Happy New Year!

The New Moon of Monday, September 29, is an important one to many people of the world. In the Hebrew Calendar, it marks Rosh Hashanah (literally, ‘head of the year’) which is the beginning of year 5769. On Tuesday night, September 30, Muslims across the world will see the first slender crescent of this lunar cycle. That will mark the end of Ramadan and the beginning of the next month, Shawwal. 1 Shawwal is ‘Eid ul Fitr, one of the greatest holidays in the Islamic calendar. This week, then, is a good time to think about the Moon, why it’s here, how it orbits, and how we have used it to measure time.

Moon and stars
Creative Commons License photo credit: joiseyshowaa

Unlike our months, Hebrew and Islamic months begin with the New Moon. Because twelve lunar months add to only 354 days, less than the 365.25 day solar year, an extra month is occasionally needed to keep the months roughly aligned with the seasons. In a 19 year cycle, years 3, 6, 8, 11, 14, 17, and 19 have the extra month. The year that is ending, 5678, is number 11 in its cycle and was a leap year.

Interestingly, the Jewish year has two ‘beginnings’. Tishrei (the month which begins now) is the first month of the civil calendar, and the month where 5678 becomes 5679. However, it is actually the seventh month of the religious calendar, which begins at Nisan (the month of Passover).

The Islamic calendar functions slightly differently. Its months begin with the first visible crescent low in the west at dusk, which is not with the actual New Moon. Keep in mind that at New Moon, the Moon is in line with the Earth and Sun, and the entire near side of the Moon has nighttime (and is therefore dark). The New Moon is visible, therefore, only if it blocks the Sun during an eclipse.

Since this New Moon occurs early Monday morning, the 29th, we expect it to be visible by Tuesday evening, the 30th. Observant Muslims, then, will continue to fast in daylight hours Monday and Tuesday. Upon seeing the Moon Tuesday night, they will know that Ramadan has become Shawwal, and they may break their fast on Wednesday.

Due to early controversy as to which years would have it, Muhammad outlawed the 13th month that kept Islamic months tied to the seasons. As a result, Ramadan (and each other month in that calendar) begins 11 days earlier each year according to our Gregorian calendar.

The Moon is Earth’s only natural satellite, orbiting our planet once every 27.3 days. However, a cycle of moon phases (say, from New Moon to the next New Moon), takes 29.54 days. This is because the Earth itself is moving during each 27.3 day Moon orbit. Since it is much easier to observe the Moon’s changing phase cycle than to observe the Sun directly, the 29.54 day phase cycle was the basis of many ancient calendars. Words for ‘moon’ and ‘month’ are related in English and are identical in many other languages. There is some evidence that our word ‘moon’ is ultimately related to an Indo-European word for ‘measure.’ Given how long we’ve measured time by the Moon, it is easy to take its presence for granted.

Released to Public: Jupiter Montage (NASA)
Creative Commons License photo credit: pingnews.com

However, our Moon is quite remarkable in several ways. Moons in our solar system are generally much smaller than the planet they orbit. Jupiter and Saturn, for example, are about 25 times bigger across than their biggest moons. Earth, though, is only 3.67 times the diameter of our Moon. Also, moons usually orbit in the same plane as their planet’s equator. Our Moon, though, orbits within about 5 degrees of Earth’s orbital plane, called the ecliptic, which is not the plane of the equator since Earth is tilted 23.5 degrees on its axis.

This leads most astronomers to believe that the Moon did not form with the Earth, but is the result of a collision with with an object roughly the size of Mars. According to this theory, the impactor (sometimes called ‘Theia’) struck a glancing blow on the Earth and was completely destroyed, and the Moon formed from the debris of Theia’s and Earth’s mantles.

This impact is what left Earth with a Moon much larger than what a planet Earth’s size would normally have, and left that Moon near Earth’s orbital plane (where the impact occured). Our relatively big moon has crucial effects not only on our tides, but also on the stability of Earth’s tilt.

