in the northeast, runs very high, as is known to be the case in mid-winter. But now take the position of the ecliptic in mid-summer. Then, at sunset, the tropic of Cancer is in the northwest, and the tropic of Capricorn in the southeast; consequently, the new moons run high and the full moons low.

It is a natural consequence of this arrangement, to render the moon's light the most beneficial to us, by giving it to us in greatest abundance, when we have least of the sun's light, and giving it to us most sparingly, when the sun's light is greatest. Thus, during the long nights of Winter, the full moon runs high, and continues a very long time above the horizon; while in mid-summer, the full moon runs low, and is above the horizon for a much shorter period. This arrangement operates very favorably to the inhabitants of the polar regions. At the season when the sun is absent, and they have constant night, then the moon, during the second and third quarters, embracing the season of full moon, is continually above the horizon, compensating in no small degree for the absence of the sun; while, during the Summer months, when the sun is constantly above the horizon, and the light of the moon is not needed, then she is above the horizon during the first and last quarters, when her light is least, affording at that time her greatest light to the inhabitants of the other hemisphere, from whom the sun is withdrawn.