If lunar orbit with the plane of

If the plane of the lunar orbit coincided with the plane of the ecliptic, then the eclipses of the Sun and the Moon would occur monthly. In each new moon, the Moon would be on the straight line between the Earth and the Sun and would block it with its opaque body. Because of this, every time there would be observed a phenomenon, which we call a solar eclipse. Quite exactly in each full moon, the Moon would fall into the shadow cast by the Earth in the direction opposite to the Sun, that is, there would be a lunar eclipse (Figure 63).

The scheme of eclipses of the Moon and the Sun
Figure 63 – The scheme of eclipses of the Moon and the Sun.

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But the lunar orbit is inclined to the ecliptic, so on the new moon and the full moon, the Moon most often passes above or below the ecliptic and no eclipses occur (Figure 64).

Eclipses come only when a new moon or full moon happens near one of the two nodes of the lunar orbit, that is, near the points of intersection of the lunar orbit with the plane of the ecliptic (Figure 64). In other words, the Sun and the Moon must simultaneously be near the nodes of the lunar orbit.

The Moon’s orbit and its nodes
Figure 64 – The Moon’s orbit and its nodes.

Since these nodes are two, and the Sun passes a full circle on the ecliptic for a year, then there are two periods each year (separated by a gap of six months), when eclipses can occur. The location of the nodes of the lunar orbit is gradually changing, so the time of the onset of eclipses is shifted to earlier dates. A more accurate consideration of the question shows that annually there should be at least two and no more than five solar eclipses. On the other hand, there can not be more than three lunar eclipses in a year, but they may not be at all. Most often in the year there are two solar and two lunar eclipses.

But sometimes there are years when there are seven eclipses. And in ancient times it was noticed that after the expiration of eighteen years of ten days the eclipses are repeated. So, for example, if in any year there were seven eclipses (which all were in the same place, of course, were not visible), then in eighteen years the year will come again, in which there will be seven eclipses. In this case, each of them will be 10 days later than it was eighteen years ago.


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