The Eccentricity Of The Orbits Of Earth And Moon

The terrestrial orbit about the Sun is not a circle, its deviation from such a shape being defined by a quantity that astronomers call the eccentricity. The symbol used for this is e. A circle is defined as having e = 0.0 precisely, whereas the Earth has e = 0.0167 in the present epoch. Over many millennia this value changes and reaches a maximum value of almost 0.06 at times. This affects the climate because the influx of solar energy to our planet would then vary between perihelion and aphelion by a larger proportion than at present. The noncircularity of the orbit also causes the speed variation mentioned above. The effect is like a child on a playground swing, the highest velocity being achieved as the swing moves through the lowest point in the oscillation.

Currently we pass perihelion in early January and aphelion in early July (often on July 4, in fact). In consequence the Earth is moving slowest in July, during the warmest season in the Northern Hemisphere, soon after the summer solstice, and as a result summers in the north tend to be longer but cooler (the Sun being more distant) than those in the Southern Hemisphere. Similarly the winters in the north are shorter and milder than they would be otherwise. This will not persist forever because the dates of perihelion and aphelion advance by about one day every sixty years in the calendar we use. (That calendar was designed with a leap year scheme aimed at keeping the spring equinox on about the same date for ecclesiastical purposes, in particular the calcula tion of the date of Easter. If we wanted to keep perihelion and aphelion on the same dates instead then we would need to revise the calendar, and insert some extra leap years, rather than losing some as we do at present, as in 1800, 1900, 2100, 2200, and so on. Further matters concerning the calendar are discussed below.)

Now let's consider the Moon. The shape of the lunar orbit about the barycenter is likewise noncircular, having an eccentricity e = 0.0549. With an average separation of 238,850 miles, the lunar distance varies between about 225,740 miles at perigee and 251,970 miles at apogee, so long as that eccentricity is maintained. In fact, it is not. While the Moon is in a secure orbit (that is, it is gravitationally bound to the Earth), the attraction of the Sun perturbs its path in a cyclic fashion, and the lunar eccentricity varies fairly rapidly between 0.044 and 0.067.

This means that the barycenter moves rather erratically back and forth within the Earth, but let us lay that aside for simplicity, and in the following discussions and illustrations just imagine the Moon to orbit the center of the Earth. Keep in mind, though, the fact that effects like the motion of the barycenter are significant if one wants to compute accurate eclipse paths.

Figure A-2 shows the shape of the lunar orbit, compared to a circle. The Earth—Moon distance only changes by a small amount, but that is very significant with respect to the nature of eclipses. When the Earth is at its mean distance from the Sun, the solar orb has an apparent angular diameter of 0.533 degrees. That is the size of the light source that the Moon must entirely obscure to produce a total solar eclipse. Using the perigee distance of 225,740 miles mentioned above, with a diameter of 2,160 miles, the Moon subtends an angle of 0.548 degrees, and so is able to cover the Sun completely: a total eclipse. At apogee the lunar angular diameter is

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