N' N'' is called the line of nodes of the moon's orbit ([§ 39]), and the two positions of the earth in its orbit, diametrically opposite each other, at which N' N'' points exactly toward the sun, we shall call the nodes of the lunar orbit. Strictly speaking, the nodes are those points of the sky against which the moon's center is projected at the moment when in its orbital motion it cuts through the plane of the earth's orbit. Bearing in mind these definitions, we may condense much of what precedes into the proposition: Eclipses of either sun or moon can occur only when the earth is at or near one of the nodes of the moon's orbit. Corresponding to these positions of the earth there are in each year two seasons, about six months apart, at which times, and at these only, eclipses can occur. Thus in the year 1900 the earth passed these two points on June 2d and November 24th respectively, and the following list of eclipses which occurred in that year shows that all of them were within a few days of one or the other of these dates:
Eclipses of the Year 1900
| Total solar eclipse | May 28th. |
| Partial lunar eclipse | June 12th. |
| Annular (solar) eclipse | November 21st. |
68. Eclipse limits.—If the earth is exactly at the node at the time of new moon, the moon's shadow will fall centrally upon it and will produce an eclipse visible within the torrid zone, since this is that part of the earth's surface nearest the plane of its orbit. If the earth is near but not at the node, the new moon will stand a little north or south of the plane of the earth's orbit, and its shadow will strike the earth farther north or south than before, producing an eclipse in the temperate or frigid zones; or the shadow may even pass entirely above or below the earth, producing no eclipse whatever, or at most a partial eclipse visible near the north or south pole. Just how many days' motion the earth may be away from the node and still permit an eclipse is shown in the following brief table of eclipse limits, as they are called:
Solar Eclipse Limits
| If at any new moon the earth is | ||||
| Less than 10 days away | from | a | node, | a central eclipse is certain. |
| Between 10 and 16 days | " | " | " | some kind of eclipse is certain. |
| Between 16 and 19 days | " | " | " | a partial eclipse is possible. |
| More than 19 days | " | " | " | no eclipse is possible. |
Lunar Eclipse Limits
| If at any full moon the earth is | ||||
| Less than 4 days away | from | a | node, | a total eclipse is certain. |
| Between 4 and 10 days | " | " | " | some kind of eclipse is certain. |
| Between 10 and 14 days | " | " | " | a partial eclipse is possible. |
| More than 14 days | " | " | " | no eclipse is possible. |
From this table of eclipse limits we may draw some interesting conclusions about the frequency with which eclipses occur.
69. Number of eclipses in a year.—Whenever the earth passes a node of the moon's orbit a new moon must occur at some time during the 2 × 16 days that the earth remains inside the limits where some kind of eclipse is certain, and there must therefore be an eclipse of the sun every time the earth passes a node of the moon's orbit. But, since there are two nodes past which the earth moves at least once in each year, there must be at least two solar eclipses every year. Can there be more than two? On the average, will central or partial eclipses be the more numerous?