How long is a year? On what day does a year begin? These are questions that people struggled with for thousands of years. To answer them, ancient people developed the classical liberal arts. The liberal arts curriculum included the Quadrivium, which were the four arts of number, space, and time:
- Mathematics was the art of number.
- Geometry was the art of number and space.
- Music was the art of number and time.
- Astronomy was the art of number, space, and time.
Astronomy helps you understand your place in the universe. It also enables you to figure out how long a year is. The choice of when they new year should start is arbitrary.
In ancient times, there were two basic ways to make a calendar. One was based on the apparent motions of the sun. The other was based on the phases of the moon. You could try to combine the two approaches, so that you would have a solar year that was divided into lunar months. The problem was that the lunar and solar systems of measuring time did not mesh:
- If you divided a lunar cycle into days, you would have a fraction of a day left over.
- If you divided the solar cycle into months, you would have a fraction of a month left over.
- Even if you divided the solar cycle into days, you would have a fraction of a day left over.
One problem was what to do with the fractions. Another problem was how to decide when a new year should start.
To ancient people, it seemed that both the sun and the moon were traveling around the earth. However, the moon seemed to travel more slowly than the sun. Every day, the moon would rise a bit later and set a bit later, relative to the sunrise and sunset. When the sun catches up to the moon again, the moon becomes invisible to the naked eye. This invisible phase of the moon is called the new moon. (If the new moon passes directly in front of the sun, it produces a solar eclipse.)
As the moon lags behind the sun, a sliver of light appears on the edge closest to the sun. Thus, we call it a crescent moon. The word crescent came from the Latin word for growing. Originally, it meant that the moon was progressing toward the full moon. Today, however, English‐speaking people use the word crescent to mean a curve that is wide in the middle and pointed at both ends, like a pointy banana. English speakers use the word waxing to mean a moon that seems to be growing, as more of the surface that faces us is lit. When more than half of the lunar surface that faces us is lit, the moon is described as gibbous. As the lunar surface that we can see begins to fall into darkness, it is called a waning gibbous moon. When the lunar surface has become almost completely dark, right before the full moon, it is called a waning crescent moon. Here’s a video from the National Science Teachers Association that explains the phases of the moon.
The period of time that it takes for the moon to go from new moon to new moon is called a lunation or a synodic month. Nowadays, the average length of a synodic month is roughly 29.530588 days (29 days, 12 hours, 44 minutes, and 3 seconds). However, it can range from 29.26 to 29.80 days because the moon’s orbit around the earth is elliptical (oval), and because the sun is having its own gravitational effect on the moon. For this reason, a month in a traditional lunar calendar did not begin until the crescent moon became visible.
The Islamic calendar consists of 12 synodic months. Each of those months officially begins when the crescent moon becomes visible in the sky. However, the Islamic year is about 11 days shorter than the solar year. For this reason, the month of Ramadan occurs about 11 days earlier, relative to the solar calendar that is commonly used today, than it had occurred the year before. As a result, Ramadan will slowly cycle through the seasons of the year. The cycle takes about 33 years.
For agricultural people who live in a climate with distinct seasons, this mismatch of the lunar calendar with the solar year creates problems. You could not easily use the lunar calendar to plan agricultural activities. Instead, you would probably prefer a calendar based on the solar year.
There are two types of solar year. One is called the tropical year, the other is called the sidereal year. The tropical year is the time it takes for the sun to go through the cycle of seasons, as seen on earth. The sidereal year is the time it takes for the sun to reach the same apparent position with regard to the stars in the background. Today, of course, we know that this apparent motion of the sun is an illusion that results from the fact that the earth is traveling around the sun. The difference between the tropical and sidereal year is tiny, only about 1 degree per century.
As you can see in this video, the difference between the tropical and sidereal year is due to a wobble in the earth’s axis of rotation. As a result, the position of the sun at the time of the vernal equinox (marked in the video as the sign of Ares, the ram) makes a complete circle through the constellations that make up the zodiac. The North pole also seems to be pointing at different stars at different points in the cycle. The cycle takes about 26,000 years to complete.
When making their own calendars, ancient people had to decide whether to base it on the moon or the sun. It was easier to base it on the moon, because it was easy to tell when a new month had begun. Unfortunately, a lunar calendar soon falls out of step with the solar calendar, which you need for predicting the seasons of the year. There are two ways to solve this problem. One is to add an extra eleven days to the end of the year. But then, the months of the year will no longer start at the beginning of a lunation. The other solution was to throw in an extra month (called an intercalary month) every two or three years. But then, the dates of the calendar will not match the same point in the solar season from year to year. The Hebrew calendar is a lunisolar calendar that uses intercalary months. That is why the Jewish holidays do not always fall on the same date in the solar calendar that is commonly used today.
The early Romans had a 10‐month calendar. (The names September through December were based on the Latin words for seventh through 10th). Eventually, two more months were added to the beginning of the year, so that the calendar began on January 1.
The calendar that is commonly used throughout the world today was derived from the Julian calendar, which was established by the Roman Emperor Julius Caesar in the year 709 AUC (ad urbe condita meant after the founding of Rome). That year is now described as 45 BC (before Christ) or 45 BCE (before the common era). At the time, Rome had been using a lunisolar calendar with intercalary months. Unfortunately, public officials had been adding extra intercalary months to lengthen their terms of office. This practice caused great confusion. To solve this problem, the Julian calendar had a 365‐day year, with a leap day thrown in once every four years to keep the calendar aligned with the solar years.
The calendar that is used in most of the world today is the Gregorian calendar, which was introduced by Pope Gregory XIII in October of 1582. It revised the Julian calendar by making a 0.002% correction to the length of the year. (Russia did not adopt the Gregorian calendar until February of 1918, which is why the dates of the events of the Russian Revolution are confusing to people in other countries.) The Gregorian calendar involved these corrections to the Julian calendar:
Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 are not leap years, but the years 1600 and 2000 are.
Different societies have used different calendars, and they have chosen different dates for the beginning of the New Year. The Romans chose January 1 as the day of the New Year, probably because it was roughly 11 days after the winter solstice. (The 11 days were originally the correction for the difference between the solar and lunar calendars.) In contrast, the Chinese New Year is based on a lunar calendar. The winter solstice must always fall in the 11th month of the Chinese calendar. As a result, Chinese New Year falls on the second new moon after the winter solstice (the third new moon if there is an intercalary month). As a result, Chinese New Year usually falls in late January or early February.
Other societies have chosen other days as their New Year’s Day. Often, these traditional New Year’s Days continue to be celebrated, even among people who have adopted the Gregorian calendar for practical purposes. For example, Persians still celebrate Nowruz on the day of the vernal equinox. Likewise, the Jewish holiday of Rosh Hashanah represents the first day of the Hebrew calendar, even though it usually falls in September of the Gregorian calendar.