Earth

FIGURE A-2. The orbit of the Moon about the Earth (more strictly, about the barycenter) is not circular. Here the lighter curve is a circle centered on the Earth, while the heavier line is the elliptical lunar orbit. The Earth is shown to scale; the size of the Moon is equivalent only to about the width of the line depicting its path.

only 0.491 degrees, and so this time when the centers of Sun and Moon line up the latter cannot completely obscure the former, and so there must be a bright ring around its circumference: an annular eclipse. (The effect of the varying lunar distance was shown schematically in Figure 2.1.) Note that these angular sizes were calculated using the average eccentricity of the lunar orbit. The figures will change slightly as the eccentricity varies. For simplicity, in further discussions of the lunar orbit we will depict that orbit as circular, but remember that it is actually an ellipse.

Apart from the above we must also take into account the noncircularity of the Earth's heliocentric orbit. This results in the apparent size of the Sun oscillating during the year, altering the target the Moon must obscure. The small eccentricity of the terrestrial orbit results in our separation diminishing to near 91.4 million miles at perihelion before growing to 94.5 million miles at aphelion, the apparent diameter of the Sun therefore changing between 0.542 and 0.524 degrees. Obviously this will also affect whether a solar eclipse is total or annular, if the Moon happens to be at a distance giving it an apparent size near those solar limits.

There are other complications. It was effectively assumed above that the potential observer is at the barycenter, which is not realistic of course, since it is deep underground! The size of the Earth is a significant fraction of the Earth—Moon separation, and so the angular size of the Moon someone will see depends to some extent upon his or her location on the surface of the planet. Imagine, for instance, that you are gazing at a full moon that has just risen above the eastern horizon at sunset. Six hours later, at midnight, you will be several thousand miles closer to it, and by sunrise you will have receded from the Moon again, all because of the Earth's rotation. This movement alters the angular dimension of the Moon by about a hundredth of a degree, and this may be critical when considering whether an eclipse seen from a certain location will be total or annular.

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