Tisha B'Av and the moon

This year I attended a discussion of the Jewish holiday Tisha B'Av lead by Rabbi Nickerson at Temple Isaiah. Indirectly, this led me to do a lot of learning about the moon. How did I get from Tisha B'Av to the moon?

Well, first I learned that Tisha B'Av just means the ninth day of the month of Av. (Well, its deeper meaning is the commemoration of the destruction of the Temples, but that's not what I'm concerned with here.) I noted with surprise that this year the ninth of Av was also the ninth of August. I'm too lazy to figure out how often this happens, but my guess is that it is pretty evenly distributed and thus happens only about once every 30 months (2.5 years).

Then I remembered something I learned from Joshua Mason-Barkin when one time he led our Torah study at Temple Isaiah: Jewish months start around the time of the new moon.

So that got me thinking: this August, the day of the month will correspond to the phases of the moon. This is no big deal for a Jewish month (it literally happens all the time), but is kind of special for a Gregorian month. Wikipedia helped me make the following guesses for the big four phases of the moon in August. (The key piece of information was that a quarter of a synodic month is about 7.38 days).

1. I guessed that the new moon must have been around day 1 (Aug 1).
2. I guessed that the first quarter must have been around day 8.4 (Aug 8).
3. I guessed that the full moon would be around day 15.8 (Aug 16).
4. I guessed that the last quarter would be around day 23.1 (Aug 23).
5. I guessed that another new moon would be around day 30.5 (Aug 31).

I wasn't quite right, but I was close. Here are the exact answers from Griffith Observatory's LA-customized run of the US Naval Observatory's MICA software. (The only sense in which this is LA-customized is with respect to the time zone, i.e. the phases of the moon (unlike moonrise and moonset times!) are global.)

1. new moon: Jul 30 11:40
2. first quarter: Aug 6 16:08
3. full moon: Aug 13 11:57
4. last quarter: Aug 21 14:54
5. new moon: Aug 28 20:04

Here's a calendar visually showing the phases of the moon for each day in August 2011.

The main source of my errors is that the new moon wasn't exactly at 00:00 on August 1. It was actually about 1.5 days before that, Jul 30 11:40. Jewish months start around the time of the new moon, but not exactly at the new moon. To be fair, the month of Av started at sunset on July 31, which was a little closer to the new moon than 00:00 on August 1.

How far off is the start of the Jewish month from the new moon? What were the sources of my errors other than this main one? What's up with the times of moonrise and moonset? Are they related to the phase of the moon? What are some good ways to visualize the relationship between moonrise, moonset, sunrise, sunset, the Gregorian date, and the Jewish date?

I will try to cover some of the questions in a follow-up blog post.

Tisha B'Av commemorates the sometimes-tragic consequences of the irreconcilable differences between Jewish and Gentile civilizations. But this year it landed in harmony with the secular calendar, bringing me closer to the solar system we live in and bringing me closer to the great ancient civilizations that tried, and almost succeeded, in reconciling the irreconcilable motions of the earth, the moon, and the sun.