Lunar Eclipse December 21, 2010

If your local weather will cooperate, plan on going to bed a little later than usual on the night of December 21 so you can get a glimpse of the night sky during a total eclipse of the moon. The fact that an eclipse will occur on that date, and at a particular time (beginning at ~ 06:33, totality lasting 72 minutes beginning at ~ 07:41, and the ending of the eclipse at ~ 10:00; all times given as Universal Time) has been known since the days of Isaac Newton and Edmund Halley. The mathematics of eclipse prediction is the subject of this post.

Julian Date

In order to make reliable predictions of future events (and even to confirm the date and time of past events), astronomers have long used a mathematical construct knows as the Julian Date.

The Julian Date, Year, etc. is decimal number that is based on the amount of time that has elapsed since 1200 hrs (noon, relative to the longitude of the future Royal Observatory at Greenwich) on January 1, 4713 BCE (Julian Year 0; "Year Zero"). As an example, I posted this article on the afternoon of December 19, 2010, which gave a Julian Date of 2455550.46225.

Universal Time

In order to minimize the confusion that would result if every observatory in the world used its local time when making predictions or observations of astronomical events, international treaty and scientific consensus has established a "World Standard Time," known as "Universal Time," which is based on the moment that the sun is observed to be due south ("local noon") of an observer at the Royal Observatory in Greenwich, England, UK. The logic behind Universal Time had its origin with attempts by sailors to keep from getting lost on the way to the New World.

Until about the time of Christopher Columbus, there wasn't a reliable method for determining your position if you happened to be at sea on a ship and away from any recognizable landmark on shore. It was known, however, that the circumference of the Earth was ~ 24,900 miles, that there were 24 hours in a day, and that there were 360 degrees in a circle. Once an adequately reliable clock was available, all you had to do was determine when the sun was due south of your position and then note the time in Greenwich (which you took from your shipboard clock that has been set to Greenwich time before you set sail). Since the circumference of the Earth is ~ 24,900 miles, and there are 360 ° in a circle, then each minute of deviation (either ahead or behind) from noon at Greenwich meant that you were 24900 / (60 • 24)= ~ 17.3 miles east or west of the longitude at Greenwich. Thus, every 15 º of longitude marks a difference of 1 hour from Greenwich time.

Universal Time is used in conjunction with Julian Dates to predict future astronomical events such as eclipses.

You can use these observations to derive your local time for the various stages of the eclipse, as given above: subtract the following time zone correction factors from Universal Time (UT): AST (Canadian Maritimes) = UT-4 hours; EST = UT-5 hours; CST = UT-6 hours; MST = UT-7 hours, and PST = UT-8 hours.

Saros Cycle

According to the best available archaeological data, the astronomer/priests of ancient Mesopotamia were aware of slight differences in the lengths of time separating certain observed lunar events such as the time from one new moon to another or the time that the moon would pass through certain points in the sky. When observed over time, this led to several different values for the average length of the lunar month (anywhere from 27.21222 days to 29.53059 days). Simple algebra can demonstrate that the lengths of time separating such various events will coincide exactly once every 6585.3213 day, or about every 18 years 11.33 days. Rather than being a mere mathematical curiosity, the Saros Cycle is at the heart of eclipse astronomy.

Recall that a solar eclipse can occur only at the time of a new moon, and that a lunar eclipse can occur only at a full moon. If a solar eclipse is observed on a given, day at a given location, then there will be another solar eclipse observable at that location three Saros Cycles later (because of the extra 0.33 days included in one Saros Cycle). The ancient Chaldeans noticed this pattern in lunar eclipses (which are much more frequent than solar eclipses) and later passed on this knowledge to the Greeks. (As an aside, the mathematician and natural philosopher Thales of Miletus is said to have used the Saros Cycle to predict a solar eclipse in the sixth-century BCE).

Although it probably doesn't mean much to nerds such as myself I plan not only to watch the eclipse this Tuesday night. And I plan to give thankful remembrance to those long-gone Sumerian, Persian, and Greek astronomers who took the time to write down what they saw in the heavens.

Thanks, guys! You did a good job!

See Also:

NASA Science News. "Solstice Lunar Eclipse." (Dated: 17 December 2010, Accessed 19 December 2010).

Fred Espenak. "Eclipses and the Saros." NASA Goddard Spaceflight Center.(Dated 28 August, 2009, Accessed 19 December, 2010).

Visit Ephemeris.com to learn more about astronomy in the ancient Middle East.

The Royal Observatory at Greenwich maintains an excellent set of in-depth web pages.

For the serious amateur astronomer, and for the non-geek with a major case of data obsession, this link contains just about everything you could possibly want to know about the upcoming lunar eclipse as well as the Saros Cycle.