Astroprof’s Page

Months

Published on Sep 8, 2008 at 6:08 pm. 1 Comment.
Filed under calendars.

Early in the semester, I cover a lot of background topics. Among those topics is time keeping: calendars and such. A lot of people don’t think of the calendar as having any astronomical connections, but it does. The basic unit of the calendar, the day, is clearly related to the rotation of the Earth, and the year is associated with the motion of the Earth around the Sun. But, the months are also astronomical in origin.

A month, or “moonth,” used to be the length of the cycle of the Moon’s phases, about 29.5 days. Actually, some calendars today, such as the Jewish calendar or the Islamic calendar, still use that for months. But, the calendar that most of us use long ago discarded the cycle of the Moon’s phases as the determining factor for the month. The problem is that 12 lunar months is 354 days long, over a week and a half short of the length of time that it takes the Earth to orbit the Sun. Since the seasons are tied to Earth’s motion around the Sun, such a calendar would be out of sync with the seasons. Indeed, that is true of the Islamic calendar, but if you don’t care if the seasons are not tied to particular times of the year, then that is not a problem. A 13 month year, though, is too long, being over 383 days long. Of course, you can switch back and forth between 12 month and 13 month years as needed, such as with the Jewish calendar, to keep the calendar in sync with the seasons. Or, you can do what the Romans did and quit tying the month to the Moon. The number of days in each month was determined by a combination of aesthetic and political concerns. The story of the calendar is actually a very interesting read, but it is not what this particular blog entry is all about.

What I wanted to write about today is several different uses of the term “month.” As everyone already knows, a month is a division of the calendar. Most of us use the Gregorian calendar, so a month is a 30 0r 31 day period of time (except for February), twelve of which make up the year. And, as you can tell from what I’ve already said, a month can also refer to a cycle of the Moon’s phases. That particular use of the term we call specifically the synodic month. The synodic month is about 29.5 days long. More exactly, it is 29 days 12 hours 44 minutes 2.9 seconds long, on average. I need to add the “on average” to that because of perturbations to the Moon’s orbit from the Sun and planets.

But, there are more months out there than the calendar month or the synodic month. In particular, another month commonly used by astronomers is the sidereal month. As the Moon orbits Earth, the Earth is also moving around the Sun. Since the phases of the Moon are determined by the relative position of the Moon, Earth, and Sun, the Earth’s motion around the Sun means that the Moon actually has to travel a little more than one complete orbit in order for it to line up with the Sun and Earth the same way that it did one month earlier. Thus, the synodic month, the length of time that it takes to complete one cycle of its phases, takes longer than the actual orbital period of the Moon. But, the orbital period of the Moon is also called a “month.” To differentiate it from the synodic month, the time that the Moon takes to make one complete orbit of the Earth is called the sidereal month, an it is about 27.3 days. To be more precise, the sidereal month is 27 days 7 hours 43 minutes 11.6 seconds. The sidereal month can be regarded as the time that it takes the Moon to make one complete orbit against the background sky.

Another month that astronomers use is the anomalistic month. The Moon’s orbit about the Earth is slightly elliptical. The anomalistic month is the time between two perigees. Perigee is the closest point in the Moon’s orbit to Earth. The anomalistic month averages 27 days 13 hours 18 minutes 33.1 seconds. So, why is the anomalistic month longer than the sidereal month? That is because the Moon’s orbit precesses a bit. Each time around, the Moon’s orbit shifts a little bit, so the Moon reaches perigee a little farther around the Earth than it did the last time.

There are other months, too. The tropical month is the time that it takes the Moon to move through 24 hours of right ascension (the celestial equivalent of longitude). The tropical month is 27 days 7 hours 43 minutes 4.7 seconds long. Another way of putting this is that the tropical month is the time that it takes the Moon to pass the point in the sky marked by the vernal equinox until it passes that point again. But, doesn’t that sound like the same thing as the sidereal month? That would be one complete orbit against the background sky, right? As you can see, the tropical month and the sidereal month are nearly the same, but not quite. So, why is the tropical month a few seconds shorter than the sidereal month? Well, it would be if it were not for the fact that the equinoxes (and hence the celestial coordinates, which are tied to the equinoxes) shift slightly each year due to the 26,000 year precession cycle of Earth’s axis. The Earth is tilted by about 23.5 degrees as it orbits the Sun. Since the tilt is fairly fixed in direction in space, this is the reason that we have seasons. However, the tilt is not absolutely fixed. It swings through space with a period of 26,000 years. That means that in the time that it takes the Moon to complete one orbit, the equinoxes have shifted slightly (very slightly!).

One final month that I want to write about is the draconic month. The Moon’s orbit around the Earth is not exactly in the same plane as the ecliptic (the plane of Earth’s orbit around the Sun). So, seen against the sky, the Moon’s orbit moves north and south of the ecliptic. The points where the Moon’s orbit cross the ecliptic are the nodes of the orbit. Those nodes are important, because if there happens to be a Full Moon or a New Moon when the Moon is very near a node, then an eclipse can occur (either a lunar eclipse or a solar eclipse, depending upon the phase). But, just as the Earth’s axial tilt precesses, so does the whole orbit of the Moon. Thus, each orbit the tilt of the Moon’s orbit shifts slightly. That is why eclipse seasons do not occur exactly six months apart. The draconic month is the time that it takes the Moon’s orbit to go from one node (descending, if it is moving south, or ascending, if it is moving north) until it reaches that corresponding node again. The length of the draconic month averages about 27 days 5 hours 5 minutes 35.9 seconds.

Tonight, I cover all of these aspects of months with my astronomy students. Most have never realized that calendry could be so complicated.

-Astroprof