A Text-Book of Astronomy

by George C. Comstock

D. Wherever the moon may be in the sky, it turns always the same face toward the earth, as is shown by the fact that the dark markings which appear on its surface stand always upon (nearly) the same part of its disk. It does not always turn the same face toward the sun, for the boundary line between the illumined and unillumined parts of the moon shifts from one side to the other as the phase changes, dividing at each moment day from night upon the moon and illustrating by its slow progress that upon the moon the day and the month are of equal length (29.5 terrestrial days), instead of being time units of different lengths as with us.

Fig. 53.—Motion of moon and earth relative to the sun.

92. The moon's motion.—The student should compare the results of his own observations, as well as the preceding section, with [Fig. 53], in which the lines with dates printed on them are all supposed to radiate from the sun and to represent the direction from the sun of earth and moon upon the given dates which are arbitrarily assumed for the sake of illustration, any other set would do equally well. The black dots, small and large, represent the moon revolving about the earth, but having the circular path shown in [Fig. 34] (ellipse) transformed by the earth's forward motion into the peculiar sinuous line here shown. With respect to both earth and sun, the moon's orbit deviates but little from a circle, since the sinuous curve of [Fig. 53] follows very closely the earth's orbit around the sun and is almost identical with it. For clearness of representation the distance between earth and moon in the figure has been made ten times too great, and to get a proper idea of the moon's orbit with reference to the sun, we must suppose the moon moved up toward the earth until its distance from the line of the earth's orbit is only a tenth part of what it is in the figure. When this is done, the moon's path becomes almost indistinguishable from that of the earth, as may be seen in the figure, where the attempt has been made to show both lines, and it is to be especially noted that this real orbit of the moon is everywhere concave toward the sun.

The phase presented by the moon at different parts of its path is indicated by the row of circles at the right, and the student should show why a new moon is associated with June 30th and a full moon with July 15th, etc. What was the date of first quarter? Third quarter?

We may find in [Fig. 53] another effect of the same kind as that noted above in C. Between noon, June 30th, and noon, July 3d, the earth makes upon its axis three complete revolutions with respect to the sun, but the meridian which points toward the moon at noon on June 30th will not point toward it at noon on July 3d, since the moon has moved into a new position and is now 37° away from the meridian. Verify this statement by measuring, in [Fig. 53], with the protractor, the moon's angular distance from the meridian at noon on July 3d. When will the meridian overtake the moon?

93. Harvest moon.—The interval between two successive transits of the meridian past the moon is called a lunar day, and the student should show from the figure that on the average a lunar day is 51 minutes longer than a solar day—i. e., upon the average each day the moon comes to the meridian 51 minutes of solar time later than on the day before. It is also true that on the average the moon rises and sets 51 minutes later each day than on the day before. But there is a good deal of irregularity in the retardation of the time of moonrise and moonset, since the time of rising depends largely upon the particular point of the horizon at which the moon appears, and between two days this point may change so much on account of the moon's orbital motion as to make the retardation considerably greater or less than its average value. In northern latitudes this effect is particularly marked in the month of September, when the eastern horizon is nearly parallel with the moon's apparent path in the sky, and near the time of full moon in that month the moon rises on several successive nights at nearly the same hour, and in less degree the same is true for October. This highly convenient arrangement of moonlight has caused the full moons of these two months to be christened respectively the Harvest Moon and the Hunter's Moon.

94. Size and mass of the moon.—It has been shown in [Chapter I] how the distance of the moon from the earth may be measured and its diameter determined by means of angles, and without enlarging upon the details of these observations, we note as their result that the moon is a globe 2,163 miles in diameter, and distant from the earth on the average about 240,000 miles. But, as we have seen in [Chapter VII], this distance changes to the extent of a few thousand miles, sometimes less, sometimes greater, mainly on account of the elliptic shape of the moon's orbit about the earth, but also in part from the disturbing influence of other bodies, such as the sun, which pull the moon to and fro, backward and forward, to quite an appreciable extent.

From the known diameter of the moon it is a matter of elementary geometry to derive in miles the area of its surface and its volume or solid contents. Leaving this as an exercise for the student, we adopt the earth as the standard of comparison and find that the diameter of the moon is rather more than a quarter, 4/15, that of the earth, the area of its surface is a trifle more than 1/14 that of the earth, and its volume a little more than 1/49 of the earth's. So much is pure geometry, but we may combine with it some mechanical principles which enable us to go a step farther and to "weigh" the moon—i. e., determine its mass and the average density of the material of which it is made.