annotate the lunar month in terms of "earth days" explain...?

Question

why an eclipse is only possible at certain positions of the Moon in this inclined orbit. Also explain why eclipses are very difficult to predict. What is the saros cycle?

Answer 1

An eclipse (lunar or solar) only happens when the Moon, Earth, and Sun are lined up. Solar eclipses happen when the moon is between the Earth and Sun, and lunar obviously when the moon is behind the Earth relative to the sun. However Ecliipses don't happen every time the three line up, or we'd have them every month.

This is due to the moon's inclination relative to the ecliptic plane ( the plane on which the Earth orbits the sun). Because of this inclination, most of the time when it is between Earth and the sun or behind earth, it is too high or low to be involved in an eclipse. However, when the moon crosses one of these conjunction points when it also crosses an orbital node (where it crosses the ecliptic plane) then an eclipse does occur- it is precisely in front of the sun, or precisely behind the Earth.

The line of nodes of the moon's orbit precesses. This means it rotates about the Earth. It takes 18.6 years for one complete cycle. Also, because the Earth orbits the sun, the nodes end up lining up 2 times per year.

A Saros cycle is slightly longer than 18 years. It comes from the fact that 223 synodic months is approximately equal to 242 draconic months which is approximately equal to 239 anomalistic months.

A synodic month is the amount of time between passages of the same right assencion of the sun. It is what we know as a lunation, on which the month was originally based and is about 29.5 days. Lunar phases repeat every lunation. A draconic month is the amount of time it takes for the moon to return to the same node of it's orbit. Because the nodes precess as I mentioned before, this means it takes a tad less time to do this than it does to make a complete orbit. The anomalistic month is the amount of time it takes between passages of the perigee of its orbit (closest point to Earth). This is important to eclipses because the distance of the moon from Earth determines whether or not the moon's disk is big enough to cover the disk of the sun (total eclipse) or not (annular eclipse).

Because this approximately 18 year period contains a nearly integer amount of these three different month types, this is the period of time between which the positional relationship between the Earth, moon, and sun is repeated almost exactly. Essentially, one Saros after a particular eclipse, nearly the same exact eclipse will occur again. One thing to keep in mind though is that the exact length of time in a Saros includes a fraction of a day (approximately a third) so that means one Saros later, the Earth will be rotated a different way, so that the eclipse happens 8 hours later than it did last time.

Because the relationship between the different months isn't exact, each eclipse in a particular Saros cycle will be slightly different. They have a beginning and an end. A particular Saros cycle lasts about a millienia, give or take a few centuries.

Every eclipse you see (lunar or solar) has a Saros cycle number. That same exact eclipse (almost exact anyway) will occur 18 years and 11.333 days later.