The Motion of the Moon

In a recent survey of high school graduates, less than a third could correctly explain the cause of lunar phases. Given this dearth of knowledge about our closest celestial companion, I would like to discuss briefly the motion of the moon about the earth.

To first order, the moon orbits the earth in on a circular path, in the same plane as the earth's circular orbit around the sun. This approximation accurately reproduces the lunar phases (see this site for illustrations), which are caused simply by the relative angle of the earth, moon and sun, and by the fact that the sun can only illuminate half of the (opaque) moon. One can simulate the lunar phases readily by placing a slide or overhead projector at one end of a room, standing in the beam at the opposite end of the room with a basketball in hand, then rotating around and watching the shadow on the basketball change shape.

However, if that simple description of the moon's orbit were complete, there would be a solar eclipse (in the tropics) and a lunar eclipse for one hemisphere every lunar month (29.5 days), because every month the moon would pass directly between the earth and the sun (solar eclipse), and then pass directly behind the earth from the sun two weeks later (lunar eclipse). The analogous situations with the basketball are that, when holding the ball between yourself and the projector, the ball would obscure the projector, and while holding the ball away from the projector, your head would cast a shadow on the ball...

Eclipses, however, occur approximately every six months. This is because the orbit of the moon about the earth is not in the same plane as the earth's orbit about the sun (the ecliptic). The moon's orbit is inclined by about 5 degrees to the ecliptic. Therefore, only twice during the lunar month does the moon's orbit intercept the ecliptic (think of dividing a ring with a plane at some oblique angle; the ring will suffer two cuts). These two points are called nodes, and the line connecting them is called the line of nodes.

This line of nodes points in roughly the same direction throughout the year, as the earth orbits the sun, and twice a year the line intesects the sun. If the moon is near full at that time, there is a good chance for a lunar eclipse. If the moon is near new at that time, there is a good chance for a solar eclipse. We're currently in the midst of some bad luck, because the sun's crossings of

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