Earth’s orbital tilt of about 23 and a half degrees as it goes around the Sun causes the seasons. The axis precesses, describing an aparent circle roughly every 26,000 years, but the amount of tilt (obliquity) stays nearly the same. Because the Moon acts a counterweight, the obliquity varies only between 22.1 degrees and 24.5 degrees over about 41,00 years (we are now at 23.44 degrees and decreasing). Even this orderly variation, called the Milankovitch cycle, is enough to influence our Ice Ages. Imagine the impact on Earth’s climate if there were no Moon, and the obliquity varied chaotically. This is exactly what happens at Mars, where the tiny moons Phobos and Deimos are not massive enough to influence Mars’ tilt.

Public Domain: Apollo 8 Looks at the Moon (NARA/NASA)
Creative Commons License photo credit: pingnews.com

One thing our Moon does have in common with most others is that it orbits the Earth and rotates on its own axis at the same rate. This is called ‘synchronous rotation’ and it occurs because the Moon is not exactly uniform in composition. From the time the Moon formed, the slightly heavier side was attracted to the Earth. Over time, this effect de-spun the Moon until it attained synchronous rotation. The Moon’s gravitational attraction also de-spins the Earth, although much more slowly as the Moon is less massive. As it does so, the Moon moves slightly farther from the Earth (just over 3 cm per year). The Moon is now 1.5 meters farther away that it was when Apollo astronauts went there. Don’t worry, though, by the time the Moon is far enough away to escape, the Sun will have become a red giant and swallowed both Earth and Moon anyway.

What is the shape of the Moon’s trajectory around the Sun? Perhaps not what you’d expect.

So, I encourage every one to watch for the reappearance of the Moon in the evening sky this week, even if you aren’t celebrating a New Year or an ‘Eid. The Earth’s companion gives all of us something to appreciate.

Great Caesar’s Ghost!

DSCF2360.JPG
Creative Commons License photo credit: glacial23

Why is this month called July? The short answer is that July is named for Julius Caesar. The longer answer involves the ancient Romans’ attempt to keep track of the year.

There are two bright lights in the sky which can help us mark the passage of a year: the Sun and the Moon. Since the year is defined by the Earth’s motion around the Sun, it is best to measure it using the Sun’s apparent changing position among the stars. However, this observation is difficult, since we do not see the Sun and the background stars at the same time. The first ancient culture to do this was ancient Egypt, where the rising of Sirius just before the Sun occurred right before the annual flood of the Nile. Egyptians marked the beginning of each new year with this event.

Sirius vanishes for several months each year when Earth’s orbital motion puts the swath of sky containing Sirius on the far side of the Sun, and therefore behind the Sun from our point of view. Eventually, Earth’s continued motion brings that swath of sky from behind the Sun, allowing Sirius to rise just before dawn. To measure years by the reappearance of Sirius, then, is to measure them by the positions of the Earth and the Sun–a solar calendar.

Lune
Creative Commons License photo credit: ComputerHotline

The Moon, by contrast, is much easier to observe each clear night. Most ancient cultures, including the ancient Romans, measured months by tracking the cycle of lunar phases from new to full and back to new. Since a lunar phase cycle takes 29.5 days on average, we might expect the month lengths to alternate between 30 and 29 days. However, the Romans considered even numbers unfortunate, so their months, beginning with March, had the following lengths:

Martius 31, Aprilis 29, Maius 31, Junius 29, Quintilis 31, Sextilis 29, September 29, October 31, November 29, December 29, Januarius 29, Februarius 28

Yes, January and February were tacked on to the end of the year at first (the Romans originally did not count days at all between December and March) and later moved to the beginning. (In 153 BC, Roman consuls began to take office as of January 1, making that the start of the civil year). February was given an even number of days (making it unfortunate) so that the year as a whole would be fortunate, with an odd number of days.

