**Are you ready to learn the halachos of Kiddush Hachodesh? The Rambam says that even a kid can learn how the calendar works! Get ready!**

*Today in Rambam, we are going to start learning about how the Beis Din knows when we COULD see the moon! This might be a little bit hard to understand (it’s a lot of math), but the Rambam says that even a kid can learn these halachos in a few days. Let’s try!*

*– We are going to divide an hour into 1080 parts (not like seconds!) so it will be easier to figure out the numbers.*

*– Every day is 24 hours long – about 12 hours of daytime, and 12 hours of night.*

(The sun and the moon go in a circle around us, but the moon goes much faster! Since the moon is a ball, we can only see half of it at a time. When the sun shines on that part, we can see the moon. As the moon goes around fast, the part where the sun can shine on it keeps changing, so it looks like the moon gets bigger and smaller. When the sun and moon meet it is called the **molad**, the sun is only shining on the part of the moon we CAN’T see, and that’s when the month ends.)

**Moon (Lunar) Years:**

– It takes the moon **29 days, 12 hours, and 793 parts** to meet back up with the sun, so this is how long a month is for the moon.

– A LUNAR year is 12 months long. If you do the math, you will see that a moon year is **354 days, 8 hours, and 876 parts**.

– A LEAP year for the moon is 13 months long, so it is **385 days, 21 hours, and 5 parts**.

**Sun (Solar) Years:**

– A SUN year is **365 days and 6 hours**. That means it’s **10 days, 21 hours, and 204 parts** LONGER than a regular lunar year.

*It can get very confusing to have all of these numbers! The Rambam tells us which numbers are important: Only the ones that show us which day of the week we should be looking for the moon, and what time the sun will meet up with the moon. To figure this out, we can take away all of the weeks (7 days) from our numbers. So if we would have 8 days, 2 hours, and 21 parts, we only need to think about ONE day, 2 hours, and 21 parts.*

*So here’s how to figure out the molad for the next month: Add 1 day, 12 hours, and 793 parts to the **molad **from last month. (This is why if the molad is on Tuesday one month, usually the next month it will be on Wednesday.)*

*The very first time when the sun and moon met was on Yom Sheini, when Hashem made them! This was on Monday night, 5 hours and 204 parts after Shkiah. That’s the day we start figuring everything out from.*

Since we need to make sure that the Yomim Tovim happen in the right times of the year (like Pesach needs to be in the spring), we need to also think about the SOLAR year. This is why the Chachomim figured out the **machzor** – a pattern of 19 LUNAR years (12 regular years and 7 leap years) that is almost exactly as long as 19 SOLAR years! *(The difference every 19 years is only 1 hour and 485 parts!)*

Here’s the pattern of a Machzor: The THIRD year, the SIXTH year, the EIGHTH year, the ELEVENTH year, the FOURTEENTH year, the SEVENTEENTH year, and the NINETEENTH year are leap years (13 lunar months) and the rest are regular years (12 months).

*The Rambam tells us some shortcuts to figure out the molad for the beginning of the next Machzor: Add 2 days, 16 hours, and 595 parts to the molad from the last Machzor. You can also figure out the molad for ANY year using this shortcut, only with remembering the time of the first molad! Figure out how many years it was since the first molad, and split it up into 19 (divide by 19). However many years are left is which year of THIS machzor you’re in. Add 2 days, 16 hours, and 595 parts for each of these groups of 19. Then add 4 days, 8 hours, and 876 parts for every regular year since this machzor started, and 5 days, 21 hours, and 589 minutes for each leap year since this machzor started. This will tell you the molad for Tishrei. Phew!*

**Sometimes Rosh Chodesh Tishrei gets pushed off:**

– If the molad is even one drop after Chatzos (the middle of the day), Rosh Chodesh has to be the next day.

– Rosh Hashana (Rosh Chodesh Tishrei) is not allowed to be on Sunday, Wednesday, or Friday. So if the molad is on one of these days, Rosh Chodesh will be the NEXT day. (So if the Molad is on Friday, Rosh Hashana/Rosh Chodesh will be on Shabbos.) And if the molad is after Chatzos on Tuesday, Rosh Hashana isn’t until Thursday!

– In a regular year, if the molad is at night on Tuesday, at least 9 hours and 204 parts since the night started, Rosh Chodesh has to be pushed off.

– In a year after a leap year, if the molad is on Monday morning, at least 3 hours and 589 parts since the morning started, Rosh Chodesh has to be pushed off.

*Are you wondering why Rosh Hashana can’t be on Sunday, Wednesday, or Friday? It’s because all of these numbers are AVERAGES, meaning how fast the sun and moon USUALLY go. For Rosh Hashana, we need to MAKE SURE it’s already the molad, so the Chachomim decided that every other day, they would push off Rosh Chodesh (Tuesday – yes, Wednesday – push it off, Thursday- yes, Friday – push it off, Shabbos – yes, Sunday – push it off, Monday – yes.)*

**Rosh Chodesh has to be a whole day** – it says in the Torah to figure out DAYS of the month, not hours! Since a lunar month is 29 and a half days (plus 793 parts) like we said before, we need to make some months 29 days (chaser – missing), and some month thirty days (malei – full). *(Because those 793 “extra” parts add up, some years have more months that are malei or chaser.)*

*So every 30th day is Rosh Chodesh. Either it’s the first day of the next month, or it’s the last day of the month before – the first day of Rosh Chodesh. That’s why some months have 1 day of Rosh Chodesh, and some months have two.*

The months of the year follow a pattern of malei and chaser:

TISHREI is always malei (30 days), and TEVES is always chaser. From Shevat, they take turns – Shevat is malei, Adar is chaser, Nissan is malei, Iyar is chaser, etc. (In a leap year, Adar Alef is malei, and Adar Beis is chaser.)

But what about Cheshvan and Kislev? Sometimes they are BOTH malei, sometimes they are BOTH chaser, and sometimes Cheshvan is chaser and Kislev is malei.

If BOTH are malei – the year is called Shalem (whole)

If BOTH are chaser – the year is called Chaser

If Cheshvan is chaser and Kislev is malei, the year is called Kesidran – because the months go in a pattern – malei chaser, malei chaser, etc.

*Here is a trick to figure out which kind of year it will be: Check what day Rosh Hashana is in that year, and then what day Rosh Hashana is the NEXT year. See how many days are in middle of those two days (there are 2 days between Monday and Thursday).*

*For a regular year: If you get 2 days, it means it will be a Chaser year. If there are 3 days, it will be a Kesidran year. If there are 4 days, it will be a Shalem year.*

*For a leap year: If you get 4 days, it means it will be a Chaser year. If there are 5 days, it will be a Kesidran year. If there are 6 days, it will be a Shalem year.*

*Here are some hints to make sure you did your math right:*

*– If Rosh Hashana is on Tuesday, the year will be Kesidran.*

*– If Rosh Hashana is on Shabbos or Monday, it CAN’T be kesidran.*

*– If Rosh Hashana is on Thursday in a regular year, it CAN’T be chaser.*

*– If Rosh Hashana is on Thursday in a leap year, it CAN’T be kesidran.*