Astronomy: The Science of the Heavenly Bodies

by David P. Todd

As we know that the moon is, like the earth, a nonluminous body, and shines only by virtue of the sunlight falling upon it, clearly an entire half of the moon's globe must be perpetually illumined by sunlight. The varying phases then are due simply to that part of the illuminated hemisphere which is turned toward us. New moon is entirely invisible because the sunward hemisphere is turned wholly away from us, while at full moon we see the lunar disk complete because we are on the same side of the moon that the sun is and practically in line with both sun and moon.

If we could visit the moon, we should see the earth in exactly complementary phase. At new moon here we should be enjoying full earth there, and full moon here would be coincident with new or dark earth there. The narrow crescent of new moon here would be the period of gibbous earth there; and it is the reflection of sunlight from this gibbous earth which illuminates the part of the moon but faintly seen at this time, popularly known as the "old moon in the new moon's arms." Its greater visibility at some times than at others is due to greater prevalence of clouded area in the reflecting regions of the earth turned toward the moon, and the higher reflective power of clouds than that possessed by mere land and water.

As the moon goes all the way round the sky every month, the same as the sun does in a year, and travels in nearly the same path, clearly it must also go north and south every month as the sun does. So in midsummer when the sun runs high upon the meridian, we expect to find full moons running low, and likewise in midwinter the full moon always runs high, as almost everyone has sometimes or other noticed.

This eastward or true orbital motion of the moon is responsible for another relation which soon comes to light when we begin to observe the moon; and that is the later hour of rising or setting each night. Our clock time is regulated by the sun, which also is moving eastward about 1° daily, or twice its own breadth. So the moon's eastward gain on the sun amounts to about 12 degrees daily, and one degree being equal to 4 minutes, the retarded time of moonrise or moonset each day amounts to very nearly 50 minutes on the average; though sometimes the delay will be less than a half hour and at other times it will exceed an hour and a quarter. The season of least retardation of rising of the full moon is in the autumn, and so the moon that falls in late September or October is known as the Harvest moon, and the next succeeding full moon is called the Hunter's moon.

Lunation is a term sometimes given to the moon's period from any definite phase round to the same phase again. Its length is the true period of the moon's revolution once around the earth, from the sun all the way round till it overtakes the sun again. The synodic period is another name for lunation, and its true length is 29 and one-half days, or very accurately 29 d. 12 h. 44 m. 2.7 s. as calculated by astronomers with great exactness from many thousand revolutions of the moon. But if we want the true period of the moon round the earth as referred to a star, it is much shorter than this, amounting to only 27 days and nearly one-third. This is called the moon's sidereal period of revolution, because it is the time elapsed while she is traveling eastward from a given star around to coincidence with the same star again.

If we study the moon's path in the sky more critically, we shall find that it does not quite follow the ecliptic, or the sun's path, but that twice each month she deviates from the ecliptic, once to the north and once to the south of it, by roughly ten times her own breadth. More accurately this angle is 5°8'40", an almost invariable quantity, and it is therefore known as an astronomical constant, or the inclination of the moon's orbit to the ecliptic. So the moon's orbit must intersect the ecliptic, and as both are great circles in the sky, the points of intersection are known as the moon's nodes, one ascending and the other descending, and the nodes are 180 degrees apart.

The figure of the moon's orbit is not circular, although it deviates only slightly from that form. But like the paths of all other satellites round their primary planets, and of the planets themselves round the sun, the moon's orbit is also an ellipse. The distance of the moon's center from the earth's center is therefore perpetually changing; the point of nearest approach is called perigee, and that of farthest recession, apogee.

The moon's distance from the earth is easier and simpler to be ascertained than that of any other heavenly body, because it is the nearest. An outline of the method of finding this distance is not difficult to present; and it resembles in every particular the method a surveyor uses to find the distance of some inaccessible point which he cannot measure directly. Up and down a stream, for example, he measures the length of a line, and from each end of it he measures the angle between the other end of the line and the object on the opposite side of the stream whose distance he wishes to find out. Then he applies the science of trigonometry to these three measures, two of angles and one the length of the side or base included between them, and a few minutes' calculation gives the distance of the inaccessible object from either end of the base line.

Now in like manner, to transfer the process to the sky, let the two ends of the base be represented by two astronomical observatories, for example, Greenwich in the northern hemisphere and Cape Town in the southern. The base line is the chord or straight line through the earth connecting the two observatories, and we know the length of this line pretty accurately, because we know the size of the earth. The angles measured are somewhat different from those in the terrestrial example, but the process amounts to the same thing because the astronomers at the two observatories measure the angular distance of the center of the moon from the zenith, each using his own zenith at the same time; and the same science of trigonometry enables them to figure out the length of any side of the triangles involved. The side which belongs to both triangles is the distance from the center of the earth to the center of the moon, and the average of many hundred measures of this gives 238,800 miles, or about ten times the distance round the equator of the earth.

We have said that the orbit in which the moon travels round the earth is practically a circle, but the earth's center is found not at the center of this orbit, but set to one side, or eccentrically, so that the distance spanning the centers of the two bodies is sometimes as small as 221,610 miles at perigee, and 252,970 miles at apogee. The moon's speed in this orbit averages rather more than half a mile every second of time—more accurately 3,350 feet a second, or 2,290 miles per hour.