Unfortunately, there is not an even number of lunar phase cycles per solar year. A cycle of 12 lunar months is 354 days long, 11 days shorter than the cycle of seasons which is about 365.25 days long. (The Roman calendar outlined above has 355 days, because the Romans preferred odd numbers). If this is not corrected, each month occurs 11 days earlier each year, compared to the start of the seasons, and months are no longer associated with the seasons. This is exactly what happens in the Muslim calendar. To keep months roughly aligned with the seasons, an extra 13th lunar month must be added to some years, as in the Hebrew calendar. Thus, the Romans periodically added an extra month, called Intercalaris, between February and March. After all, February was originally at the end of the year.

Martes 13
But is it really? Ordinary Romans didn’t
know.
Creative Commons License photo credit: kozumel

However, it was up to the Roman priests to decide which years would have the extra month. Priests often used this power to arbitrarily shorten the terms of political opponents and lengthen the terms of their friends. Also, the extra month was considered unlucky and avoided in times of crisis, such as the Second Punic War against Carthage. By Caesar’s time the calendar had become so chaotic that regular Roman citizens, especially those far from Rome, did not know the date.

Even as he waged civil war against his rivals for power in Rome, Caesar began many popular reforms as dictator. He offered citizenship to many more Romans and enlarged the Senate to provide more representation. He canceled one fourth of all debts. And he reformed the calendar so even the average Roman could know the date.

While in Egypt, he consulted the Greek astronomer Sosigenes, who told him of the Egyptian solar year of 365 days. Caesar thus decided to add ten days to the 355 day Roman calendar. First, in 46 BC, he realigned the months with their traditional seasons by using Intercalaris and by adding two more months between November and December. 46 BC thus became a 445-day year, the ‘last year of confusion.’ Beginning in 45 BC, the new 365 day Julian Calendar was to come into effect. Caesar added 2 days each to January, ‘Sextilis’, and December, and one day each to April, June, September, and November. The original long months (March, May, Quintilis, and October) remained 31 days long. February, the ‘unlucky’ month devoted to religious rituals, also remained unchanged.

The extra month Intercalaris was dropped forever, replaced by an extra leap day every four years. As Romans had added the extra month in late February, Ceasar placed leap day there as well. The year took its modern shape starting in 45 BC:

January 31, February 28 (29), March 31, April 30, May 31, June 30, Quintilis 31, Sextilis 31, September 30, October 31, November 30, December 31

Julius Caesar
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get directly down

On the Ides of March (March 15), 44 BC, Julius Caesar was assassinated. The Roman Senate felt that a fitting tribute, given Caesar’s work with the calendar, would be to name a month of the year after him. Caesar had been born on the 4th day to the Ides of Quintilis (Quintilis 12th). When that month came around in 44 BC, the Senate proclaimed that from that year on, Quintilis shall be known as Julius (or July in English).

Romans at first counted inclusively, i.e. 1, 2, 3, 4/1, 2, 3, 4/1, 2, 3…. This led them to use leap years too often. The first Roman emperor, Caesar Augustus, noticed this and suppressed all leap years between 9 BC and AD 8. In recognition of this, the Senate offered Augustus a month, and he chose Sextilis, the month when his greatest victories had occurred. Thus Sextilis became August.

As it turns out, the year is not exactly 365.25 days long; its closer to 365.2422 days. The Julian year is thus 11.8 minutes too long on average. There is some evidence that Caesar, Sosigenes et al. knew of the error but considered it insignificant. However, those 11.8 minutes add up to 1 day about every 130 years. In 1582, Pope Gregory XIII noticed that the year had gotten off by 10 days since AD 325, when the Nicene council set the rule for calculating the date of Easter. The Pope decreed that October 15 would follow October 4, 1582, and that century years are leap years only if they are divisible by 400 (thus 2000 was a leap year, but 2100, 2200, and 2300 will not be). Our current calendar, then, is the Gregorian calendar, not the Julian.

But consider this: Pope Gregory did not change the length of the year, nor the lengths of the months, nor the fact the the leap day is in February. All of these decisions by Julius Caesar remain in effect. Caesar, then, still deserves his place of honor in the year.

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